Ricardo Maldonado · independent research program · 2025–2026
Could a higher-dimensional “blast” have sparked our Big Bang?
HDBLAST asks whether a violent gravitational event in a fifth dimension could have transferred energy into our four-dimensional universe and started the hot Big Bang. The equations, code, results, failures and corrections are all public.
The idea
Our universe may behave like a thin shell (a “brane”) inside a larger five-dimensional space filled with gravity and a scalar field. If the shell sits in an unstable balance, like a ball on a hilltop, it can roll off and release energy. HDBLAST asks whether such an event could have produced the hot, dense state where the standard Big Bang story begins. It would extend that well-tested story, not replace it.
6 November 2026: evaluated background evolution and finite-Sobolev quadratic forcing. The initial radial-root/inverse-flow conversion now has fixed-product H14/H13 bounds T1<10^5200, T2<10^10000. The new checkpoint evaluates the complete ordered background lower maps, including P=DV−Omega V. With C=10^150000, their bounds are l_t≤2C, l_w≤9C, l_0≤40C.
For the retained linear solution with the stated homogeneous shell/outer boundary setup, G_bg(t,0)<exp(10^150000) on 0≤t≤13/8000000. Hence ||V1||H1+||V1,t||L2<10^5203 exp(10^150000). The complete quadratic source obeys ||F2||H12≤10^240 (10^152000)^2 N14^2, where N14=||V1||H14+||V1,t||H13, and its initial value satisfies ||F2(0)||H12<10^315000. The principal-variation term and its factor two are included.
Current priority: evolved high-order commutator/normal-recovery and time-source bounds, followed by the actual-family metric patch, admitted amplitude and proper-time/actual-area observable remainder. These remain open. The conditional bounds have no SI energy calibration and do not confirm a cosmological origin. Eight primary papers were reviewed for applicability and theorem revisions; neighboring bubble/brane models retain their distinct hypotheses.
Proofs and replay · Recent literature and applicability · Initial transport.
6 November 2026 UTC: complete initial wave data, pointwise PDE coefficient budgets and a conditional energy propagator. For the selected actual weighted canonical curve, the affine lapse and zero shift complete the initial physical metric/scalar relative-harmonic wave Cauchy data through the second amplitude derivative at zero. Their raw, unstraightened positive-background norm satisfies W2<10^4000; it combines H14 field values and H13 time velocities. This does not bound the nonlinear radial-root or inverse-flow straightened H14 data.
After the literal background-subtracted boundary flow, the transformed PDE is quadratic in the first jet. On 0≤z≤6ell, |t|≤13ell/8, ||V||_*≤.001, every mixed base/state coefficient derivative through total order 16 has sum of absolute entries <10^150000, with ell=10^-6. These are pointwise coefficient derivatives, not evolved-solution derivatives; an actual solution's first-jet bound remains unevaluated.
The explicit sixteen-field auxiliary energy propagator retains the moving angular frame and interior radial cross fluxes. Its conditional majorant is K≤237+(12/5)U_t+(18/5)U_x+36000l_t+18000l_w+135l_0, where U_t,U_x are actual normalized-metric first-jet budgets and l_t,l_w,l_0 are complete transformed lower-order map budgets. The physical metric patch, exact cross traces and homogeneous four-Dirichlet/twelve-Neumann shell rows must hold for each frozen iterate; an outer wall or separately established support condition is also required. The actual evolved budgets, complete quadratic forcing and high-order closure remain open.
These are very conservative analytic budgets in fixed model normalization, without SI calibration. They supply no evolved norm, nonlinear amplitude interval, proper-clock or actual-area estimate, finite nonlinear remainder or confirmation of a physical origin. This GitHub working checkpoint includes no new Zenodo edition or journal submission.
Capsule and replay guide · Initial gauge Cauchy completion · Transformed coefficient envelope · Conditional energy majorant.
6 November 2026 UTC: quantified auxiliary boundary flow and a conditional metric-energy patch. The literal proper-y, boundary-frozen, background-subtracted flow exists for |z|≤8ell, with chart and inverse Jacobian norms <1.01. Mixed state and normal-coordinate z jets through total order 18 are <10^126 on |z|≤6ell, ||u||_*≤.003. Here ell=10^-6; the auxiliary flow parameter is not physical time.
The inner state ball ||u||_*≤.001 has flow images <.00101, which imply the full physical-metric patch ||Gamma-J||op<1/40, including all four radial cross components. Conditional on this metric patch throughout the candidate coordinate slab and the exact boundary identities for every frozen iterate, the sixteen-field auxiliary principal energy obeys 1/72000≤e[V]/Q_fixed≤1/2 for nonzero Q_fixed. Radial coordinate causal speed is <11/10<2, and the homogeneous four-Dirichlet/twelve-Neumann shell flux is exactly zero.
These are chart, pointwise coercivity and coordinate-speed results under the retained background premises. They supply no evolved-field bound, proper-clock construction, common physical domain, finite nonlinear remainder or physical-origin discovery; the actual nonlinear family's membership in the patch remains to be established.
Capsule and replay guide · Literal boundary-flow proof · Conditional metric-energy certificate.
6 November 2026 UTC: conditional full covariant second initial-jet budgets. For the specified new weight member, the retained weighted-inverse and background premises give ||h2||_H14<10^2131 and ||tau2||_H13<10^355, with tau2=pi2/rho0 normalized by the fixed background volume density. These are second amplitude derivatives at zero. The full geometric Sobolev norm is ||T||_Hm^2=sum_(j=0)^m integral |nabla_gamma0^j T|_gamma0^2 dvol_gamma0, using background covariant derivatives and the full sphere volume 2pi^2.
The canonical-to-physical conversions for K2 and Pi2 retain the known quadratic first-field terms. Although the canonical data have phi2=varpi2=0, the physical normal scalar momentum Pi2 is nonzero. On each bulk copy the complete physical ADM initial budget satisfies I2=||h2||_H14+||K2||_H13+||phi2||_H14+||Pi2||_H13<10^2132.
The newly specified weights retain the actual first seed and affine scalar and scalar-density prescription; the historical weights remain unrecovered. These extremely conservative upper budgets use the fixed model normalization, without SI calibration, and do not estimate a measured size. Uniform amplitude control, a common nonlinear development, evolved-field bounds and the finite-amplitude quadrupole remainder remain open.
Capsule and replay guide · Complete physical second Cauchy jet · References.
6 November 2026 UTC: quantified initial weighted corrections, conditional on the retained analytic premises. For the actual scalar-harmonic degrees 0,2,4 of the quadratic constraint source, explicit compact comparison tensors and the selected correction's minimum-energy property give N(h2)<2.5e40 and N(tau2)<2e17 for one explicitly specified new weight member. Here tau2=pi2/rho0, with fixed background volume density rho0, and N(T)^2=integral rho^3 |dy| <|T|^2_gamma0>_S3,prob uses the round probability measure on the sphere.
These are initial second amplitude derivatives at zero in model normalization, retaining the exact-initial-data/weighted-domain theorem and background branch as premises. The new member keeps the actual first seed and affine scalar and scalar-density prescription; it does not identify the unspecified historical weights. Quantitative H14/H13 control, evolved second fields, a common nonlinear target cylinder and a finite-amplitude radius remain open.
Capsule and replay guide · Initial metric output bound · References.
5 November 2026 (Los Angeles; 6 November UTC): evaluated scalar-curvature source and a conditional compensation test. At fixed registered affine amplitude e=0, on 0≤q≤T=25ell/16, with proper q=-tau/rho_b and ell=10^-6, the actual first physical scalar coefficient satisfies |S|<51500 and |S_q|<3.107e12. Subscript 2 means the second amplitude derivative, twice the e^2 Taylor coefficient; these are model-normalized coefficients without SI calibration.
At T, the known scalar-curvature source integral satisfies I_R>1.17e9, giving a zero-data particular contribution <-1.17e9 to the weighted second relative log-area derivative. The full denominator obeys D2/D0=K_D-I_R-I_Z. Here I_Z is the weighted Green integral of the unresolved Z=rho_b^2 P'_b <psi2>_w-<electricWeyl2>_w, with fixed weight <f>_w=<Y^2 f>/<Y^2>. Both second fields include the full physical event, shell, observer, normal and tangent pullbacks.
Only if additionally D2(T)≥0 would compensation require Zmax=sup|Z|>1.35e21. The actual Zmax, compensation and sign of the total second area derivative remain unknown. Positive physical area D_e>0 does not require D2≥0; negative D2 is compatible with positive area at sufficiently small amplitude. No finite-amplitude remainder, effective amplitude radius, physical energy, force, net focusing or Big Bang origin follows.
The full family and original proper Gaussian observer map are assumed to exist on one common target cylinder through T, retaining the physical anchor, labels and field, matching, reconstruction, constraint, gauge and uniqueness premises. The binding's 3ell/2 coordinate slab alone is insufficient. The retained first linear proof covers 3ell; it does not prove the nonlinear cylinder. This GitHub working checkpoint includes no new Zenodo edition or journal submission. Capsule and replay guide · Curvature-source bound · References.
5 November 2026 (Los Angeles; 6 November UTC): evaluated known quadratic proper-area sources. For the registered affine amplitude e, at e=0 and throughout 0≤q≤25ell/16, with proper q=-tau/rho_b and ell=10^-6, this conditional calculation evaluates first-field quadratic density, expansion-square and shear-square contributions. It retains the fixed physical anchor, transported labels and the branch, smooth-development, reconstruction, gauge, uniqueness and observer-domain premises. Subscript 2 denotes the second amplitude derivative, twice the e^2 Taylor coefficient.
For the normalized denominator with fixed weight <f>_w=<Y^2 f>/<Y^2>, the exact decomposition is D2/D0=K_D+<L2_R>_w, where the known sum satisfies -3.65e-16<K_D<5.357e-16. The remaining transfer contains the full pulled-back intrinsic-curvature derivative R2, including field, embedding, clock and observer variations. If a future bound supplies Cr≥sup_{0≤q≤25ell/16}|<R2(q)>_w|, then |<L2_R>_w|≤8.614e-13 Cr. Cr is unevaluated; the transfer uses only the retained full nonlinear quiet interval through ell/4.
This is no bound on the total D2, full nonlinear remainder or effective amplitude radius. The signs of the known terms do not establish net focusing, a physical force or a Big Bang origin. This GitHub working checkpoint includes no new Zenodo edition or journal submission. Research capsule · Quadratic area bound · References.
5 November 2026 (Los Angeles; 6 November UTC): evaluated first proper-cut metric and area bounds. For the registered affine amplitude e, at e=0 and throughout 0≤q≤25ell/16, with proper q=-tau/rho_b and ell=10^-6, the normalized physical cut metric satisfies sup||G'_0||op<2.4e-8 and the relative actual-area density satisfies sup|j'_0|<3.5e-8. Here G_0=Id, j_0=1, and operator norms use background-orthonormal frames. These evaluated first derivatives retain the master, background, reconstruction, gauge and uniqueness premises.
The calculation includes the proper-clock and angular observer pullbacks. Fields, the original physical anchor and transported labels are jointly gauge transported, so no numerical gauge-wave solve is needed for these physical first coefficients. It uses the retained actual future master trace and same-state past transfer, without a new PDE run. The longitudinal coordinate components t1,n1 are not harmonic clock U1 bounds or calibrated physical time shifts.
Conditional route beyond the first derivative: if a uniform second cut-metric bound Q(a)=sup_{|e|≤a}||G''_e||op is later established on this same proper-time cylinder, Taylor's formula gives sup_{|e|≤a}||G_e-Id||op ≤ a P0+a^2 Q(a)/2, where P0=sup||G'_0||op<2.4e-8. This checkpoint supplies no Q(a), full nonlinear parameter-box bound, effective amplitude radius, finite-amplitude remainder or interacting central zero.
It does not confirm a Big Bang origin. This GitHub working checkpoint includes no new Zenodo edition or journal submission. Research capsule · First proper-cut bound · References.
5 November 2026 (Los Angeles): a conditional exact quiet interval and delayed observer budgets. Retaining the full nonlinear PDE existence, finite-propagation and uniqueness hypotheses, the actual radial speed bound c_*=2, complete gauge and fixed physical shell joining, the selected exact family's actual-area quadrupole obeys M_e(-rho_b q)=0 on the closed interval 0≤q≤ell/4, where q=-tau/rho_b and ell=10^-6. The whole observer state is amplitude independent there. Its continuation restarts with zero first and second amplitude variations, preserving the physical anchor, transported labels and proper-time origin.
The active duration in q shortens from 25ell/16 to 21ell/16. With identical coefficient inputs, the sufficient V majorant improves by a factor at most 21/25; the H, C and P2 terms of the W majorant improve by factors at most 9261/15625, 441/625 and 21/25. The sufficient clock-drift guard becomes c<1/42 rather than c<1/50. The post-reset coefficients and effective amplitude radius remain unevaluated.
This protected early zero does not establish the later interacting central zero. The argument applies retained nonlinear PDE premises without verifying them anew and does not confirm a Big Bang origin. This GitHub working checkpoint includes no new Zenodo edition or journal submission. Research capsule · Exact quiet window and delayed budgets · References.
5 November 2026 (Los Angeles): conditional observer-domain criteria. This checkpoint gives sufficient tests for a common observer domain on a finite proper-time cylinder. If the normal proper geodesic flow exists, its cuts have positive metrics and the reference time direction is future timelike, standard Gauss orthogonality makes the graph clock strictly monotone. This prevents crossings of the candidate map throughout the cylinder. Physical injectivity also requires the shell identification to be an embedding.
Separate ambient-chord estimates test global embedding quantitatively. A first-exit ODE bootstrap starts from coefficient bounds on a fixed regular neighborhood and, with its nonexit guard, obtains the candidate interval before using parameter-variation estimates. The rational guards b,eta≤1/8 and c<1/50 are sufficient inputs that still need validation for the model.
The stated horizon covers only the retained coarse central zero bracket, excluding the later linear zero and tail. PDE constants and an effective amplitude radius remain unevaluated. These established geometric and ODE methods supply no new field-equation existence theorem, radiation or Big Bang proof. This GitHub working checkpoint includes no new Zenodo edition or journal submission. Capsule and replay · Embedding test · Normal-observer clock · Flow bootstrap.
5 November 2026 (Los Angeles): conditional nonlinear observable budgets. This working checkpoint spells out what must be bounded to certify a finite nonlinear shell response. It follows the quadrupole moment at fixed actual proper time, using the full pulled-back scalar and actual area on common noncrossing observer cuts.
Established determinant, parameter-dependent ODE and Taylor methods give conditional metric, observer-flow and error budgets. The determinant coefficient 5/4 is sharp; the correlated normalized-moment bound is sufficient, with no claim of optimal moment constants. An odd-family residual preserves exact A_e=eSY cancellation for any positive area density. A nonzero scalar–area cross example shows why separate projected terms cannot be discarded. Oddness and C2 regularity alone give no cubic remainder.
The selected family, regularity and common observer-domain premises remain assumptions. Clock, embedding and transported-label variations are included, but the nonlinear constants and an effective amplitude window remain unevaluated. No new PDE existence theorem, physical-source selection, radiation or Big Bang proof is supplied. This GitHub working checkpoint includes no new Zenodo edition or journal submission. Capsule and replay · Metric and area bound · Odd remainder · Observer-flow budget.
4 November 2026 (Los Angeles): characteristic bounds for the past scalar response of a timelike shell. For the same registered linear packet, with ell=10^-6 and matched proper-clock magnitudes, a velocity-only characteristic argument gives |S(-t)-S(t)|<1/40=.025 on 0≤t≤3ell and <1/40000=.000025 on 1.96ell≤t≤3ell. These are absolute differences of first physical scalar coefficients in model units; neither individual amplitude is bounded by these ceilings.
The retained actual future certificates now supply at least one past amplitude zero in each of (-1.49999ell,-1.49998ell) and (-1.97ell,-1.96ell), plus the continuous tail -1/1500<S(-t)<-1/4000 for 2ell≤t≤3ell. The tail sign concerns the coefficient S, not a globally negative angular field. No uniqueness or total zero count is asserted. A separate norm/cross-term estimate gives 6.06e11<C_minus<7.44e11 for the past first-field quadratic scalar norm. It is not physical energy or a finite-amplitude nonlinear response law.
The argument retains boundary mass, spring and complete forcing history, while crediting established characteristic and kernel methods. Earlier actual waveform certificates remain premises; their old campaign is not rerun. No new numerical PDE, field/source/bump oracle, effective nonlinear amplitude window, radiation mechanism or cosmological origin is supplied. Earlier conditional nonlinear-family constructions and qualitative familywise sign results are preserved. Capsule and replay · Primary proof · Working note · TeX source. Prepared for author and specialist review; no new Zenodo edition accompanies this GitHub checkpoint.
4 November 2026 (Los Angeles): a past–future scalar comparison and a narrower past-zero bracket. For the same registered first state and shell normalization, with ell=10^-6, the actual first physical scalar coefficient obeys sup_(0≤t≤3ell)|S(-t)-S(t)|<B=264000000001/13738809600<20 in model units. The comparison uses matched shell proper-clock magnitudes. This bounds an absolute difference; neither individual amplitude is asserted to be below 20.
Using the retained same-state future waveform certificate gives S(-5ell/4)<-37376 and S(-7ell/4)>37379, first supplying a coarse past zero in (-7ell/4,-5ell/4). Retained whole-cell CSV enclosures then place at least one zero in (-6145ell/4096,-6143ell/4096), of width ell/2048: a 1024-fold width reduction from that coarse half-ell past bracket. This establishes neither uniqueness nor an optimal bracket. The original finest future-zero brackets and tiny-tail signs are not transferred. The earlier certificate and CSV are premises, not a newly replayed campaign. Time reflection and graph-energy estimates are established methods, which the proof credits.
The comparison concerns a first linear coefficient; it supplies no relative-error guarantee, finite nonlinear amplitude bound, physical-energy law, radiation result or cosmological origin. An earlier conditional complete future second-order Taylor coefficient already exists; a quantitative particular past baseline and controlled nonlinear defect remain distinct tasks. Capsule and replay · Primary proof · Working note · TeX source. The note is for author and specialist review. No new Zenodo edition accompanies this GitHub checkpoint.
4 November 2026 (Los Angeles): a pointwise scalar-trace bound through past shell contact. For the registered first packet, the actual first-order physical scalar coefficient on the shell is Phi_1=S(t)(n1^2-n2^2), with sup|S|<2.5×108 throughout -3≤x≤0, where x=t/ell and ell=10^-6. The quadrupole has zero angular mean. This is a coarse bound on a linear coefficient in fixed model units, not a measured amplitude or a bound on a finite nonlinear perturbation.
The actual dynamic shell law retains both boundary mass and spring. Its positive estimating energy satisfies (1-63ell^2/4400)E(0)≤E(x)≤E(0) on this past interval. A higher operator graph estimate supplies the pointwise normal derivative needed for the physical scalar trace. The operator, endpoint-mass Hilbert space and qualitative activation arguments follow established methods, which are credited in the proof.
The estimating energy is not identified with physical injected or Noether energy. A compatible second-order state, nonlinear past preparation, physical incoming source law, radiation production and cosmological origin remain unresolved. Capsule and replay · Primary proof · Working draft · TeX source. The paper is a working draft for author and specialist review. No new Zenodo edition accompanies this GitHub checkpoint.
5 November 2026: a local first-order characteristic precursor. Under the retained background and linear reconstruction premises, both normalized principal wave directions keep shares greater than 0.499999 on -1<x≤0, before possible past shell contact. These are master-field diagnostics, not physical energy or radiation flux.
Two compatible past characteristic face traces reproduce the registered present first packet on a local diamond. Their common corner at the interior spacetime point (x,r)=(-1/2,3/2) has value < -4e-8, while the midpoint of either face is > 0.499999. Each trace therefore has an interior zero and is nonconstant.
This is a conditional first-linear result. It does not complete second-order constraints or a nonlinear preparation, select a physical incoming law, produce radiation or establish a cosmological origin. Capsule and replay · Primary proof · Working paper · TeX source. No new Zenodo edition accompanies this GitHub checkpoint.
4 November 2026: incoming-state constraints and a continuous source ledger. The registered present packet contains both principal directions of its normalized master. Their nearly equal quadratic weights are not physical energy fluxes. A past incoming state could have developed these mixed present data through scattering; that history remains to be constructed.
Five exactly clipped continuous cells cover active area 9/32 and give a future bulk squared-source integral no greater than 8.52642 × 1024; the corresponding shell bound is 3.708321 × 1012, in model units. The forced mathematical energy is bounded by 44 times the sum of compatible initial energy and the computed source budget. The initial energy cannot simply be set to zero: absolute second initial data must satisfy the quadratic constraints. This trace estimate remains looser than the earlier Duhamel bound and gives no improved observable prediction or new proper-volume sign.
A partial null constraint, with an explicitly chosen zero second scalar trace and stated corner data, requires a geometric correction when its first-order squared terms have nonzero integral. It solves one trace constraint, not the full past problem. A stable causal inverse for normalized scalar history applies only on the retained admissible image and to the initial segment that history reaches; arbitrary histories and exterior preparations are not covered.
Proof, source budgets and reproducible checks · Working paper for review. Continuous source and operator bounds and analytic development remain conditional inputs; exact arithmetic does not re-prove the PDE. Pure scalar-dependent tension exchanges vacuum energy, not radiation. A matter sector and state, physical scale, uniform nonlinear parameter window and higher-dimensional origin remain unestablished.
4 November 2026: proper-time response bounds from an integrated preparation budget. A direct tilted mathematical energy estimate retains all five coupled mean channels. Under the retained analytic assumptions, every admitted compact mean preparation whose complete initial scalar-level area-profile difference has H1 norm at most 2 × 1031 has negative complete second coefficients for proper volume and expansion at one anchored proper time. The squared norm is the integral of the squared profile and its squared background-calibrated label derivative. Each fixed admitted exact family therefore has smaller positive volume and slower positive expansion than the background for sufficiently small nonzero parameters of either sign.
The admissible preparation image contains sequences with bounded H1 norm and arbitrarily large pointwise label derivatives, so this route bypasses the earlier pointwise criterion. No inclusion between the two specified norm balls is claimed. The continuous operator bounds and analytic development remain conditional assumptions; exact arithmetic does not re-prove them or the PDE. This estimating energy is not a physical Noether energy law.
Proof, exact bounds, preparation-image example and reproducible checks · Working paper for review. The class and radius still lack a physical selection rule. No common nonlinear parameter interval, radiation-production result, SI calibration or higher-dimensional Big Bang origin is established.
4 November 2026: robust shell responses within a specified geometric preparation class. On a physically specified initial Cauchy slice, areas of scalar-level three-spheres and their fixed background label derivative define a restricted class with R_A ≤ 2 × 1033. Under the retained analytic and background assumptions, all admitted preparations have negative second volume and expansion coefficients at one anchored proper time. Each admitted exact family therefore has positive volume and positive expansion below the background values for sufficiently small nonzero parameters of either sign. The earlier opposite-sign example lies outside this class; its dated result is preserved.
Geometric reconstruction, assumptions, exact bounds and reproducible checks · Working paper for review. The physical slice, restricted canonical sectors and class radius still need a preparation rule. The coefficient bounds supply no nonlinear amplitude interval uniform over the class. These model-unit results establish no radiation production or higher-dimensional Big Bang origin.
4 November 2026: the shell response depends on its preparation. Two declared compact second-order preparations, with the same first-order packet and constraint equations, now have certified opposite signs of their volume and expansion changes at one anchored proper time. Both remain positively expanding for sufficiently small perturbations. The earlier result is preserved for its chosen data; the first packet and constraints alone do not select the response signs.
Theorem, assumptions, two checked methods and reproducible calculations · Working paper for review. A physical model must select the second preparation or prove robustness over a justified class. The usable amplitude remains uncomputed; these model-unit results establish no radiation production or higher-dimensional Big Bang origin. No new Zenodo edition or journal submission accompanies this checkpoint.
1 November 2026: prepared proper-time shell volume. For explicitly chosen new compact mean initial data, conditional bounds give a positive shell volume and a positive expansion rate, both below their background values, at one registered proper time for sufficiently small nonzero perturbations of either sign. This is a different nonlinear completion from the earlier weighted-only family whose mean data were not numerically specified. The preparation is a mathematical choice; the result does not select a physical generator or establish a signed time history.
Statement, preparation, assumptions and reproducible calculations · Working paper for review. The usable amplitude interval is uncomputed, and all quantities use model units without SI calibration. These results establish no radiation production, observational signal or higher-dimensional Big Bang origin. No new Zenodo edition or journal submission accompanies this checkpoint.
1 November 2026: intrinsic shell geometry and the remaining scalar mean. Continuous rational bounds now give positive second-order corrections to averaged spatial curvature and the expansion-variance/shear term for the retained conditional model. They quantify a correction needed when relating the shell's volume to its spatial curvature. The full volume history still requires an unknown second scalar mean; these results establish no created radiation or higher-dimensional Big Bang origin.
Derivation, assumptions, data and reproducible calculations. The earlier proper-time bulk-observer result is a separate curvature calculation. All numbers use model units with no SI calibration or effective perturbation-amplitude window. No new Zenodo edition or journal submission accompanies this checkpoint.
26 October 2026: conditional registered screen magnetic curvature. On the exterior angular sphere at (x,r)=(1/4,5/4), before shell contact, the projection of the second parameter derivative of the screen magnetic tensor onto the selected TT pair is Π_pair H″(0)=h(T+ − T−). The calculation combines the linear second-response TT term with the complete scalar quadratic term, retaining the observer, radial-normal, connection and epsilon corrections. The complete first variation of this screen tensor vanishes, and exact angular identities close the quadratic term on T+ − T−.
The coefficient h is enclosed in [-0.024929793753, -0.004128493946] and is strictly negative under the retained assumptions. Its scalar quadratic contribution is enclosed in [-0.000000000000000000690462, 0.000000000000000001996501]. These are outward rational bounds at the registered point. The projected angular field vanishes on the two registered great circles S=0 and S=1, where S=n0²+n1². The future observer is the unit normal to t=constant; the radial normal is the positive unit normal to y=constant within that spatial slice, with screen axes and orientation fixed by the registration.
This is a conditional curvature diagnostic for the registered formal response. The parent background, master, gauge, coefficient-existence and subsidiary assumptions remain in force. No gauge-invariant observer or clock anchoring has been constructed. The result establishes no physical radiation, force or detection, no finite-amplitude nonlinear family and no cosmological origin. The full second-order Einstein–matter boundary problem remains unfinished. No new Zenodo version or journal submission accompanies this checkpoint.
26 October 2026: exterior tensor derivatives enclosed at one point. Under the retained model assumptions, the tensor coefficient of the actual total formal response and all its first and second scaled coordinate derivatives are enclosed at (x,r)=(1/4,5/4), before shell contact. The two TT coefficients remain equal.
Their common value u lies in [−0.000207982516, −0.000010433243], and its scaled time derivative u_x lies in [−0.000280539069, −0.000046459086]. Both are strictly negative. The radial first derivative and all three second-derivative intervals contain zero, so their signs remain inconclusive.
This is a local result about metric coefficients in the registered gauge. It does not establish a full-domain C2 approximation, an Einstein residual bound or a physical curvature or gravitational-wave observable. Nonlinear physical realization and cosmological origin remain open. No new Zenodo version or journal submission accompanies this checkpoint.
26 October 2026: a full angular response approximation passes its accuracy target. One continuous C1 first-feedback approximation on the retained local domain D+ keeps all 23 angular slots. Its complete conditional X-error bound for values and scaled first x/r derivatives is below 1.1787044291e28, meeting the 1e29 target in the positive angular H norm.
At the exterior point (x,r)=(1/4,5/4), a separate targeted calculation of the actual total response encloses each of the two equal TT coefficients in [−0.001311761536, −0.000001509027]. This is a metric coefficient in the registered gauge, not an observed gravitational wave or a gauge-invariant tensor observable.
These numerical approximation and integral-defect certificates retain the conditional parent coefficient-existence and subsidiary assumptions. They establish no pointwise C2 Einstein residual, nonlinear or finite-amplitude physical family, or cosmological origin. No new Zenodo version or journal submission accompanies this checkpoint.
Conditional shell and anchored-volume sign bounds — 25 October 2026. Conditional bounds place N0(x,0) and J0(x,0) below zero at the retained scaled times x=9/8 and x=5/4. Under the retained parent projection assumptions and a smooth kinematical completion, the anchored proper-time volume second parameter derivative is also negative at x=9/8. Finite-amplitude volume change, a full angular Einstein solution and cosmological conclusions remain unestablished. No new Zenodo version or journal submission accompanies this checkpoint.
25 October 2026: a coupled five-mean response approximation passes its accuracy target. One continuously defined C1 approximation now includes the first coupled bulk feedback and shell boundary lift. Its complete conditional error bound is below 1.6090323e28 in the retained scaled X norm, meeting the 1e29 target. The 64 and 128 meshes gave insufficient bounds; the declared 256 limit passed. Both execution modes agree, and an independent exact integrator reproduces the stored feedback samples.
This advances the numerical construction of five mean coefficients. The full angular second-order spacetime, intrinsic observable sign, nonlinear family and physical origin remain unestablished. These are mathematical bounds under the stated model assumptions, not physical measurements. No new Zenodo version or journal submission accompanies this checkpoint.
Derivation and scope · Frozen data, source and replay · Source archive (ZIP)
23 October 2026: the initial-data precision gate passes. An exact residual comparison sharpens the same retained regular-shell branch to a beta interval of radius 9.505e-18. A separately registered recentered rational approximation has a certified initial/free-wave error below 8.519e27, meeting the 1e28 target across all 96 cells. The old candidate and its failed bound are preserved. Some illustrative component allocations are exceeded; the exact combined inequality passes.
This clears an input-accuracy bottleneck under the stated model and theorem assumptions. The evolved numerical total response and intrinsic observable sign remain unevaluated. It establishes no nonlinear physical family or higher-dimensional Big Bang origin. No new Zenodo version or journal submission accompanies this update.
Working note (PDF) · Derivations, source and checks · Source archive (ZIP).
23 October 2026: tighter response bounds and an intrinsic shell-volume prescription. A zero-region estimate tightens the conditional local response contraction bound to q = 0.000426125. A complete initial-data pilot defines one differentiable rational candidate but its certified error bound fails the chosen accuracy gate. This identifies the next precision task; it proves no impossibility. A separate derivation defines intrinsic shell volume at anchored proper time, including clock, slicing and quadratic metric terms. Its value remains unevaluated.
The numerical total response and invariant observable sign remain unevaluated. These conditional results establish no nonlinear physical family or higher-dimensional Big Bang origin. Earlier checkpoints are preserved; no new Zenodo version or journal submission accompanies this update.
Working note (PDF) · Derivations, source and checks · Source archive (ZIP).
October 2026: a positive auxiliary mean after causal contact with the shell. At scaled (x,r) = (3/2,1/4), after the past causal cone reaches the timelike shell, interval integration of the actual quadratic source and an exact closed system of five rotational means prove that the probability-normalized S³ mean of the auxiliary covariant yy response is positive. The bounds include all feedback in that mean system, including the Robin shell condition. All quadratic mean contributions of the first-order harmonics are retained before exact projection.
This conditional result concerns an auxiliary coefficient in the registered frame and gauge. The full evaluated numerical waveform remains unfinished. The retained total response U already has a conditional analytic construction and physical constraint completion; this auxiliary mean does not determine its physical interpretation. No physical force, exact nonlinear spacetime family or evidence of a higher-dimensional Big Bang origin is inferred. No new Zenodo version or journal submission accompanies this checkpoint.
Technical working note (PDF) · Editable source and reproducible calculations · Source archive (ZIP) · Verification evidence.
October 2026: certified causal bounds for an auxiliary response. Interval evaluation certifies that the angular mean of the covariant yy component of the auxiliary forced metric response is strictly positive throughout a continuous neighborhood of scaled (x,r) = (1/4,5/4), before signals from the shell can reach it. The calculation includes 20 clipped causal source cells, the certified uncertainty in the actual first-order fields and all 23 bulk amplitudes with their couplings.
This conditional, model-specific result concerns a coordinate coefficient in the stated frame and gauge. The full numerical second-order waveform, including shell interaction, remains unfinished. The auxiliary response is not established as a separate solution of the complete physical constraint system; no physical force, exact nonlinear spacetime family or evidence of a higher-dimensional Big Bang origin is inferred. No new Zenodo version or journal submission accompanies this checkpoint.
Technical working note (PDF) · Derivations, editable source and reproducible calculations · Verification evidence.
16 October 2026: complete quadratic geometric sources and an intrinsic shell diagnostic. The actual full Ricci/Einstein–scalar source adapter and exact 23-amplitude projection retain both transverse-traceless orientations. Certified interval evaluation covers 81 causal cells, 64 evolved radial-profile cells and 6 shell time cells. The bulk forcing norm satisfies FH ≤ 17387513156573, improving the retained upper bound by more than 9.8 times.
The intrinsic material-shell quadratic scalar has exactly two simple mean zeros in each scaled-time bracket [5/4,11/8] and [13/8,7/4] on the specified background time sections: four distinct zeros are certified, with others elsewhere not excluded. A separate derivative-bound corollary preserves opposite evolved second scalar-mean signs on two complete radius cells for scaled times [1/1000,1/200]. The full numerical second waveform and continuous response residual remain unfinished. These conditional formal-coefficient results establish no exact nonlinear family, physical force or higher-dimensional Big Bang origin.
Technical working note (PDF) · Derivations, editable source and reproducible calculations · Verification evidence.
15 October 2026 (Pacific): certified numerical inputs for the selected second-order response. Continuous error bounds now control the actual first master and gauge fields through scaled derivative order three. An exact 23-amplitude homogeneous bulk/boundary operator and a sharp selected-space evaluation constant, sqrt(321/19), support the next numerical calculation.
Whole-cell evaluation of the same second initial profiles tightens the global formal-response norm bound from 1.02 × 1036 to 1.03 × 1033, about 990 times smaller. These are conservative coefficient bounds, not measured field amplitudes. The full quadratic metric-source adapter and a continuously certified numerical second-response waveform remain unfinished. Conditional mathematics does not establish an exact nonlinear family, invariant force or a higher-dimensional Big Bang origin. No new Zenodo version or journal submission accompanies this checkpoint.
Technical working note (PDF) · Derivations, editable source and reproducible calculations · Verification evidence.
16 October 2026: constructive second-order continuation for one aligned quadrupole: A convergent causal integral series defines the full formal second metric–scalar coefficient for the selected registered state on the controlled shell-contact domain. Its operator has contraction factor at most 0.002109 on a 287-dimensional angular tensor-section space, retaining every generated tensor sector.
The construction joins the complete bulk and shell forcing in one common first relative-harmonic gauge, compatible second initial data, physical shell laws and subsidiary gauge constraints. Qualitative smoothness is proved separately from numerical bounds for values and first scaled derivatives.
The coarse comparison-norm cap, ‖U2‖X < 1.02 × 1036, is dominated by the inherited second initial scalar data and carries no physical signal interpretation. No candidate numerical waveform has been evaluated. This conditional coefficient construction does not establish an exact nonlinear family, a finite-amplitude remainder, an invariant force or a higher-dimensional Big Bang origin. Internal AI-assisted review does not replace external specialist review. No new Zenodo version or journal submission accompanies this checkpoint.
Research source and exact reports · Second-response construction · Bulk forcing proof · Physical shell forcing · Result status and literature context · Source ZIP · Replay and publication evidence.
16 October 2026: certified first relative-harmonic gauge wave: For the retained regular background and quadrupole, a convergent construction now gives the first coordinate gauge vector with continuous derivatives through order three. An explicit approximation has uniform error below 5.47 × 10−9 in its radial coordinate amplitude on the controlled causal triangle.
This conditional first-order result preserves the shell’s normal Dirichlet and tangential Neumann conditions. Transforming the quadratic bulk and shell sources and solving the second-order Einstein–scalar evolution remain unfinished. No invariant force or higher-dimensional Big Bang origin is established. Internal AI-assisted review does not replace external specialist review. No new Zenodo version or journal submission accompanies this checkpoint.
Research source and exact reports · Construction and error proof · Derivative bounds · Source ZIP · Replay and publication evidence.
15 October 2026: second initial norms and initial harmonic gauge: Exact rational calculations give coarse certified upper bounds for the values and first spatial covariant derivatives of all four physical second initial fields: the spatial metric, extrinsic curvature, scalar and unit-normal scalar velocity. The initial constraint-source cancellations remain exact. Explicit local initial relative-harmonic lapse and shift velocities include the quadratic terms.
These are conditional initial-data bounds in the stated frames and model units. They do not demonstrate a response, establish a physical force, solve the full second-order spacetime evolution or construct an exact finite-amplitude family. Common boundary/gauge completion and validated coupled evolution remain open. Earlier frozen checkpoints are preserved; internal AI-assisted checks do not replace external peer review.
Research source and exact reports · Second initial norms · Initial harmonic completion · Spacetime initial one-jet.
15 October 2026: explicit compact second initial constraint data: For the registered aligned packet, explicit local formulas now cancel the Hamiltonian and all four momentum constraint sources through second order. The correction remains in the original packet annulus and vanishes near the initial shell. A certified nonzero Hamiltonian source at the packet maximum rules out zero second initial data.
The construction allows nonzero second scalar and unit-normal scalar-velocity data. Physical Cauchy fields and spacetime coordinate velocities are distinguished, with the lapse conversion included. This is a conditional second initial jet, not a finite-amplitude exact initial family or a second-order spacetime evolution. Initial norms, the common gauge and boundary completion, and validated U2 evolution remain unfinished; no physical force or higher-dimensional Big Bang origin is established. Checks and independent internal AI-assisted review do not replace external peer review.
15 October 2026: interior derivatives and bulk forcing bounds: For the registered aligned quadrupole, exact rational estimates now bound every mixed first-master derivative through order three on the controlled causal triangle. A new actual-potential second-derivative bound and the reflected shell terms close this derivative calculation. Reconstruction then gives coarse continuous envelopes for all fifteen longitudinal Einstein quadratic-source components and the complete scalar source over the triangle times S3.
These are conditional bounds in the stated first longitudinal representative and adapted background frames, in model units. They do not compute the second-order response or a physical force. The earlier conditional coefficient construction retains its stated scope; quantitative U2, compatible second initial and common-gauge boundary data, and a validated coupled evolution remain unfinished. Internal AI-assisted review does not establish external peer review, novelty or a higher-dimensional Big Bang origin.
15 October 2026: continuous coordinate shell sources: The certified quadrupole now gives enclosures over 4353 continuous time cells for the actual metric trace at the shell, its proper-time derivative, and the complete one-copy coordinate scalar and isotropic Israel coefficients Sp and SK, with scalar degrees 0, 2 and 4. The metric correction has L2 norm less than 9e-13 of the one-copy material scalar source, yet changes the coordinate source signs at a scalar zero. Each of Sp and SK consequently has at least two distinct zeros inside the certified central bracket.
These results are conditional on the retained analytic inputs and the stated first longitudinal representative and derivative Taylor convention. The reduced Robin forcing norm is evaluated only for degree 4; the degree-2 Robin row is algebraic only. The norms use the background proper shell measure, and coefficient signs depend on the representative. The earlier conditional construction of the complete second coefficient retains its stated scope. No effective nonlinear amplitude or remainder, observational scale or cosmological origin is established. Independent internal checks do not replace external peer review. Full U2 remains quantitatively unresolved.
Derivation and bounds · Source and replay guide.
See the separate publication evidence for replay, CI and live-readback status. Publication evidence.
15 October 2026: quadratic material tension forcing: For the previously certified wider quadrupole (delta = 1/1000, ell = 10^-6 in model coordinates), the explicit material scalar-junction tension contribution is Q_phi = -4 psi_1^2 in the outward-normal SUM convention. It has scalar degrees 0, 2 and 4. Exact continuous enclosures give -2.3 × 10^-19 < ell^2 mean(Q_phi) < -6.7 × 10^-20 throughout 2 ≤ x ≤ 3 and 5.778 × 10^21 < ||Q_phi||_L2(dmu_0)^2 < 8.644 × 10^21 over 0 ≤ x ≤ 3, using the background proper-time measure and model units. The angular mean stays negative throughout the tail; the field vanishes on Y = 0.
This isolates the explicit material tension contribution; the complete quadratic source for bulk-coordinate unknowns and full U2 are not numerically evaluated. The earlier conditional construction of the complete second coefficient is preserved under its stated data and evolution assumptions. No effective finite amplitude, nonlinear remainder, observational scale or cosmological origin is established. Independent internal exact checks are distinct from external peer review and formal PDE verification. Earlier dated entries retain their scope. No new Zenodo version or APS submission was made.
Material tension theorem, normalization and assumptions · Reproducible calculations and independent internal checks.
Publication checks remain pending until documented in the separate final additive evidence receipt. Final additive publication evidence.
Conditional inertial shell waveform: For a newly specified wider aligned quadrupole (delta = 1/1000, ell = 10^-6 in model coordinates, T = 3ell and Z = 8ell), exact interval bounds resolve the shell response at first variation. The normalized trace H(x) = ell D(ell x) satisfies 3.2 × 10^-8 < H < 5.3 × 10^-8 throughout 2 ≤ x ≤ 3. The negative physical gain G makes the corresponding scaled physical first variation ell S negative there. At least one zero lies in each of (1.49998, 1.49999) and (1.96, 1.97); uniqueness is not asserted. The leading proper-time response coefficient satisfies 6.06 × 10^11 < C < 7.44 × 10^11 in R_epsilon = epsilon^2 C + o(epsilon^2), in the stated model normalization.
The actual-background, exact-data, gauge, regularity and whole nonlinear correction-support hypotheses remain explicit. This first-variation result does not close the full second-order nonlinear waveform or provide an effective epsilon or nonlinear remainder bound. No observational scale or higher-dimensional Big Bang origin is established. Internal AI-assisted review and finite checks are distinct from external peer review and formal PDE verification. Earlier entries retain their dated scope. No new Zenodo version or APS submission was made.
Waveform theorem, normalization and assumptions · Reproducible calculations and independent reviews.
Publication checks remain pending until documented in the separate final additive evidence receipt. Final additive publication evidence.
Conditional first-variation shell waveform: For the same specified narrow aligned quadrupole (delta = 1/1000, ell = 10^-10 in model coordinates), a continuous 4098-cell enclosure resolves the physical scalar’s linear first variation. The normalized trace H differs from its explicit comparator by less than 1.0000004 × 10^-7 on 0 ≤ x ≤ 3; the negative physical gain reverses its sign. The leading proper-time response coefficient now satisfies 6.06 × 10^15 < C < 7.44 × 10^15 in R_epsilon = epsilon^2 C + o(epsilon^2).
The retained background, exact-data, gauge, regularity and nonlinear support hypotheses remain explicit. The post-pulse estimate |H| < 4.752 × 10^-14 on 2 ≤ x ≤ 3 is a small-tail bound. No finite-amplitude nonlinear waveform, observed time scale or higher-dimensional Big Bang origin is established. Next: a wider state with a validated background and an effective nonlinear remainder estimate. Internal AI-assisted review and finite checks are distinct from external peer review. Earlier entries retain their original scope. No new Zenodo version or APS submission was made.
Waveform theorem, normalization and assumptions · Reproducible calculations and independent reviews · Continuous-cell enclosure data.
Conditional quantitative shell-response bound: For the retained regular branch at delta = 1/1000 and one newly specified narrow aligned quadrupole (ell = 10^-10 in model coordinates), a free-wave comparison and exact-rational bounds give 10^15 < C < 4 × 10^17 for the leading proper-time response coefficient in R_epsilon = epsilon^2 C + o(epsilon^2). The estimate controls the physical derivative at the shell, with its positive boundary inertia.
This is a coarse conditional analytic enclosure in the stated model normalization. It gives no numerical waveform, effective nonlinear amplitude range, observational scale or evidence for a higher-dimensional Big Bang origin. The background, exact-data, gauge, regularity and full nonlinear support hypotheses remain explicit. Internal AI-assisted reviews and finite arithmetic checks are distinct from external peer review. Earlier entries retain their checkpoint scope. No new Zenodo version or APS submission was made.
Quantitative theorem, normalization and assumptions · Reproducible arithmetic and independent reviews.
Conditional nonzero physical shell response: For one explicitly specified aligned quadrupole with nonzero displacement and velocity, the full coupled Einstein–scalar shell equations now imply a nonzero physical first scalar response. In the retained conditional exact nonlinear family, a squared scalar-response measure over a finite intrinsic proper-time window has a strictly positive leading quadratic coefficient.
The result retains the stated background, exact-data, support, regularity and finite-region hypotheses. It is qualitative: no numerical waveform, response magnitude, effective amplitude threshold or exact nonlinear first-arrival time is supplied. Internal AI-assisted review and finite reproducible checks are distinct; external peer review, global stability and a higher-dimensional origin of the Big Bang are not established. Earlier dated entries retain their original scope. No new Zenodo version or APS submission was made.
Physical response theorem and assumptions · Derivations and reproducible checks.
Exact nonlinear shell evolution at fixed finite regularity: Under the stated background, support and exact-data hypotheses, the selected aligned quadrupole has a small exact Einstein–scalar family on both copies of the controlled positive-cone region for a prescribed finite shell-interaction interval. The construction satisfies the physical shell laws and constraints, with H^14/H^13 evolution and C² parameter dependence in a lower norm.
This is internally reviewed conditional mathematics. The actual first-arrival time and a nonzero gauge-invariant shell response remain to be calculated. No global stability, observational agreement or higher-dimensional origin of the Big Bang is established. The analytic proofs and finite algebra checks are documented separately; no new Zenodo version or APS submission accompanies this checkpoint. Earlier dated entries retain their original scope.
Theorem, proof and assumptions · Reproducible checks and scope.
All-angular linear shell-contact estimate — 14 October 2026 (Pacific): On the registered Einstein–scalar background and a fixed controlled positive-cone collar, the full sixteen-field linear system now has a positive auxiliary Sobolev control estimate independent of angular frequency and of the full tensorial SO(4) cutoff. A bounded change of field variables removes the complete nonsymmetric twelve-row Robin matrix without changing the common wave principal part. Smooth compatible data and forcing give a unique smooth linear solution; the same method controls subsidiary constraint propagation.
Smooth boundary forcing is handled by an explicit lift with its declared regularity cost. No estimate for arbitrary L² Neumann forcing is claimed. The positive norm is analytic control, not physical gravitational energy or a stability result. A separate exact local change of nonlinear boundary variables converts all twelve physical and normal-gauge laws to homogeneous Neumann conditions while preserving the common quasilinear wave principal symbol. This is an algebraic reduction; an exact nonlinear perturbation family through shell contact remains open. The previously established exact initial-data family at fixed high finite Sobolev regularity and the earlier complete second-order coefficient are preserved.
Primary-literature comparisons do not transfer other models' theorems automatically. Internal AI-assisted review is not external peer review; external novelty and a higher-dimensional Big Bang origin remain unestablished. This is a GitHub-only checkpoint, with no new Zenodo version or APS submission. Artifact identifiers use 15 October UTC; this work began 14 October Pacific time. Earlier dated entries retain their original scope.
Estimate, assumptions and reproducible checks · Linear proof · Exact nonlinear boundary reduction.
Complete second-order coefficient through shell contact (14 October 2026): For the specified copy-even commuting quadrupole packet, the unchanged first-order scalar reconstruction cannot satisfy the quadratic degree-four angular equation. The continuation therefore keeps all metric and scalar fields, with their complete quadratic bulk sources and physical shell boundary conditions.
Under the stated background, localization and initial-data hypotheses, a boundary-preserving relative harmonic gauge and a convergent characteristic construction give a smooth complete second Taylor coefficient through first shell contact on a controlled positive-cone collar. It includes scalar degrees zero, two and four and tensor degree two. The construction satisfies all Einstein–scalar equations, induced-field matching and Israel/scalar shell laws through second order, with propagation of the sourced constraints.
This is a conditional coefficient construction. An exact nonlinear family through contact, estimates uniform over all angular modes, nonlinear stability and a higher-dimensional Big Bang origin remain unestablished. Internal AI-assisted proof review is not external peer review, and external novelty is not established. This is a GitHub-only checkpoint, with no new Zenodo version or APS submission. Earlier dated entries, including earlier entries from 14 October, retain their original scope.
Construction, assumptions and reproducible checks · Complete coefficient proof.
Quadratic tensor forcing and a tensor sector through shell contact (14 October 2026): For the specified quadrupole Y = n₁² − n₂² in the fixed longitudinal first-order gauge, the complete gravity-plus-scalar quadratic source has a nonzero transverse traceless angular component wherever either scalar amplitude is nonzero: its coefficient is 16u² + 8v²/3. Thus the two contributions cannot cancel there. A velocity-only packet can have zero source on its initial slice and develop it later.
For even first-order master data, the corresponding forced second-order tensor sector has homogeneous Neumann shell data and a conditional evolution through first contact on a controlled collar. The full coupled scalar and tensor second-order boundary problem and a nonlinear solution through contact remain open.
Derivation, assumptions and reproducible checks. These statements use the specified background, first-order gauge and parity. They establish no Big Bang origin or external novelty; internal proof review is not external peer review. This is a GitHub-only checkpoint, with no new Zenodo version or APS submission. Earlier dated entries retain their original scope.
Exact localized initial data and short precontact evolution (14 October 2026): Under the stated background assumptions and weighted nonlinear estimates, the reflection-invariant quadrupole sector admits a family of exact nonlinear initial data at a chosen high finite Sobolev regularity. A sufficiently short precontact Cauchy evolution keeps the fields equal to the background in a collar of the shell, so its junction conditions remain unchanged there.
The nonlinear boundary problem through shell contact remains open. The theorem concerns high finite regularity; no spatial smoothness to all orders, Big Bang conclusion or external novelty is established. The proof received internal AI-assisted review, which is not external peer review. Proof, assumptions and limits. This is a GitHub-only checkpoint, with no new Zenodo version or APS submission. Earlier dated entries retain their original scope.
Formal continuation by reflection symmetry (14 October 2026): For the restricted commuting quadrupoles of the localized checkpoint, simultaneous diagonalization makes the first-order data invariant under coordinate reflections. These reflections force all ten local symmetry compatibility pairings to vanish at every finite constraint order. Under the stated localization hypotheses, recursive constraint solving and averaging over the reflection group construct localized formal initial data to all orders. This is a formal series: convergence, an exact nonlinear solution and full evolution through shell contact are not established. Derivation, assumptions and limits.
Localized second-order initial data (14 October 2026): On the time-symmetric regular Einstein–scalar slice, the ten symmetry tests are necessary and sufficient for compactly supported second-order initial-data corrections for smooth packets of fixed reflection parity in an annulus away from the shell and cone vertex, under the stated background and localization assumptions. The note gives an explicit correction for A = B = diag(1,−1,0,0). The correction vanishes near the shell, so the initial second-order junction conditions hold with zero shell displacement and tilt.
An areal-radius-weighted monopole identity fixes a spherical metric moment for first-order packets in the reconstruction gauge. Its negative sign for velocity packets is a statement in that gauge: the moment changes under first-order gauge transformations and is not yet a physical mass or energy observable.
Full second-order evolution through shell contact, quadratic interface sources, convergence of the higher-order formal series and nonlinear existence remain open. This result does not establish a higher-dimensional Big Bang origin. Technical note · Calculations and supporting material · Results and limits. This is a GitHub-only checkpoint; Zenodo 23335485 remains the latest archived spectral edition. No new Zenodo version or APS submission accompanies it.
Shell symmetry obstruction (13 October 2026): On the fixed regular Einstein–scalar two-interior shell, the completed nonlinear Noether identity retains both gravitational boundary terms, moving embeddings and the single common shell action. An independent ADM constraint calculation verifies a nonzero second-order obstruction for an explicit compact rotating quadrupole: it cannot be the tangent to a parameter-C² exact classical family satisfying full shell matching. The example can be chosen among smooth non-gauge linear solutions that reach the shell.
Within degree-two data with one fixed radial profile and reflection parity, all ten necessary Lorentz symmetry tests vanish exactly when the displacement and velocity matrices commute, [A,B]=0. Passing these tests does not establish second-order solvability or nonlinear existence. The result establishes no nonlinear growth, stability, Big Bang origin or APS readiness. Normal and optimized portable replay each check 81 positive algebra checks and 21 wrong-formula controls, counted separately.
Technical note · Proofs and portable replay · Results and limits. This is a GitHub-only research checkpoint. Zenodo 23335485 remains the latest archived spectral edition; no new Zenodo edition or APS submission accompanies this continuation.
Conditional evolution through shell contact (13 October 2026): On the fixed regular Einstein–scalar background, an explicit characteristic construction gives a smooth family from compact radial data in a sufficiently thin annulus, with a fixed finite set of angular harmonics of degree at least two. The family includes paired solutions that activate the shell after first arrival on a controlled finite slab. Both reflection parities satisfy the complete induced-field, Israel and scalar junctions without harmonic division, and nonzero states are not pure gauge. An explicit pair with the same reflection parity has a nonzero total physical symplectic pairing, conserved after contact with the odd moving-shell cut term included. The pairing is weakly nondegenerate on this smooth thin-annulus data image.
This conditional linearized result concerns a new collar-supported family. It does not continue the earlier near-cone flux pair to contact or establish a nonzero local shell flux, physical energy, unrestricted angular completion, nonlinear stability, cosmological evidence, external originality or APS readiness. Normal and optimized portable replay each check 84 positive exact identities and 14 wrong-formula controls, counted separately.
Technical note · Proofs and portable replay · Results and limits. This is a GitHub-only checkpoint. Zenodo 23335485 remains the latest archived spectral edition; no new Zenodo edition or APS submission accompanies this continuation.
Earlier local coupled cone evolution (13 October 2026): A regular wave equation now reconstructs smooth solutions of all linearized Einstein–scalar equations across the cone. Compact initial data give two non-gauge solutions with nonzero local symplectic flux. Both reflection parities satisfy the shell junctions before the waves reach the shell. The physical Cauchy symplectic form is nondegenerate on the image of smooth compact master data supported in a sufficiently small spatial ball.
Evolution to shell contact of that original near-cone flux pair remains open; the new collar family above has a separate after-contact proof. The full physical state space and nonlinear stability remain open. This antisymmetric symplectic flux is not a positive energy or reheating calculation, and a higher-dimensional Big Bang origin remains unestablished.
Technical note · Proofs and reproducible code · Results and limits. This is a GitHub research continuation. Zenodo 23335485 remains the preceding archived spectral edition; no new APS submission was made.
Current and physical-domain audit (13 October 2026): The Einstein–scalar action now supplies an explicit symplectic current, including unequal spectral values and the doubled-shell balance. Under stated asymptotic hypotheses for actual solutions, its null-cone limit is a scalar symplectic flux. Exact flat test-field examples show that fixed-time radial closure does not imply zero characteristic flux, and that radial and inertial energy completions can differ. The physical state space of the registered gravitational model remains open.
Technical note · Derivations and code · Results and limits. This continuation is published on GitHub; Zenodo 23335485 remains the preceding archived spectral edition. No new APS submission was made. A higher-dimensional Big Bang origin remains unestablished.
Conditional spectral result (13 October 2026): At every fixed 0 < delta ≤ 0.002, the entire scalar spectrum in both reflection parities is separated strictly from zero in the specified self-adjoint, finite-energy regular-cone realization. The proof gives a positive bound as a function of the background; it does not assign a numerical value or a uniform bound as delta approaches zero. An action calculation, including the moving-shell boundary terms, verifies the local kinetic coefficients of generic even and odd scalar modes. Exceptional harmonics are treated separately. The tensor sector has one even massless radial profile, and every nonzero tensor mass obeys m_T ≥ 3H_b/2.
This concerns the regular branch near phi = +1 of the same fixed action. The original hilltop shell remains a distinct unstable solution; no evolution connecting the two is proved. Global physical-state coverage, admissible diffeomorphisms and cone symplectic flux retain the declared assumptions. No nonlinear stability, reheating mechanism or higher-dimensional Big Bang origin is established. Normal and optimized portable Python replay each pass 103 exact checks and 30 wrong-formula controls, counted separately. Proof, assumptions and portable replay · Claim ledger and gap functional.
Verified publication (13 October 2026): Zenodo 23335485, version 2026.10.13-regular-shell-spectra, contains 35 files / 454,964,066 bytes. It preserves all 33 files from 23294979 and adds the new scientific capsule and overview. Complete public readback verified every filename, size and MD5/SHA256 checksum. Publication proof and complete inventory.
Scalar-boundary result (11 October 2026): an exact response identity and sharper error bounds certify the registered model's regular local branch for every 0 < delta ≤ 0.002, extending the earlier 1.09155 × 10−7 guarantee. The proof gives strict shell-matching monotonicity, RT ≤ −H² < 0, under its stated hypotheses. The uniform scalar and curvature remainder constants satisfy Keta < 3.196 and KH < 0.254. Curvature is below that of the separate complete boundary theory with scalar-independent detuning: H² − Hconstant² < −0.000423 delta² throughout that interval. These conditional mathematical results concern the specified local branch; dynamical stability and a higher-dimensional Big Bang origin remain unestablished. Proof, exact certificates and reproducible calculations · Bounded primary-literature update · Verified Zenodo edition 23294979. The 8 October checkpoint remains preserved.
Verified publication (11 October 2026): Zenodo 23294979, version 2026.10.11-scalar-response-monotonicity, contains 33 files / 454,129,865 bytes in the preserved concept DOI family 17088132. It retains all 31 files from edition 23244754 and adds the scalar-response scientific capsule and overview. Saved metadata and every file's name, size, MD5 and SHA256 were checked before publication and by complete anonymous public readback afterward. Publication proof and complete inventory.
Completed research (8 October 2026 UTC): 98,304 saved-endpoint comparisons. Normal and optimized runs compare every retained node at eta = -4 and -3.5 with exact prescribed flow from its exact saved incoming state at eta = -4.5. Nine scientific files agree byte for byte, independently checked. Maximum Cartesian L1 discrepancy bounds are U < 2.520 × 10−16 and W < 3.158 × 10−15. The 1e-18 gate concerns target-enclosure radii, not saved-state errors. Exact endpoint results and finite-weight bounds.
Separate conditional analytic models: the stable flat five-dimensional half-space response/noise model and its incident-packet extension passed independent analytic review. An exact four-dimensional continuum replica prevents dimensional identification from these observables. In the static linear incident model, smooth compact continuum packets away from threshold with zero bound-mode position and velocity projections produce transient brane storage and eventual reflection, without permanent capture or thermalization. Model assumptions and reviews.
Retained endpoints do not recover the unsaved dense path. Full continuous pressure/contact/time/momentum/UV certification remains UNRESOLVED, metric calibration FAIL, higher-dimensional Big Bang cause NOT_ESTABLISHED and external novelty NOT_ASSESSED. Fresh normal/optimized portable replay and numerical/bulk-model CI passed. Final-document-head CI and live site deployment are recorded separately in the final delivery receipt. The preserved 8 October Zenodo edition is 23244754 (31 files / 453,646,943 bytes). Replay and CI evidence. Current research and publication status.
Earlier findings (through 7 Oct 2026)
| Result | Status |
|---|---|
| A specific 5D Einstein–scalar model is fixed in advance: W(φ)=1−φ+φ³/3, shell tension σ=2W+δ(1+cφ), δ=0.001 | Definition |
| Within the model, the registered shell solution exists (computer-assisted proof, locally unique; a statement about the equations, not about nature) | Certified (conditional) |
| An unstable scalar mode, m² ≈ −7.7179 H², growth e1.657 Hτ (numerically the only one). No unstable mode in the tensor, vector or special-harmonic sectors (mode stability, not full linear stability). | Certified (mode) / Numerical (uniqueness) / Exact (other sectors) |
| A closed-form 4D theory matches the 5D spectrum to ~10⁻⁶ and predicted the turnaround before the 5D simulation confirmed it | Exact + Numerical |
| Full nonlinear 5D evolution: two fates, relaxation toward an empty de Sitter brane (endpoint not yet reached in the simulations) or reversal and collapse | Numerical |
| No hot, radiation-filled universe from the shell's own homogeneous, classical motion (no added matter) | Negative |
| Corrected late-time static solution (numerical); a proposed matter extension with an exact energy-exchange law | Numerical / Exact (proposal) |
| July 2026 gravitational-radiation claim withdrawn after audit | Withdrawn |
| Pulsar-timing “knee” signature: screened on public data, not derived from the 5D model; strict registered test failed | Screening / Negative |
| New (27 Sept): the corrected end state is linearly stable in the tested sectors; two independent methods agree | Numerical (audited) |
| New (27 Sept): exact series for the end state through eighth order, confirmed to 30–40 digits | Exact |
| New (27 Sept): particle production and six other heating routes give no radiation era in the registered model; leftover vacuum energy is the obstacle | Negative (conditional) |
| New (27 Sept): an added tension term cancels the leftover vacuum, but “dark radiation” stays above observational limits so far | Inconclusive |
| New (28 Sept): with the tension tuned to cancel the leftover vacuum (a model change) and a stand-in energy-transfer formula, a radiation-dominated phase appears; “dark radiation” is 7.3% of the radiation at one transfer rate, within the conservative limit | Numerical (conditional, fine-tuned) |
| New (30 Sept): at a stronger transfer rate the “dark radiation” falls to 2.1%, within the strict current limit (3%). But the phase lasts under half an expansion e-fold before leftover negative vacuum energy recollapses the shell, needs the tension tuned to about 1 part in 10⁴, and still uses the stand-in formula | Numerical (model-internal, conditional) |
| New (30 Sept): replacing the stand-in with particle production derived from the matter extension: with particle masses below the 5D gravity scale, “dark radiation” stays far larger than the radiation (no steady state reached in 32 runs) | Inconclusive, leaning negative |
| New (30 Sept): the same test at the registered δ = 0.001 is not completed (numerical breakdown diagnosed but not yet fixed) | Inconclusive |
| New (1 Oct): an energy bound includes both decay radiation and particles that have not yet decayed. In two locally screened archived crossings, the budget remains far below the radiation target at the tested endpoint. | Analytical bound / Exploratory calculation, conditional |
| New (1 Oct): an executed saved-trajectory audit finds an earlier radiation-dominated sampled interval of about 0.314 e-fold in the finer Y = 2 run under a new diagnostic that avoids cancellation by negative vacuum. Its later plateau fails this diagnostic. The earlier registered verdict is preserved. | Post hoc diagnostic |
| New (1 Oct): the particle-mode integrator passes 90 exact pulse checks and 30 fine normalization checks, supplying a verified control for the next physical test. | Registered numerical control |
| New (1 Oct, quantum modes): modes on the archived source-free tuned shell give an integrated count 0.0503% below the corrected estimate for the declared state and momentum band. Quantum coherence adds 10.96% to the particle-only scalar current and reverses the relative pressure’s sign. Ten registered variants and independent mode checks pass. | Numerical: prescribed background, relative stress |
| New (1 Oct, quantum matching): the proposed matter loop requires additional potential and intrinsic-curvature terms in the shell action. The curved-shell absolute source and finite matching coefficients remain unresolved. | Analytical EFT requirement |
| New (1 Oct Pacific / 2 Oct UTC, curved-source readiness): eight reconstruction controls pass after a documented numerical repair. The archived interpolation and initial state have separate ultraviolet obstructions; smoother fits show initial-boundary derivative sensitivity. Exact-rational subtraction checks and 18 independent toy evolutions pass. | Readiness audit: absolute curved source unresolved |
| New (2 Oct): a flat-background quantum source through a mass-zero crossing passes eight registered variants, exact scattering, energy/work and independent pressure-trace checks. Potential and curvature matching are fixed at a stated reference. | Numerical benchmark: prescribed background, fixed convention |
| New (2 Oct): omitting curvature matching makes pressure drift with the regulator despite excellent energy conservation. The direct physical-mode representation shows cutoff convergence and obeys an exact finite-cutoff trace identity. Finite-regulator sources still change by several percent. | Analytical and numerical checks |
| New (2 Oct, massive de Sitter sources): Four common-reference quantum-vacuum cases pass 57 checks, a separate proper-time calculation and an exact direct-pressure check at one curved point. Nineteen classical integrations resolve a tiny stationary response and correct its roundoff-limited sign. | Exact algebra / Numerical, internally checked |
| New (2 Oct, stationary quantum closure): Both quantum sources enter a regular bulk-and-shell solve: 48 roots pass 1,584 corrected checks and independent comparisons. Resolved nonlinear feedback occurs only where the declared gravity hierarchy screen fails. | Numerical stationary model, physical limits unresolved |
| New (2 Oct, causal response): Independent forced modes pass 36 finite-cutoff comparisons and 17 controls. Both tested pulses retain negative variance response after their sources vanish. | Fixed geometry; stress, stability and heating untested |
| New (2 Oct, matched stress): Independently computed density and pressure pass 180 core comparisons, finite-cutoff trace/contact checks and a separate energy ledger. Stress tail bounds and raw modes are retained. | Linear response on fixed geometry; heating untested |
| New (3 Oct, source-operator prerequisite): Two independent methods certify moment and source-primitive integrals at nine registered momenta, with uniform analytic model bounds and a conservative whole-interval radius covering both implementations below 1.373 × 10⁻²⁸. | Conditional certificate; full stress/conservation certificate unresolved |
| New (5 Oct): Exact finite-band stress/error kernels bound the analytic source-truncation contribution throughout the interval. A normalized state change between probes shows why the incoming state needs a separate bound. | Conditional exact mathematics; full numerical certificate unresolved |
| New (7 Oct): Two independent methods enclose the prescribed vacuum response at all nine registered momentum probes; all 36 complex enclosures intersect and meet the 10⁻²⁰ gate. | Target certificate at fixed probes; full certificate unresolved |
Previous result (7 October 2026): incoming-state error enclosed at every saved node. Four authenticated archives contain 49,152 capsule-node occurrences. Their original binary80 values are decoded exactly and compared with a certified prescribed target at every node. The normalized W = w/epsilon discrepancy has a Cartesian L1 upper bound below 1.914 × 10⁻¹⁴ on the coarse grid and 5.776 × 10⁻¹⁶ on the fine grid; normalized U is below 1.571 × 10⁻¹⁶. The larger coarse W values cluster near the upper momentum cutoff. This measured difference is not a proof of continuum convergence or its mechanism. Exact result, reproduction and limits.
The original incoming-state error is now ENCLOSED at the saved nodes. Exact continuous-time error transport gives density, pressure, work and pressure-time-integral bounds for twelve fixed finite-weight sums, conditional on identical subsequent physical forcing and full contacts. It does not enclose the later numerical trajectory, continuous momentum integral, contact defects or ultraviolet tail. Eight scientific artifacts reproduce byte for byte in normal and optimized Python; a separate serialized-output audit independently checks all node summaries. The full twelve-case certificate remains UNRESOLVED, metric calibration FAIL, the Big Bang origin NOT_ESTABLISHED, and external novelty NOT_ASSESSED.
A bounded literature refresh uses 22 searches and selected primary passages from eight papers. The conditional dimensional-identifiability argument shows why equal complete effective inputs can give equal observed probability laws. The physical next step needs an action-derived prediction that differs from specified four-dimensional rivals.
Previous checkpoint (7 October 2026): error bounds for the prescribed vacuum response. Two independent methods compute the response to two smooth sources, starting from the specified Bunch–Davies vacuum condition before the sources turn on. They cover nine momentum probes and two normalized response quantities: 18 cases and 36 complex enclosures. All 36 pairs of enclosures intersect. Their largest complete error radii are below 1.555 × 10⁻²¹ and 3.138 × 10⁻²³, within the fixed 10⁻²⁰ gate. The zero-momentum probe is the analytic continuation of the response. Result, reproduction and limits.
A separate certificate bounds only the prehistory source representation and coefficient error. With identical later forcing and full contacts, their contributions to scaled pressure and density are below 1.625 × 10⁻¹⁸ and 4.094 × 10⁻²¹ throughout the time interval [−9/2, −7/2], at momentum cutoffs 64, 128 and 256. These continuous bounds exclude phase and solver arithmetic across the momentum band. At that earlier stage, retained binary80 mode errors were NOT_ENCLOSED; the later comparison above encloses them at every saved incoming node, the full twelve-case certificate remains UNRESOLVED, and metric calibration remains FAIL. A higher-dimensional Big Bang origin remains unestablished.
Previous result (7 October 2026, Pacific): conditional incoming-state transfer. Exact density and pressure formulas retain the phase of homogeneous state errors when forcing and full contacts are identical. First-order normalization does not bound the state amplitude. With normalization drift independently controlled, a proved incoming-state amplitude bound gives conditional finite-band stress-error bounds. The direct operators also give an exact signed pressure time primitive. No actual state enclosure, physical trajectory or full twelve-case certificate is supplied; the ultraviolet tail remains outside the result. Metric calibration remains FAIL and a higher-dimensional Big Bang origin remains NOT_ESTABLISHED. Result, proof and limits.
Previous result (5 October 2026 UTC): exact finite-band stress/error mathematics. The analytic source Taylor-truncation contribution at K=256 is below 5.5 × 10⁻²⁸ for scaled density and 2.2 × 10⁻²⁵ for scaled pressure throughout the declared time interval. These are conditional bounds for one error component. Incoming-state, arithmetic, contact and quadrature errors still need separate bounds; a smooth normalized state can pass all nine probes and conservation while changing integrated stress. Three exact verification routes and a clean six-run archive replay pass. The full twelve-case certificate remains UNRESOLVED and metric calibration stays FAIL. Result, proof and limits · Standalone exact replay.
Previous result (3 October 2026, Pacific): conditional source-operator certificate. Two independently implemented enclosure methods pass all 1,170 moment rows and 130 source-primitive rows per route for two smooth sources, 64 panels and nine registered momenta. The largest conservative whole-interval enclosure radius across both implementations is below 1.373 × 10⁻²⁸, within the fixed 10⁻²⁶ limit. Analytic model bounds cover real momentum k ∈ [0,256]; complete computed widths are certified at the nine probes. The full twelve-case pressure/contact conservation certificate remains unresolved and metric calibration stays FAIL. A higher-dimensional cause of the Big Bang remains NOT_ESTABLISHED; external mathematical novelty is NOT_ASSESSED. Research manuscript: result and limits · Standalone archive replay. A fresh standalone archive replay reproduces both numerical payloads and scientific frames exactly.
Fresh archive reproduction evidence.
Previous result (2 October 2026, Pacific): active-source ledger diagnosis. Two independently implemented calculations identify sampling error in the retained conservation ledger during the registered active-source interval. All twelve consistency cases pass; eight meet the fixed attribution threshold. A fresh standalone archive replay reproduces every registered scientific value exactly. Small signed residuals involve cancellation and are not certified total-error bounds. Earlier metric calibration remains FAIL; continuum accuracy, coupled evolution and a higher-dimensional cause of the Big Bang remain unestablished. Measured result and limits · Exact fresh reproduction.
Earlier verified publication (7 October 2026, Pacific): main-family record 23114217, DOI 10.5281/zenodo.23114217, is published with 23 files / 440,222,994 bytes. Authenticated and direct public readback confirm the published record; all attachment bytes matched size, MD5 and SHA256 before publication. Its semantic version 2026.10.03-verified-source-operator archives the frozen 3 October packet. That frozen archive excludes the later 5 and 7 October mathematics. The proof guide discloses the exact reviewed Notes HTML serialization and preserved original literal comparison failure. Previous main 22347452 and separate companion 23111008 are retained. Automatic GitHub archiving stays OFF; no new integration-toggle inspection is claimed.
Previous source-free ledger diagnosis: Two independent implementations identify time-integration error after the compact source ends. All twelve consistency cases pass; eight meet the fixed attribution threshold. The previous metric calibration remains FAIL. That result concerns the interval after forcing; the active-source interval is checked separately above. Coupled dynamics and heating remain unresolved. Measured results and reproducible evidence.
Registered metric response: scientific FAIL. A memory-only repair completes all twelve primary observations and four independent evolutions at 103,400 KiB peak memory, within the unchanged 256 MiB limit. Fifty-nine conservation endpoint/refinement checks still fail. The earlier quadrature and resource failures remain preserved. Reproduction-control success does not establish calibration. General metric, actual-root, bulk/state response, stability and heating remain unresolved. Failure evidence and next steps · Standalone reproduction.
Registered matched stress: The new test calibrates both physical minimal density and pressure with complete fixed-reference subtraction and an independent conservation ledger. Negative after-pulse relative density describes coherent vacuum polarization; it does not establish heating or negative total energy. Metric response and coupled evolution remain open. Results and scope · Self-contained reproduction.
Earlier causal calibration: That variance-only experiment checked scalar memory on fixed de Sitter geometry and proposed the separate stress test now completed above. It calculated no heating. Results and limits · Self-contained reproduction.
The paired quantum sources now close a stationary bulk-and-shell problem numerically. Only the smallest tested positive coupling passes the sampled gravity hierarchy screen; its curvature shift is tiny. Stability, causal evolution and heating remain open. Stationary results and limits · Fresh reproduction.
New (2 Oct, massive de Sitter sources): Both quantum sources are derived from one action in the declared finite convention. These are static vacuum benchmarks and a classical differential response; physical mass and coupling choices, causal time-dependent backreaction and heating remain open. Results and scope · Independent internal review · Fresh reproduction.
Smooth curved-background quantum-source control: a separately registered K384 follow-up passes all 13 acceptance groups. The pressure change from K192 to K384 is 0.2291% of its global comparison scale. The original experiment remains FAIL: its flat control passed, while curved pressure exceeded its original cutoff tolerance. The calculation retains coherent stress and scalar source and checks their common-action exchange when the mass squared touches zero. This is finite-cutoff evidence on a prescribed background; coupled shell evolution, backreaction and thermal radiation remain unestablished. Results and preserved outcomes · Reproduce the calculation · Claims and next steps.
The new curved-source readiness audit quantifies two obstacles to extending the finite-band calculation: geometry interpolation and initial-state preparation. Agreement in the field and expansion rate does not establish reliable high derivatives. Its controls pass; the absolute source on the archived shell, backreaction and a hot Big Bang remain unestablished. Measured results and limitations.
The registered homogeneous model has not produced a hot Big Bang. Tuned variants using a stand-in transfer formula briefly meet the earlier radiation criterion and then recollapse. The new quantum-mode calculation reproduces the corrected integrated count closely for its declared setup, while showing that coherence matters for the scalar force and pressure. Its endpoint excitations are not a radiation fluid. The 2 October checkpoint supplies an absolute source in a fixed matching convention for a flat-space pulse, including the curvature contribution to pressure. Curved-shell matching, coupled evolution, decay and thermalization remain unresolved. Read the matched-source checkpoint. Read the quantum-mode checkpoint; the earlier 1 October diagnostic retains its original scope.
What comes next
Next quantitative step: bound the initial nonlinear radial-root and inverse boundary-flow Sobolev map; then evaluate product/commutator constants, normal recovery and the complete quadratic forcing, and establish the actual family's uniform metric-patch membership. A common physical shell/observer domain, proper clock, full-family Q(a), actual area, finite nonlinear remainder and quantitative central-zero goal still require compatible control on one admitted amplitude interval.
Next quantitative step: bound coefficient derivatives, lower-order terms and the actual coupled second evolution; establish uniform patch membership and a common physical shell/observer domain on one admitted amplitude interval. The proper clock, full-family Q(a), finite nonlinear remainder and quantitative central-zero goal remain open.
Current priority: bound the actual coupled second evolution of the scalar, metric and anisotropic Weyl fields from the complete physical initial jet. Establish a common physical target cylinder and compatible shell, clock/observer, embedding, area and denominator estimates, with uniform parameter control on one admitted amplitude interval beyond the initial derivatives at zero. The full-family Q(a), finite-amplitude quadrupole remainder and quantitative central-zero goal remain open.
Earlier priority: quantify the high-order weighted inverse and its initial output in H14 for the metric and H13 for the momentum; then bound the actual coupled second-scalar and anisotropic-Weyl histories. Establish their common nonlinear target cylinder with compatible physical shell, clock/observer, embedding, area and denominator bounds on one admitted amplitude interval. The full-family Q(a), nonlinear remainder and quantitative central-zero goal remain open.
Earlier priority: recover and instantiate the actual weighted constraint inverse and bound the three second-scalar projections plus the two nonconstant anisotropic-Weyl stress projections. Establish the common cylinder and compatible uniform mixed metric, scalar, observer/clock, embedding, area and denominator bounds on one admitted amplitude interval. The original full-family Q(a), nonlinear remainder and quantitative central-zero goal continues.
Next priority: bound the actual weighted curvature projection <R2>_w or an equivalent second-field evolution, then establish compatible uniform mixed field and observer bounds and a common domain on one admitted amplitude interval. The full-family metric bound Q(a), scalar and odd-remainder budgets and quantitative central-zero guard remain part of the original priority.
Next priority: establish compatible uniform full-family metric and observer-domain bounds, including Q(a) on a fixed admissible neighborhood, then combine the conditional metric estimate with the scalar and remainder budgets. No numerical amplitude radius follows from the evaluated first derivatives alone.
Next priority: evaluate uniform post-reset coefficient bounds and a fixed admissible neighborhood for the same full nonlinear family, then combine them with the physical observer-domain and remainder budgets to test a quantitative central-zero guard.
Next priority: validate a fixed regular coefficient neighborhood, compatible initial data and the shell identification; evaluate the observer-domain and observable budgets on the same family, then test a quantitative nonlinear remainder guard.
Next priority: certify the common noncrossing observer domain and evaluate compatible full-pullback metric, scalar and continuity-modulus budgets; then test a remainder guard for the specified preparation and physical source.
Next priority: compute an effective amplitude interval and control the nonlinear remainder for a specified compatible past preparation and physical source, then establish physical scales and observables. Earlier conditional nonlinear families and qualitative familywise signs do not provide these missing quantitative bounds for the chosen past state.
Next priority: obtain a quantitative particular past second-order baseline and control its nonlinear defect/remainder for a specified physical incoming source. The earlier formal complete future Taylor coefficient does not supply these quantitative past estimates.
Next priority: construct a compatible second-order state and nonlinear past development for a specified physical incoming source. Control the remainder and physical scale before interpreting coefficient bounds as finite physical amplitudes or radiation.
Next priority: connect these local face traces to a specified compatible past state and source, extend through shell interaction, and complete the second constraints and nonlinear remainder. The local first-order construction does not supply a physical preparation or radiation law.
Current priority: specify one past incoming state and any source, satisfy all constraints, shell junctions and corner conditions, and prove that its evolution reproduces the registered present first packet. Transport and bound the complete present data, including compatible initial energy. A full matter model, physical scale and uniform nonlinear remainder control remain necessary.
Previous incoming-state target: derive one physical preparation map and a preparation-sensitive bound on the initial scalar-level H1 norm from a specified action and state. Control the nonlinear remainder uniformly over the resulting class; a matter-energy ledger, proper-time history and physical scale remain necessary.
Previous preparation-control target: supply a physical action, state or generating process that selects or justifies the initial slice, allowed preparation class and its radius. A uniform nonlinear amplitude bound would require additional remainder control; a proper-time history, matter energy ledger and physical scale remain necessary.
Previous geometric-preparation target: specify a physical action, state or generating process that selects the second initial preparation, or define a justified class and certify robust predictions. A numerical amplitude window, proper-time history, matter energy ledger and physical scale remain necessary.
Previous preparation target: test dependence on admissible mean preparations and how physical dynamics could select them; extend the result to a registered time history; bound the nonlinear remainder and amplitude window; and specify matter interactions, an energy ledger and a physical scale.
Previous target: determine the second scalar mean for explicitly specified initial weights, then evaluate the complete intrinsic proper-time volume and expansion. A hot-radiation model also needs stated matter interactions, an energy budget and a physical scale.
Retained source-study targets: certify the evolution between saved times, full contacts, time integration, continuous momentum quadrature and the ultraviolet remainder. The incoming-state and later-endpoint errors are enclosed at the retained nodes; they do not recover the unsaved dense path or certify the continuum between nodes. Preserve the twelve cases and inherited 2 × 10⁻⁸ gate before another unchanged metric calibration. Endpoint result and remaining terms.
Stability
Is the corrected late-time solution stable, and does the blast actually end there?
Particle production
Can the blast's energy become particles and a lasting radiation era, with backreaction included?
Reliable simulations
Control the numerical errors in long five-dimensional evolutions.
New ingredients
Screen matter couplings, bulk “dark radiation”, bubble-universe constructions and a contracting (collapse) phase.
For the hypothesis to become credible it needs a working mechanism, a unique quantitative prediction, independent reproduction, peer review and observational tests. It can fail at any step, and failures will be published.
Explore the research
- All-node retained-state comparison and exact fixed-weight error transport: included errors, reproduction and limits
- Bunch–Davies prehistory response and continuous representation certificate: two independent methods, included errors and limits
- Current status: latest verified research, limits and actual Zenodo publication
- Conditional incoming-state theorem: exact transfer, finite-band bounds and state-normalization limits
- Finite-band stress/error theorem: conditional analytic truncation bounds, state counterexample and exact proof replay
- Conditional source-operator certificate: measured bounds, premises and limits · standalone archive replay
- Completed active-source diagnosis and standalone archive: registration, original failure, disclosed repair and exact reproduction
- Plain-language guide
- Program map: model, chronology, claims ledger and falsification tests
- Research checkpoints: reports, code, data and internal AI referee reviews (not external peer review)
- All Zenodo records
- 27 Sept 2026 checkpoint: stability, exact series, particle production, new mechanisms
- 28 Sept 2026 tuned-vacuum test and 30 Sept 2026 checkpoint: radiation phase, dark-radiation limits, fine-tuning
- 1 October 2026 checkpoint: energy bounds, radiation duration and exact mode controls
- 1 October quantum modes: results, coherence, quantum matching, data and reproduction
- 2 October matched quantum source: pressure matching, regulator and cutoff tests, data, figures and reproduction
Cite
Verified publication (8 October 2026 UTC): 23244754, DOI 10.5281/zenodo.23244754, version 2026.10.08-later-state-and-bulk-response, contains 31 files / 453,646,943 bytes in concept 17088132. All 29 previous files are retained; fresh complete size/MD5/SHA256 streams passed before and after publication, with final public readback at 2026-10-08T17:52:21.331322+00:00. The additions are a compact supplement and overview; the full source replay package is pinned separately at immutable commit 52126b98d3e4b24680017fa2537b8449bd75d94f. Publication proof and complete inventory.
Preserved previous edition (7 October 2026):
The main-family edition 23228395, DOI 10.5281/zenodo.23228395, contains 29 files / 451,598,148 bytes. Complete attachment streams matched every filename, size, MD5 and SHA256 before and after publication. It preserves all 27 files from 23225288 and adds a compact scientific supplement and a revised original overview. The scientific supplement contains all registered checkpoint code, exact proofs, compact outputs, independent reviews and original figures. The complete replay package and full node-level checkpoint evidence remain pinned to immutable GitHub commit 13a30ef46f5c90c1b01ae83b609db65fd0f8a709, including the original replay inputs and both large node-level payloads. The saved publication proof preserves the witnesses and earlier editions.
The preserved previous main-family edition 23225288 (DOI 10.5281/zenodo.23225288) contains 27 files totaling 448,387,915 bytes. Every file was fully streamed and matched its size, MD5 and SHA256 before and after publication. It preserves the earlier 23 files and adds the Ward, incoming-state and BD prehistory archives plus an overview. The saved publication proof and offline verifier record the metadata, checksums and preserved earlier editions.
Maldonado, R. HDBLAST: higher-dimensional blast research program. Zenodo, doi:10.5281/zenodo.17088132 (all versions). Previous published main version: 23114217, 2026.10.03-verified-source-operator. Separate static-branch companion: 23111008, preserving the original September study, concept 22922927. Each Zenodo record states its own licence.
Specialists are invited to check the work and report errors through GitHub issues.