04Extra dimensions · early Universe
15 October 2026: continuous coordinate shell sources: 4353 continuous time cells enclose the metric boundary trace and derivative and the complete one-copy coordinate scalar/isotropic shell sources. A correction below 9e-13 in relative L2 still changes signs at scalar zeros; each coordinate coefficient has at least two central zeros. Degree-4 Robin norm only; conditional on retained analytic inputs and the stated representative. 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: The explicit material tension contribution Q_phi = -4 psi_1^2 has scalar degrees 0, 2 and 4, a strictly negative continuous mean tail, and an enclosed squared L2 norm in model units. The complete coordinate source and full U2 remain unevaluated; the earlier conditional second-coefficient construction is preserved. Result and assumptions. Publication evidence remains pending until the final additive receipt.
Conditional inertial shell waveform: A specified wider quadrupole has a signed post-pulse first-variation tail, two zero brackets and a leading coefficient interval in model units. No zero uniqueness, finite-amplitude nonlinear waveform or effective epsilon is asserted. Result and assumptions. Publication evidence remains pending until the final additive receipt.
Conditional first-variation shell waveform: For the same narrow state, a continuous 4098-cell first-variation envelope and a negative physical gain give 6.06 × 10^15 < C < 7.44 × 10^15. This conditional result supplies no finite-amplitude nonlinear waveform or observed time scale. The next target is an effective nonlinear remainder. Waveform theorem, normalization and assumptions.
Conditional quantitative shell-response bound: A newly specified narrow quadrupole has a positive leading response coefficient enclosed by exact-rational bounds under the retained hypotheses. The interval uses model units; no waveform or effective nonlinear amplitude is supplied. Result, normalization and limits.
Conditional physical shell response: An explicit aligned quadrupole has a qualitatively nonzero physical scalar response under the retained hypotheses, with a positive leading proper-time-window coefficient in the exact nonlinear family. Numerical magnitudes and cosmological implications remain open. Response theorem and limits.
HDBLAST: conditional exact shell evolution: A selected aligned quadrupole now has a small exact nonlinear family on a controlled finite region and shell-interaction interval, under stated assumptions. Physical constraints and shell laws hold; an observable nonzero shell response remains to be calculated. Result and limits.
All-angular linear shell-contact estimate · 14 October 2026 (Pacific): The complete sixteen-field linear Einstein–scalar system has positive auxiliary control uniform over the full tensorial angular cutoff on the registered background and controlled collar. A bounded transformation handles all twelve nonsymmetric Robin rows. Smooth boundary lifting has a declared regularity cost; this is not physical energy or nonlinear stability. The earlier exact initial-data family at fixed finite Sobolev regularity is retained. An exact nonlinear family through shell contact and a Big Bang origin remain open. Estimate and limits.
Complete second-order coefficient through shell contact · 14 October 2026: For the specified even quadrupole and compatible localized initial constraints, a conditional construction gives the complete metric and scalar second Taylor coefficient through first shell contact on a controlled collar, with the physical boundary laws and constraint propagation. Exact nonlinear contact existence and a Big Bang origin remain open. Earlier dated entries below retain their original scope. Construction and limits.
Quadratic tensor source and conditional tensor evolution through contact · 14 October 2026: In the specified quadrupole gauge, gravity and scalar contributions give a tensor-source coefficient 16u² + 8v²/3. The even tensor sector admits a conditional forced evolution through first contact on a controlled collar. The full coupled nonlinear contact problem remains open. Derivation and limits.
Exact localized initial data and short precontact evolution · 14 October 2026: Conditional nonlinear initial-data families at high finite Sobolev regularity preserve the background shell collar for a sufficiently short evolution before contact. The through-contact boundary problem remains open. Internal proof review is not external peer review. Proof and limits.
Formal continuation by reflection symmetry · 14 October 2026: Coordinate reflections remove all ten local compatibility obstructions at every finite constraint order for the restricted commuting quadrupoles. Recursive localization and group averaging construct formal initial data. Convergence, exact nonlinear solutions and full shell-contact evolution remain open. Derivation and limits.
14 October 2026: Conditional second-order initial-data sufficiency for fixed-parity packets in an annulus away from the shell and vertex, with a gauge-fixed monopole identity. Full second-order shell-contact evolution and nonlinear existence remain open. Technical note.
Higher-dimensional Big Bang research: 98,304 saved-endpoint comparisons completed, with independently checked normal/optimized agreement. Separate conditional bulk-response and incident-packet models give no dimensional identification or permanent capture in the defined static model. The full continuous certificate and a hot Big Bang mechanism remain unresolved.
Retained-endpoint results and conditional bulk models · 8 October 2026 UTC
Endpoint results and finite-weight bounds · Conditional bulk and incident models · Current status
Zenodo 23244754 · 31 files · Fresh portable replay and source CI passed. Final-document CI and site deployment have separate delivery evidence.
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