HDBLAST: Conditional Scalar Spectral Positivity and Tensor Mass Thresholds on Regular de Sitter Shells

13 October 2026: conditional scalar spectral positivity and tensor mass thresholds

This edition adds a self-contained research checkpoint for the registered five-dimensional Einstein-scalar shell theory with two regular interiors joined at a de Sitter shell. It concerns the regular branch near phi=+1, using eta=phi-1, which is a distinct solution of the same action as the earlier unstable hilltop branch. The prior branch instability is preserved; no evolution between these solutions is proved.

For every fixed 0<delta<=0.002 in the exact rational model certified by the unchanged static proof basis, the closed finite-energy scalar radial operators in both reflection parities have their entire mu^2 spectra bounded below by explicit positive background-dependent functionals. Those functionals are proved finite and positive but are not given numerically certified values, and no uniform positive gap as delta tends to zero is established. The scalar essential threshold is mu^2=9/4.

The full local Einstein-Hilbert, Gibbons-Hawking-York and shell-action calculation gives positive generic scalar kinetic coefficients. The odd calculation includes the moving integration domain and graph boundary. Constant and translation-type harmonic subspaces are treated separately; these exceptions do not remove every harmonic at the corresponding mass values. Global gauge admissibility, physical state-space completeness and cone symplectic flux remain conditional.

The transverse-traceless tensor result identifies the even massless profile as the only radial state below mu_T^2=9/4; the entire nonzero even spectrum and odd spectrum lie at or above that threshold. Established partner-operator methods are applied to an exact negative potential bound over the certified branch tube. The specific Jacobi identities and sign-controlled branch application are distinguished from established soft-boundary Sturm-Liouville, enlarged-norm and ground-state methods; no global priority claim is made.

The scientific ZIP contains the technical manuscript and reproducible supporting proofs, local-action derivations, independent reviews, primary-literature context and portable scripts. Its fresh replay passes 103 new exact identity/sign checks and 30 deliberate wrong-formula controls in each of normal and optimized Python, with identical receipts, unchanged sources, corruption rejection and replay of the previous static arithmetic. Symbolic checks validate specified formulas and inputs, not analytic proof completeness. Substantial AI assistance and separate internal AI-assisted review are disclosed; these are not external peer review or experimental evidence.

These are conditional linear spectral and local-action results for the stated radial realization. They do not establish global time evolution or a semigroup bound, vector-sector stability, nonlinear attraction, quantum decay, a cosmological energy-transfer/reheating history, observational preference, or a higher-dimensional Big Bang origin. The delta=0 divided scalar formulation is outside the theorem. The scalar-independent-detuning comparator in the static basis is a separate boundary theory.

All 33 files of published record 23294979, totaling 454,129,865 bytes, are retained unchanged; exactly two named new attachments are added. The edition remains in concept DOI 10.5281/zenodo.17088132. Companion record 23111008 remains in its separate concept family 22922927. The old description and Notes below remain dated historical provenance; their then-current counts and claims are not rewritten.

Preserved Description from published record 23294979

11 October 2026: controlled scalar-boundary response and endpoint monotonicity

This edition adds a self-contained mathematical and computational checkpoint for a specified five-dimensional Einstein-scalar boundary-value problem with two identical regular interiors joined at a four-dimensional de Sitter brane. It is a conditional mathematical result for that model, not evidence that a higher-dimensional blast caused the Big Bang.

The new proof derives regular-center Jacobi identities and strict monotonicity of the moving-endpoint metric residual along the scalar-junction locus. This removes the earlier sufficient absolute slope restriction. A revised derivative scale, sharper endpoint estimate and exact rational inequalities extend the certified branch interval of the registered exact-decimal polynomial model from approximately 1.09155e-7 to every 0<delta<=0.002. Existence and uniqueness apply within the explicitly specified weighted neighborhood and radial domain, not globally.

For k=1/9, W(x)=1/3+x^2+x^3/3, c=2/(1.0357712571566784)-4/3 interpreted using the exact decimal rational, and f(x)=1+c+cx, the uniform expansion remainders satisfy |beta-alpha*delta|<3.196*delta^2 and |H^2-a1*delta-a2*delta^2|<0.254*delta^3. Here alpha=-f1/[4(w-2k)], a1=k*f0/3, a2=f0^2/36-k*f1^2/[24(w-2k)], w=W''(0), f0=f(0), and f1=f'(0). The exact certificate also proves strict curvature reduction relative to the separate boundary theory with constant detuning f=f0 throughout the interval. That comparator is not a constant-scalar solution of the original scalar-dependent boundary condition.

The package contains the proof, exact-arithmetic producer, independently implemented checker, reproducible exact rational comparisons, an analytic-bound figure and source provenance. Separate internal AI-assisted reviews and exact checks support the stated estimates; they are not external peer review, proof-assistant formalization or observational confirmation. The certified expansion remainder is not a certified rounding, integration or shooting-error bound for archived floating-point ODE trajectories.

The standard bulk equations, junction identities and earlier curved-brane constructions are credited to the primary literature. The advance is the explicit controlled branch argument and its evaluated domain, without a claim of established external priority. Perturbative stability, a cosmological energy-transfer and reheating mechanism, a distinctive observational likelihood, and a demonstrated higher-dimensional origin remain open. Earlier full continuous pressure/contact/time, momentum and ultraviolet certification remains unresolved; the historical metric-calibration failure is preserved.

All 31 files from published record 23244754 are retained unchanged, and the two new files are a scientific supplement ZIP and a readable overview. This is an additive release in concept DOI 10.5281/zenodo.17088132. The separate scalar companion record 23111008 remains in its own concept family 22922927. The dated historical description below is preserved as provenance; its file counts and current-checkpoint wording refer to that earlier edition.

Preserved Description from published record 23244754

8 October 2026: retained later-state endpoints and a separately scoped causal bulk-response testbed

This checkpoint encloses the saved later-state difference from exact forced evolution beginning at the same exact represented incoming state at eta=-9/2. It covers 49,152 capsule-node occurrences, 98,304 endpoint comparisons and 24 fixed finite weighted cases at eta=-4,-7/2 and K=64,128,256. The maximum normalized Cartesian complex L1 errors obey ||Delta U||1<2.520e-16 and ||Delta W||1<3.158e-15. All 48 signed finite R/P anchor intervals exclude zero; finite triangle bounds are R<2.352e-14 and P<2.053e-11. Exact rational DATA and the 24-row CSV remain authoritative. The target export radii, U<7.574e-29 and W<1.263e-28, satisfy the 1e-18 uncertainty gate; that gate is not a bound on historical endpoint error. The earlier incoming Bunch-Davies mismatch is separate.

The publicly authenticated source freeze, registered normal/optimized executions, independent exported-certificate/receipt review and complete fresh portable normal/optimized replay pass. All nine stable scientific files match exactly. Independent readback checks every serialized endpoint and finite aggregate without independently redecoding the original archives or constructing another flow. Source/flow truth also depends on the authenticated implementation and reviewed analytic proof. No cause separation, unsaved historical continuous solver path, momentum convergence or full pressure/contact/time/UV certificate is claimed.

A separately defined stable flat 4+1-dimensional Robin half-space scalar action yields a causal retarded kernel, positive spectral measure and Gaussian response/noise laws. An explicit four-dimensional continuum of free fields reproduces those laws, so these observables alone do not identify extra-dimensional geometry. The incident-wave extension gives unit reflection, a division-free resonant response and decaying local boundary energy for smooth pure-continuum packets with both bound-mode projections zero. Within this static linear single-port model those packets do not produce permanent capture/reheating. The conclusion is conditional on the declared action/state, rather than a general exclusion of HDBLAST. Gravity, time-dependent cosmology, nonlinear energy transfer and observational likelihood remain open.

The bounded literature update records 12 queries and 8 selected primary-source readings, including verified 2026 papers. Only original synthesis and compact provenance are delivered; no raw third-party article bodies or exhaustive web-review claim is included.

The compact supplement is not a standalone numerical replay package. The complete new source-replay package is pinned at Git commit 52126b98d3e4b24680017fa2537b8449bd75d94f: https://github.com/maldonado-research/HDblast/tree/52126b98d3e4b24680017fa2537b8449bd75d94f/research/HDBLAST_RETAINED_ENDPOINT_FLOW_PACKAGE_20261008. PAYLOAD_MANIFEST SHA256 976e92a7a14ecb13ed04cbb9f7ed15fff3a285bd40175a28929dff53677d0752; REPLAY_PINS SHA256 1407dc4bcf0a312d1bc23a29e93e3c1149071f4ce2705ccbbeef430e82446d68; helper SHA256 5de25511aea5579b7e0ebe94208ee1584d0869ca248fa8939cdbb29ed25ff6fd; actual portable-replay receipt SHA256 7d0ccaceb86586143a9a2e47e23fa324eb302fef1cc730b5fa91cc8d34116c41. The 11 original dependencies are separately pinned at older commit 13a30ef46f5c90c1b01ae83b609db65fd0f8a709; it supplies old input bytes, rather than new endpoint science. The supplement omission/leaf manifests identify every required external leaf and checksum.

This additive candidate follows record 23228395 in concept DOI 10.5281/zenodo.17088132 and preserves all 29 inherited files. The sealed31-file inventory totals 453646943 bytes. Saved metadata and complete fresh MD5/SHA256 streams for all 31 draft/public files are independent publication requirements; prepared attachments are not a publication outcome. Full continuous pressure/contact/time/momentum/UV certification remains UNRESOLVED, historical metric calibration FAIL, higher-dimensional Big Bang origin NOT_ESTABLISHED and external novelty NOT_ASSESSED. AI-assisted internal checks are not external peer review or proof-assistant formalization. Automatic GitHub-to-Zenodo archiving is historically OFF, untouched; no fresh account setting inspection is claimed.

Preserved description of published record 23228395

This scientific checkpoint encloses the difference between exact represented incoming first-order states retained in four source/resolution capsules and the prescribed Bunch-Davies prehistory target. It covers all 49,152 capsule-node occurrences, 20 selected exact-reader arrays and 12 registered finite weighted prefixes at K=64,128,256. All registered stored-minus-target error rectangles are ENCLOSED. Capsule identities remain separate even when their momentum values coincide.

The fixed reader preserves represented binary80 values as exact rationals, including momenta, quadrature weights and u_1/w_1. It uses U=u_1/epsilon_represented and W=w_1/epsilon_represented without projecting or renormalizing the saved state. The preregistered target engine uses global degree 832 and Arb precision 512. Every exported U rectangle and every exported W rectangle passes the complete L1-radius gate of at most 1e-18. This gate controls certified target uncertainty, not incoming mismatch or stress error.

Certified positive lower and upper brackets resolve nonzero incoming mismatch. On the complete K=256 prefixes, coarse-capsule maximum normalized Cartesian complex L1 W errors are approximately 1.91e-14 at retained momenta near 255.86 and 255.90, while fine-capsule maxima are approximately 5.3-5.8e-16. These are decimal display approximations; exact outward brackets and maximizing-node witnesses in RESULTS.md are authoritative. These observations do not establish the cause of the errors or a convergence theorem.

Exact finite-weight transport encloses signed anchor differences and phase-uniform linear density/pressure differences on eta in [-4.5,-3.5], using the represented measure dk*k^2/(2 Pi_represented^2) and the inherited a_0(eta)^4/epsilon_represented scaled R/P convention. Subsequent forcing remains active; the difference evolves homogeneously under identical forcing and complete contacts. These bounds concern the twelve fixed finite represented weighted prefixes. They do not establish continuum interpolation or quadrature, later saved numerical-trajectory accuracy, full source/contact error or ultraviolet completion.

Actual normal and optimized registered executions pass, all eight stable scientific artifacts agree byte for byte, and independent saved-output review passes. Analytic bounds, compact summaries, source certificates, execution receipts, exact norm witnesses and original figures are in the scientific supplement. Complete target-node exports and replay inputs are pinned on GitHub. The scientific source was publicly frozen before execution at Git commit bedcca7e86995da1230c12a20fae3755b31f4a94. The complete standalone replay package, including all eight original/compact inputs and node-level exports, is available at immutable GitHub commit 13a30ef46f5c90c1b01ae83b609db65fd0f8a709 (https://github.com/maldonado-research/HDblast/tree/13a30ef46f5c90c1b01ae83b609db65fd0f8a709/research/HDBLAST_STORED_STATE_COMPARISON_PACKAGE_20261007). The smaller Zenodo supplement archives 159 unchanged checkpoint files and explicit external replay references. The fresh archive extraction passes complete saved-output verification and full normal/optimized replay, reproducing all eight scientific artifacts exactly. External pins bind that successfully replayed full archive, its completed receipt and the separate scientific supplement. The full 240,135,519-byte archive remains a prepared asset after two managed cloud credential-proxy HTTP 401 upload refusals; it is not a Zenodo attachment in this edition.

The full continuum pressure/contact certificate remains UNRESOLVED, historical metric calibration FAIL, higher-dimensional Big Bang causation NOT_ESTABLISHED and external novelty NOT_ASSESSED. Internal AI-assisted checks are not external peer review or proof-assistant formalization. Literature access comprises 46 recorded TLS GET responses with status 200 and eight selected primary-source passage readings. This is bounded coverage, not an exhaustive search or full-paper/proof verification; private caches and third-party paper bodies are excluded.

This is an additive edition in the existing concept family 10.5281/zenodo.17088132, following record 23225288. All 27 prior files are preserved and the scientific publication supplement plus an original overview are the two intended additions. Final file counts, content hashes and delivery status come from the sealed release inventory and complete public content readback.