🇯🇵 日本語要約
B19では、合成した発散ゼロ3次元渦度場について、boundary-core量、Biot--Savart strain、符号付きstrain alignment、production/dissipation balanceを同時に調べます。単一のray-independentなスカラーしきい値への崩壊は得られず、代わりに方向依存の上流boundary-core channel群が、下流のproduction-versus-dissipation / total-balance構造へ接続するという整理が得られました。これは有限の合成場に対する診断結果であり、Navier--Stokes正則性問題の証明ではありません。
BIG-B19 studies synthetic divergence-free three-dimensional vorticity fields using boundary-core concentration, Biot--Savart strain, signed strain alignment, finite-window dynamics, and enstrophy-balance diagnostics.
The integrated B19 study combines a reduced shrinking-core scaling model with synthetic divergence-free vorticity fields, periodic Biot--Savart strain readout, signed strain--vorticity alignment, high-vorticity gates, short-time viscous evolution, numerical robustness controls, local perturbations, and directional continuation.
Under the stated stretching-versus-leakage assumptions, the reduced scaling model identifies an energy-compatible concentration window with a critical thickness exponent
Local-neighborhood tests show heterogeneous robustness across boundary-core channel classes. Controlled continuation around a fragile late-delayed channel resolves three directional local growth--decay boundaries. Reduction tests using 21 single observables and eight predeclared two-coordinate portraits do not yield a robust ray-independent upstream reduction. Mechanism comparison instead supports a channel-family interpretation: distinct direction-dependent upstream boundary-core pathways can feed into a common downstream finite-window production-versus-dissipation organization.
The principal integrated result is therefore not a universal boundary threshold, but a reproducible boundary-core channel-family structure within the tested numerical construction.
The B19 follow-up studies the finite-window response surface
F_ray(T,epsilon)=Delta Z(T,epsilon;ray) and treats the growth/decay boundary as its derived zero set.
The original T=0.010 brackets do not persist as fixed sign-separating boundaries when the observation horizon is extended. In the sampled continuation family, p01 and p02 show outward-moving detected zero contours while retaining a decreasing transverse epsilon-response. The p03 direction behaves differently: its detected zero contour moves rapidly outward and leaves the sampled epsilon-domain, after which the response changes from globally decreasing to mixed and then globally increasing. Deterministic epsilon- and time-thinning controls preserve this p03 orientation-reversal ordering in all tested variants, while p01/p02 remain non-reversing.
A predeclared cone-inspired coordinate motivated by the 2026 OpenAI forced Navier--Stokes construction does not collapse the three B19 directions. This comparison is structural only.
Local-neighborhood robustness diagnostic for the B19 boundary-core channel classes. Class retention is a finite synthetic-family result, not a universal Navier--Stokes classification.
B19 is limited to the stated reduced model and constructed synthetic divergence-free vorticity families. It does not establish finite-time Navier--Stokes blow-up, a singularity criterion, a regularity criterion, a global invariant separatrix, a universal invariant manifold, a universal separatrix, or reproduction/validation of the OpenAI theorem.
Integrated record v1.1: https://zenodo.org/records/23427540
Historical v1: https://zenodo.org/records/22726848
Finite-time response follow-up v1.1: https://zenodo.org/records/23427904
Historical follow-up v1.0: https://zenodo.org/records/22769513
Author: Jun Lucis
Version 1.1 is published and publicly re-downloaded. The complete ZIP is 69,687,332 bytes, 587 members and 586 internal SHA-256 checks, all passing. SHA-256: 326bb889d33fd0c4ae33e2a1faab28ec07f947e89b5a93f02ffe6d00befd06b6.
Original scientific numbers, both tables, all four original figure rasters and formal classifications are preserved. The revised 14-page manuscript clarifies the Fourier/RK4 implementation, sampled trapezoidal balance integral, filter/spectral controls, shared seed, retrospective information, descriptive transfer screens and coarse-map directional comparisons. The historical 21 scalar candidates produce 20 finite score rows and 18 eligible transfer summaries. The 27 mapped rows include 25 evolved cases with a common seed shared by ray folds. These are internal constructed-family tests.
All 27 notebook candidates and 458 recovered result files are in the complete archive. Six later B19.21C files co-located in a source folder are provenance only, outside the integrated B19.0-20 evidence. The Japanese v0.6 PDF is an earlier draft reference translation. Original notebooks retain historical errors, interruptions, Colab paths and checkpoint dependencies.
Assessment: Basically reproducible from archived methods and saved outputs; independent rerun audit not completed. No new ODE/PDE trajectories were generated. The 1,457 saved-data check groups cover 1,182,025 numeric or label comparisons, including repeated checkpoint/input-copy checks rather than independent samples.
- Japanese audit report
- Published archive verification
- Recovered definitions and saved-result verifier
The B19.21-22 follow-up is separate from the integrated CP24 audit; its subsequent CP25 audit is documented below.
B19.21-22 Version 1.1 is published as one complete ZIP. The public redownload is byte-identical to the frozen archive: 25,020,630 bytes, 279 members, CRC and 278 internal SHA-256 hashes all pass. SHA-256: 5f921f90f450e1adfd84a78e9ececf1ccd150f3c849c4d9980356348af2e8332.
The clarified 14-page English manuscript preserves all scientific numbers, both original tables, all four original figure rasters and formal claim statuses. The Figure 1 pixels are unchanged; its caption correctly notes that every displayed T=0.010 sample is negative and the reference roots lie below the displayed epsilon ranges. The implementation, saved-sample integration, shared-history lineage, finite-domain secants/roots, deterministic thinning and historical recovery computations are distinguished explicitly.
The archive includes 18 recovered notebook candidates, 98 recovered Drive result files, immutable original public materials, seven extracted stage packages and 258 unchanged definitions in 10 namespaces. All 132 historical manifest checks pass. B19.21-A/B source notebooks are not separately recovered; archived tables support the documented algebraic checks. Original interruptions, Colab paths, duplicate helpers and checkpoints remain visible. Japanese v1.0 is an earlier reference, not a v1.1 translation.
Saved-result recomputation passes 2,100 check groups / 85,045 numeric or label comparisons, including shared and overlapping checks, not independent observations. No new ODE/PDE trajectories are generated. D/E/F reuse 38 saved scalar-diagnostic histories. Historical recovery checks and deterministic thinning do not establish independent solver, continuum or external validation.
Assessment: Basically reproducible at the archived methods and saved-output level; independent end-to-end rerun audit not completed. All original formal claim statuses are retained.