Scientific prediction and solution-class contract audit

Initial decision: Prototype evidence workflow. Revised dossier, 9 October 2026 Australia/Brisbane. Buyer demand, commercial novelty and profitability are unvalidated.

Research finding

The PDE collection contains global classical existence for a specified relativistic Vlasov–Maxwell class, periodic hard-sphere Boltzmann nonuniqueness, stable blowup for selected high-power defocusing NLS equations on a twelve-dimensional torus, exact halting-event encodings in specially forced Navier–Stokes flows, and interior infinity-harmonic regularity with a nonexplicit exponent. These results show why equation name, solution class, quantifier, regularity, forcing and observation horizon are essential to a software claim.

Problem and buyer

A scientific-computing team adopting research algorithms or preparing a model assurance report needs to explain which guarantees survive its discretization and observed regime. An unsupported statement such as entropy checks imply a unique kinetic trajectory or defocusing implies no blowup can pass through documentation if no one tracks the original theorem's domain. Initial buyer hypotheses are solver vendors and simulation R&D groups with repeated independent model reviews.

What the finding could enable

A scientific software assurance framework can attach explicit prediction contracts to runs: equation and solution class, admissible initial conditions, finite or infinite event horizon, allowed forcing, selected formal scope and numeric evidence. The new research contributes concrete challenging records and version exclusions. The immediate system combines opportunities 001 and 003 with scientific-model adapters; it is not a second general proof registry.

Technical and commercial limits

The family 376 constructions use designed forcing and exact infinite-time events, and do not show ordinary finite-horizon CFD forecasts are impossible. Family 371 is specifically twelve-dimensional with selected arbitrarily large odd powers; the inspected scope does not assert every sufficiently large odd power. Family 363's newer local conservation refinements are outside the older selected scope. Family 377 provides no explicit usable Hölder exponent. This framework can expose missing evidence but cannot supply it.

The new sparse Fourier aliasing reference gives a concrete discretization control. Source multiplication uses an infinite Fourier convolution; a finite circular grid folds frequencies. On u=e^(-ix)+e^(ix), a three-point cubic calculation adds a constant coefficient 2 absent from the exact polynomial. Five points preserve the retained band but lose full reconstruction; seven recover the full cubic. A twelve-dimensional axis fixture tests this operation only, not the source's selected large power or blowup construction.

It accepts physical complex rational Fourier coefficients, up to 12 dimensions, 32 input entries, odd powers at most 15 and bounded band/grid sizes. It caps 200,000 coefficient-pair/folding work units, 4,000 live support entries and 1,024-bit intermediate rationals. Exhaustion returns unknown. A fully materialized complex128 grid would use about 3.9 GB for 5^12 points or 221 GB for 7^12; these are illustrative storage counts, not memory lower bounds on sparse or structured implementations. No FFT, time integrator or continuum error certificate runs.

Minimal architecture

Shared proof registry -> scientific-model manifest -> obligation ledger -> paper/module/version mapping -> run and horizon manifest -> conservation and convergence evidence attachments -> gap report. A finite horizon must include its unit and exact event definition. A proof check and an empirical residual remain distinct evidence types. Permit unknown or contradicted obligations; never promote a self-reported assumption to a certified mathematical property.

Existing alternatives and differentiation

Comparator already compares selected formal theorem statements against a trusted challenge and permitted assumptions. That infrastructure does not by itself connect a production simulation, finite measurements and a continuum theorem. The proposed distinction is the model-to-statement adapter and operational evidence record. It should share storage and verification interfaces with the existing registry rather than duplicate the kernel. Comparator.

Monetization hypothesis

Test an AUD 6,000–15,000 simulation-claim review and an AUD 500–2,000 monthly team integration only for recurring reviews. A hypothetical AUD 9,000 review at 35 expert hours costed at AUD 180/hour leaves AUD 2,700 before integration, maintenance, sales and overhead; at 50 hours there is no contribution. A profitable business requires reusable adapters and repeat customers, which have not been established.

Validation experiment

Create adversarial claim records for a finite noisy inverse experiment, a Boltzmann conservation-only uniqueness assertion, a three-dimensional NLS claim that cites the twelve-dimensional result and an infinite-time particle event framed as a finite-horizon forecast. The audit should expose the scope mismatch while allowing honest records with explicitly unresolved obligations. Have a domain reviewer compare usefulness against an ordinary engineering checklist before a paid pilot is proposed.

The Fourier component passed 110 exact finite controls, including independent direct cubic expansions and budget failures. For a retained coordinate band K and odd power p, N>(p+1)K suffices to avoid folding into that band, while N>2pK suffices for full polynomial reconstruction. These are sufficient support bounds, not necessary conditions for a sparse instance. A useful simulation review should compare the implemented grid/padding convention and numerical error against this finite reference before relying on a continuum guarantee.

Conditions to reject or defer

Reject if users do not make guarantee claims, if source adapters need one-off expert work for every run, or if existing model-review processes already catch the same gaps at lower cost. Defer automatic certification, independent proof checking and numeric error certificates until suitable verified infrastructure exists.

Next concrete action

Use the implemented documentary and Fourier controls to separate source statement coverage, model applicability and finite-run observations. Test incorrect source version, unknown obligation and contradictory horizon records, then reuse the format in opportunities 026 and 027.

Pinned research sources

• Family 362: Global classical solutions of the three-dimensional relativistic Vlasov–Maxwell system.
• Family 362: selected formal scope; not independently checked here.
• Family 363: Nonuniqueness with local conservation for the hard-sphere Boltzmann equation.
• Family 363: selected formal scope; not independently checked here.
• Family 371: Stable self-similar blowup for a supercritical defocusing Schrödinger equation on the torus.
• Family 371: selected formal scope; not independently checked here.
• Family 376: Finite Instructions and Solenoidal Shear Flows.
• Family 376: selected formal scope; not independently checked here.
• Family 377: Uniform Interior $C^{1,\alpha}$ Estimates for Infinity-Harmonic Functions.

The repository statements are treated as source claims. No full proof review, buyer interview or clinical/engineering certification has been completed.