RH-W-05: First Real Weil Matrix Rational Interval

Advanced from floating-point candidates to a replayable 2×2 mathematical receipt — using two translated cubic B-splines, deliberately controlling the correlation support to within log2 so that the prime terms analytically resolve to zero, generating the first complete rational interval of a real Riemann zeta Weil matrix, and confirming the strict positive definiteness of the two-dimensional subspace using a small verifier that relies solely on Fraction.

RH_CLAIM = False — The claim status self-reported by the verifier and certificate within the package, reproduced here as is. This is a finite-dimensional local positivity certificate: "Finite-dimensional positivity ⇏ RH".

Connections

Regarding its relationship with other packages, I try to use the words from its own documents, not my interpretation.

Belongs toResearch Starting Point v0.8 · Real Matrix Pipeline

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"What is closed in this round is: real zeta Weil elements → rational interval matrix → exact verifier, within the following restricted scope: two-dimensional; cubic B-spline translation basis; maximum correlation support less than log2; prime terms are therefore zero... The first real Weil matrix has materialized from an abstract formula into a replayable, auditable rational interval object capable of rejecting false claims." — Excerpted from Sections 10 and 13 of Document 01 in this package.

GAP Ledger

From RH-W-05_subgaps_v0.1.csv within the package; the status and next steps are recorded by the package itself, not my retrospective judgment.

Reproduce

Rational interval generator → Small exact verifier → Independent floating-point cross-check:

python build_rigorous_matrix.py
python verify_matrix_certificate.py
python crosscheck_mpmath.py

01 · First Real Weil Matrix Rational Interval

Main Document — Fixed explicit formula, closed convolution of B-spline correlation functions, analytic exclusion of prime terms, tail bounds for Archimedean integrals via six-fold integration by parts, rational envelopes for transcendental constants, itemized interval ledgers, and independent floating-point crosschecks.

02 · Certificates and Trust Boundaries

Three-tier certificate architecture of L0 (mathematical specification) / L1 (rigorous numerical generation) / L2 (small exact verifier), along with a complete list of trust foundations (CPython version, libmpdec version, Decimal.exp contract).

Verification Output

Sourced from VALIDATION.txt (rational interval construction), EXACT_VERIFY.txt (exact verifier), and CROSSCHECK.txt (independent mpmath crosscheck, not entering the proof path) within the package, reproduced line by line.

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