RH-W-07: Multi-Prime Support Chamber Compiler

Advanced from a single n=2 coupling to a 9-dimensional real Weil interval matrix across five von Mangoldt layers: 2,3,4,5,7 — the full translation support window compiles a band-pass activation graph of prime powers "entering and leaving" (at the 6th lag, 2 has left the window, while 3 and 4 are still inside), and uses four rational integer witnesses to individually prove that the same direction flips from negative to positive when 2, 3, 4, and 5 are added.

RH_CLAIM = False — The claimed status output by the verifier within the package itself, reproduced here as-is. "This 9-dimensional subspace being positive definite ⇏ RH"; RH cannot be deduced backward from a positive finite matrix, and no strict sign flip was found in this round.

Connections

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

Belongs toResearch Starting Point v1.0 · Multi-Prime Chamber Compiler

Previous PackageRH-W-06: First Prime Activation and Arithmetic Support Chambers

Next PackageRH-W-08: Chamber Search and Strict Refinement

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"What truly needs to be compiled is the complete translated support window, not a single radius. As the correlation window moves along the real axis, a certain log p^k will enter and eventually leave again. This gives the prime-power activation graph a band-pass property, rather than a low-pass structure where 'the larger the support, the more all old primes are permanently retained.'" — Excerpt from Section 1 of Document 01 in this package.

GAP Ledger

From RH-W-07_subgaps_v0.1.csv within the package; the status and dependencies are recorded by the package itself, not my retrospective judgments.

Prime-power Activation Map

Sourced from prime_power_activation_graph.csv within the package — detailing which prime powers enter or leave the correlation support window across nine lags, reproduced row by row from the original data.

Reproduce

9-dimensional multi-prime matrix construction → purely rational exact verifier:

python build_multiprime_chamber.py
python verify_multiprime_certificate.py

01 · Multi-Prime Support Chamber Compiler

Main document — Why one cannot only look at the maximum support radius, fixed 9-dimensional B-spline dictionary, compiled prime-power activation map, sparse arithmetic graph decomposition, second engineering revision of the Archimedean tail bound, 9-dimensional exact positive definite certificate, and four ablation sign-flip witnesses.

02 · Certificate Architecture and GAP Update

Four-layer trust architecture of L0 (Exploration) / L1 (Interval Generation) / L2 (Exact Verifier) / L3 (Formalization, not yet complete), and the engineering rationale for fixing rational grid midpoints.

Verification Output

Sourced from VALIDATION.txt within the package, reproduced line by line — nine lag intervals, activation graphs, positive-definite margins, and four sign-flipping witnesses.

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