q1 design

Caller contract

problems/landau-legendre/compute/q1/run_all.sh

The command is network-free, resolves every path relative to itself, builds in a temporary directory, and leaves the checkout unchanged. A caller with a local clone of the OLC repository can additionally authenticate the public-log projection:

problems/landau-legendre/compute/q1/replay_olc.sh /path/to/olc

Modules and evidence boundaries

• make_rh_certificate.py creates exact rational logarithm enclosures. verify_rh_certificate.py independently reconstructs them, and verify_rh_float.c checks the two signs through a separate long double implementation. The exact Python check is authoritative. The surrounding theorem still cites the RH interval theorem and the published finite Oppermann computation.
• audit_olc.py reads tracked Git blobs from a pinned upstream commit. It projects cumulative worker rows into certs/olc_rows.tsv.gz and records their provenance and union coverage in certs/olc_public_audit.json. verify_olc_audit.py can check the projection offline. Only replay_olc.sh authenticates it against upstream.
• generate_edge.rs finds the least prime in both Oppermann halves for the last 100,000 square intervals below $2^{64}$. verify_edge.py independently rechecks every earlier candidate with the first twelve prime Miller--Rabin bases. make_edge_summary.py derives the certificate hash and exact near-miss rankings.
• verify_gap_row.py replays one published maximal-gap row with the same deterministic range. It does not claim to rescan the full source table.

Invariants

1. The RH constants reduce to $\alpha=8901/4000$, $\delta/\alpha=901/8901$, and $44/(25\alpha)=7040/8901$.
2. The exact overlap margin and the derivative margin are positive. The analytic side includes the splice point; the finite side covers the strict complement.
3. OLC selects only tracked blobs matching ^(bigdawg|phi)/data[^/]*/[^/]+\.out$. Counters are differenced in file order. A nonzero upstream countfails means a fallback was used, not that an Oppermann interval failed.
4. OLC coverage is the union of completed half-open integer ranges. Its four public-log holes do not revise the paper's result.
5. Slice endpoints use 128-bit or arbitrary-precision arithmetic. Every witness is strictly inside its half, prime, and the least prime after the left endpoint. Rankings compare exact offset-to-width ratios.

This design uses the stronger evidence boundary from arena candidate A, with candidate B's reduced constants, splice checklist, standard-library C diagnostic, and stricter parser accounting.