riemann

Geometry construction swarm and local-model pilot

2026-09-29. Construction and pipeline calibration audit, not an RH result. Reviewed main: b5bd5fa27c568ab0d2eb31d6155a0d33f3775b76; refreshed again after context handoff, with main unchanged. All 104 conclusion records, all 14 continuation inputs, current instructions/status/board, and the missing-original ledger were reviewed. This is a conclusion/dependency review, not a replay of every historical proof or certificate. Both original-evidence recovery groups remain OPEN.

Wall check: Same open gap. Closest records: OPERATOR-BRIDGES, NS47, NS94/100/101 and PR68. The geometry supplies explicit local objects and candidate specifications; none supplies its route-specific global arithmetic transfer or a new complete signed estimate. Separate operator-construction gaps are not identified with one another or with the NB lower-gain input. All freezes remain unchanged.

Construction work

Three assisting agents drafted separate lanes, followed by cyclic cross-review. They share this task’s context and are not external expert reviewers. The plan predates the drafts.

Lane Actual object / local finding Missing construction
Symplectic/contact Explicit real 4D prime-period blocks; adjusted rates and grading preserve the local weight in 6D and 8D. Composite labels pass the same algebra. Connected assembly without unwanted primitive contributions; analytic global trace, gamma/poles, domains and positivity transfer.
Arithmetic geometry Elliptic products have real dimension four, but prime-power deck maps become identities. A separate adelically metrized family on P1×P1 retains valuations before intersection. Labeled correspondences/global transfer, or a complete test-to-metric map and uniformly bounded remainder under the Hodge hypotheses.
Spectral geometry A real 4D oscillator yields a two-prime partition function. Independent passive prime ports fail contractivity (example 7/6). Coupled completion and the small-shift canonical-system construction in the existing Suzuki program.

The notes contain definitions, conditional implications, source links, explicit missing companions, and precise scope limits. Ordinary self-adjoint log-integer energies are not zeta zeros. Signed local orbit weights are not eigenvalues or positive trace values. No literal application of compact Anosov global trace theory to a noncompact disjoint union is claimed.

Peer review found no outstanding MAJOR issue in these bounded specifications. Two arithmetic-note normalization/domain clarifications and one spectral sign convention were corrected before publication. This is limited agent review, not a global proof audit or novelty assessment.

Local computation

The runner connects to existing local OpenAI-compatible services and replays bounded, explicitly coded exact checks. It never executes model text.

The pre-run protocol fixes 165 deterministic fixtures, not distinct candidate inventions. The first exact run is preserved. Review caught two minor implementation issues: a floating square-root bound in primality testing, and an unconditional support-fixture success flag. They were corrected with integer isqrt and expected-outcome comparisons. The corrected run reproduces all 165 intended outcomes; it is authoritative for the exact-arithmetic claim. See review resolution and the appended read-only replay review in symplectic.md.

Davenport–Heilbronn is not an instance of these specified local determinant/deck/Euler-product constructions. That mismatch is recorded, not called a control pass. No generic completed-function positivity inequality is proposed or tested here. NS94/100/101 retain their original scopes.

Local models: completed, stopped, no candidate admitted

The pilot used an already running qwen3.8-27b service for three proposals and three critiques, then the already installed llama3.1:8b for three audits of those critiques. All nine inference requests returned successfully. An earlier short-hostname configuration produced three validation failures before any inference; the guard was retained and a verified private address used instead. Hardware discovery is operational context, not a public research measurement or model benchmark.

The sanitized transcripts, measured usage summary, and mathematical audit are the evidence. Endpoint addresses are omitted from public transcripts; raw records remain local. All three proposals recycled the supplied contact-block template. None was admitted for computation. Critics also made errors, and the second model often repeated them. Model agreement and HTTP success establish no mathematical correctness.

The completed runs used the original prompts stored with each response. Lane-specific construction briefs and more precise reviewer instructions were added afterward. Their effect is unvalidated; no further inference or unattended batch was started. The second-model protocol bounds that calibration phase explicitly.

Next decision

Do not increase proposal volume yet. First make a construction’s object, domain/action, arithmetic data and full conditional transfer reviewable. For the contact lane, the concrete unresolved assembly issue is preserving the intended prime-period contributions without an uncancelled mixed primitive at log(6). For the metric lane, retaining local valuations does not yet identify the actual signed Weil pairing. For the canonical-system lane, independently passive Euler ports are already rejected; a coupled completed system must be defined before testing it.

These are construction questions, not scheduled computations or new registered rows. A later successful local prerequisite would still not prove RH. Under the repository gate, an RH-directed scan cannot start while its bridge remains unspecified.

Validation and publication scope

24 regression tests pass, including local HTTP/error/auth behavior, control distinctions and rejection of incomplete proposals. Pyright: zero errors/warnings on the touched Python. The standard manuscript build reports its unchanged targets up to date, 358 pages, zero undefined/duplicate references. No manuscript content or historical scientific evidence is changed.

The root README/board and OPERATOR-BRIDGES scope/source entry point here. All 104 node records, 14 input demands and freeze conditions are preserved. No manuscript version/tag, new NS row, thaw, new arithmetic estimate or claim of publication readiness. See validation.json and sha256.json for the final integrity record. HTML was checked structurally. The default-browser open command failed to find a compatible application; a Codex file-panel open request returned queued. No successful rendered or screenshot-based layout review is claimed.