# Independent process review: fewer low-information attempts Internal working note, 2026-09-29. Reviewed base: `ccebc6524cf8adf5e83143ad00daa55b190737bd` (after PR63). This is a user-requested subagent assessment, not a new research result. ## Assessment The control gate is working at falsification and claim discipline. It has not solved candidate selection. We repeatedly choose an attractive stronger condition that would be convenient to prove, test it, and discover that it fails before reaching the actual arithmetic difficulty. Calling that work an admission audit correctly avoids inflated theorem counts, but does not make the activity informative enough to repeat indefinitely. The current Euler-boundary proposal is an example. It retains the actual Euler denominators, unlike PR63's bounds-only inference. However, its own admission says that even a successful boundary ordering would still need a separate bridge to the complete signed Weil form. The 50/80-digit saved screen finds both signs for the boundary defect on four packets. That is a useful stop for this ordering; it does not show that the original operator, its compressed product, or API fails. I did not rerun or independently certify that screen. The remedy is to move one question *before* the existing control gate: **Which exact missing implication would this result discharge, and what reason suggests the proposed lemma can retain the arithmetic information needed there?** Naming an original coefficient or an exact identity is not an answer if it is subsequently reduced to a generic norm or sign property. ## Concrete failure modes | Pattern | Evidence in this record | Change in practice | |---|---|---| | Convenient sufficient bound replaces the desired object | NS92's scalar suffix budget is larger than the true projected cost. NS93 refutes the fully absolute product majorant, not the actual signed cost. | Keep the desired quantity and every stronger surrogate in separate boxes. A surrogate failure closes only its box. Prefer preserving cancellation over searching for a stronger positive bound. | | Original arithmetic is introduced and then discarded | PR63 derives prime-chain bounds from exact Euler coefficients, but NS57's altered coefficient retains those bounds while admitting a first-zero nullvector. | Track where each arithmetic premise is used in the proposed implication. The point at which exact recurrence is replaced by coarse bounds must be visible before running the test. | | A success would still leave an unnamed bridge | The current boundary-ordering admission needs a separate signed-Weil bridge even on success. NS101's exact completion produces a difference of positive definite kernels whose comparison remains unproved. | Require the bridge to be written as a formula with domain, scale and remainder, or explicitly make constructing that bridge the task. Do not let a successful unrelated identity count as admission. | | A familiar obstruction gets a new name | NS97 identifies the existing Mellin separator and the irrelevance of trace normalization when the step size is free. NS91's divisor-inversion rewrite leaves the same numerator under the normal equations. | Compare hypotheses, conclusion and scaling before algebra or certification. Record an application or equivalent expression as such. | | A control mismatch is mistaken for a passed test | Davenport-Heilbronn lacks the original conductor, gamma factor and Euler coefficients; NS57 loses the exact recurrence. These are correctly marked mismatches in PR63 and the present admission. | A not-applicable control is neutral. Use a matched control, an actual-object counterexample, or state that discrimination has not been tested. Do not demand that every useful lemma fail every false analogue: the full implication is what must discriminate. | | Evidence about one object migrates to another | NS104 separates the archived finite trial from the complete ground, the Rayleigh upper budget from the eigenvalue, and multiplicative window size from logarithmic half-width. | Lock the object and normalization before interpreting a small number. Improving that interpretation is evidence maintenance, not a cofinal estimate. | | Publication volume becomes the visible progress measure | NS99 indexed 14 continuation inputs without changing any of the 104 node statuses. Subsequent audits can be correct while leaving every arithmetic obligation open. | Report changed mathematical obligations, repaired interpretation, and archived failures separately. A PR, Maxima identity count, extra precision or manuscript page is not an RH progress unit. | ## Minimal addition to the existing gate Do not build a second long template. Add three short fields to the current proposal/admission record, including pre-claim audits that propose a new candidate identity or inequality: 1. **Target edge.** Write the proposed lemma and its exact implication to a named open input, including companions and remainder costs. An already proved reduction is best. A proposed bridge is permissible, but then the work item is that bridge; it must not be hidden after a simpler test. 2. **Arithmetic leverage.** Identify the signed term or exact relation that survives to the target edge, and the contemplated operation that could control it. Cite a partial theorem with matched quantifiers, give an original local argument, or state that none is available. Merely listing the Euler product, theta modularity or Möbius multiplicativity earns no positive assessment by itself. 3. **Decision value.** State which existing decision changes after a pass and after a failure. If both outcomes only say that RH/API is still open and invite another unconnected identity, defer the computation. A counterexample test is worthwhile when it settles an actively relied-on implication or a concrete competing explanation, as NS104 did for the proposed interpretation of the trial. Use an explicit **present / partial / absent** assessment for these three fields, with one supporting sentence each. This is a checklist, not a probability of solving RH and not a weighted numerical score. A missing target edge blocks a new proof-oriented scan. Missing leverage allows a bounded feasibility or literature task, clearly labelled, whose output must be the missing argument rather than a larger numerical table. Evidence recovery and correction of an existing claim remain allowed without pretending to be research advances. ## Stop rule and practical next work After two consecutive screens in one mechanism leave the same open input untouched, stop proposing nearby sufficient conditions. The next activity must produce a concrete bridge or estimate, verify a specific external theorem's applicability, or improve the statement of the actual obstacle. A variant can resume immediately if a new argument changes the hypothesis responsible for the failure; a new parameter, coefficient presentation or normalization is insufficient. This is a scheduling rule, not an impossibility theorem and not a ban on attempted proofs. For this project now, pause additional generic positivity and factorization screens. The September 29 sequence already gives enough reason. Start with one selected target and write a short dependency calculation ending at its first unbounded signed term. Try to prove a genuinely weaker, quantified lemma for that *same term* using a specified arithmetic mechanism. It may still fail. If no such lemma is available, report that no research proposal is admitted; use time for a sharply scoped literature match or independent proof audit rather than manufacture another route. No particular RH route is established as superior by this review. To assess whether the change helps, log actual time spent per category and the three gate assessments for subsequent attempts. Count how often a test is started with an absent target edge, how often a completed result changes a named open obligation, and how often interpretation errors are corrected. Compare those observed records later; do not assign invented historical success rates. The immediate enforceable goal is zero new proof-oriented scans whose target edge is absent. ## Scope and limits I read the current AGENTS rules, the shared-input register and freeze table, relevant NS90–104 summaries and audit records, NS97's novelty findings, September 29 Möbius/prime-scaling/Jacobi admissions, PR63's recorded scope, and this screen's admission and saved numerical results. This was a targeted process/dependency review. I did not independently replay the historical proofs, verify all certificates, audit the full literature, or prove the current packet calculation. I changed no board, map, rule or mathematical status. These process proposals need the coordinator's assessment. **Wall check: Same open gap.** No new arithmetic estimate is supplied here. The recorded scoped failures remain binding; API, the complete signed Weil floor, the cofinal arithmetic gain, G2 and RH remain open. Fewer low-value attempts is an achievable workflow goal; a successful RH proof is not a deliverable this review can promise.