# Route triage — independent subagent assessment Reviewed base: `ccebc6524cf8adf5e83143ad00daa55b190737bd` (PR #63 merged). Classification: strategy and dependency assessment; no new computation, proof audit, arithmetic estimate, or research admission. ## Decision **No new RH route is admitted on the evidence currently available.** I found no proposed next research task that combines both (i) a complete implication to one of the named missing inputs and (ii) a plausible, independently supplied estimate at the required scale. This is a statement about the inspected proposals, not an impossibility claim about RH or the fourteen input groups. **Wall check: Same open gap.** KERNEL-API still needs a full-window arithmetic injectivity argument; MOBIUS-COST still needs a signed projected cost estimate and its separate compatible margin; ZERO-GEOMETRY still needs an original-arithmetic sign mechanism. No changed coordinates or positive-factor identity supplies those inputs. Existing scoped closures are preserved; an open estimate is not relabeled a proved wall. The next action I recommend is a **targeted independent validation of the NS57 first-zero control**, whose conclusion is now being used to reject candidate implications. That is validation of a dependency, not a new RH research route. Its information value is whether an actual gate dependency is reliable, rather than whether another sufficient positivity statement fails. ## Three choices compared | Choice | Complete implication and missing input | Independent source available? | Decision | | --- | --- | --- | --- | | Another Euler/API identity | NS51 gives the sign-continuation route if actual full-window API is proved. NS58's homogeneous boundary identity is exactly the original null equation. PR #63 excludes chain-bounds-only exclusion, while retaining exact recurrences requires genuinely more information. | Exact coefficients and radical identities are available, but no estimate converting them into injectivity has been supplied. “Use the exact recurrence” is not that estimate. | Do not claim a new research row. A proposed identity first needs an explicit inequality and the place where its sign is obtained. | | Another direct Möbius cancellation transfer | NS93 gives a complete sufficient implication from bounded averaged signed cost **and** a compatible positive averaged numerator. A cost result alone is insufficient. | The inspected published cancellation theorems supply real arithmetic information but not the required changing-weight, growing-shift transfer or energy rate. The September 29 transfer audit already identifies these mismatches. | Do not repeat the same theorem substitution. Reopen only for a stated stronger theorem or a proved quantitative transfer lemma. A weaker cancellation theorem can be worthwhile on its own, but is not the missing RH estimate. | | Independently reconstruct NS57's first-zero control | Total near-radicals plus a fixed negative bounded perturbation give a negative compact test; small-window positivity, a common complete form domain, compact resolvent, and continuity give a finite first-zero nullvector. This is a complete conditional chain in the archive. | Exact source statements and proofs are archived. NS57 explicitly records author-only review; the upstream v1.36 result already has an independent adversarial review. | Preferred bounded next action. Validate the new dependency link; do not repeat all upstream proofs without a concrete discrepancy. | For the literature comparison, I reopened the primary statements rather than relying only on the earlier report. Tao's Theorem 1.3 fixes distinct affine forms, uses bounded multiplicative functions and a quantified non-pretentiousness condition, and permits a threshold depending on the forms and error. Corollary 1.5 requires a logarithmic interval ratio tending to infinity. It does not state the uniform weighted growing-shift result needed here. [Primary paper, Theorem 1.3 and Corollary 1.5](https://arxiv.org/html/1509.05422v4). Matomäki–Radziwiłł Theorem 1 treats real multiplicative functions bounded by one, a fixed interval length `2 <= h <= X`, and an exceptional set of starting points. Theorem 3 gives a mean-square comparison for integers in its specified prime-factor set, with its stated parameter restrictions and error. These do not directly give bounded energy for the variable-length suffixes in NS92. The existing normalization is `S_N = N e_N`: qualitative `e_N -> 0` does not bound the required means of `2^j e_(2^j)`. [Primary paper, Theorems 1 and 3](https://arxiv.org/html/1501.04585v4). These are scope checks of named statements, not a claim to have surveyed all later work or ruled out adapting the methods. ## One bounded next action Independently reconstruct only the logical dependency needed by PR #63: NS57 with the explicit nonzero change at `n=2`, through existence of its complete nonnegative first-zero window. Use the actual ordinary `L^2` normalization, both poles, every prime shift, both parity sectors, and the complete domain. Audit these four links: 1. A negative direction of the bounded translation perturbation is detected by a **fixed** finite near-radical combination before the window grows. 2. Its cutoff belongs to the required operator domain and the complete operator residual tends to zero; no finite-prefix residual is substituted. 3. Small-window positivity and continuity of the lowest eigenvalue survive prime-entry points. Strong continuity of compressed shifts alone must be combined with compactness and the common reference form as claimed. 4. The finite zero is an attained eigenvalue, with the stated parity and endpoint-support conclusions. Its existence must not be mistaken for a bounded-floor obstruction or for a numerical threshold. **Success:** a separately derived, dependency-linked argument validates all four links using the archived hypotheses. Record exactly which earlier lemmas were checked and which remain inherited. The change is independent validation of a reused control; no group thaws and RH has not advanced. **Failure:** identify a specific missing hypothesis, domain step, or unjustified limit and mark precisely the dependent uses for correction. Do not infer that original API becomes true or that the rejected shortcut works. If the issue can be repaired, record the added hypothesis explicitly. **Stop:** after this one dependency is assessed, either publish the findings or record an unresolved dependency. Do not turn the audit into another search for positive factors, a new family of finite windows, or a broad re-proof of the repository. ## How to encounter fewer avoidable walls The recurring selection error is choosing an attractive representation before identifying a source for the estimate it would need. A failed control is useful, but repeatedly generating easy-to-screen reformulations has diminishing information value. The proposal gate should be used as a selection mechanism, not merely as a reporting form after an idea is chosen. For the next actual research proposal, require two short items before any scan: the quantified inequality sufficient for the named input, and the independent theorem or elementary mechanism expected to establish it. Include a units/scaling check and every companion estimate. If the second item is just the target with a new name, do not start that research task. An estimate weaker than the RH target may be accepted as a standalone arithmetic theorem if its own value and limits are stated. It should not be advertised as progress toward RH without a demonstrated implication. ## Review scope and limits Read the 104 node conclusions, statuses and recorded obstructions, all 14 continuation demands, current instructions/README/board and missing-evidence ledger, NS57/58, NS92/93/98, NS100/101, the September 29 transfer audit, and PR #63's archived report and validation record. Checked the v1.36 source and its review record to avoid falsely describing it as unreviewed. NS57's `validation.json` and integration report explicitly disclaim independent review. Both historical missing-original groups remain open. No historical certificate was replayed, no new control was run, no original proof is certified by this strategy note, and no manuscript or research-map status is changed. This is an independent assessment by a separate agent, not external expert review or independent numerical replication.