# A proposed route that did not meet the assumptions

An agent was asked to check whether three published fourth-moment statements supplied an estimate for the actual expression under investigation. It found a concrete mismatch: squaring the chosen auxiliary polynomial made its effective length too large for the relevant useful ranges. One inspected input also required an endpoint condition that the chosen weight did not satisfy.

The reviewer checked the actual expression, not merely a similarly named theorem. Substituting the unsquared polynomial would have produced a different integral. This prevented an invalid direct application from being carried forward as a proof step.

The coordinator retained the failed applicability finding. The recorded cycle then selected a separate, precisely stated sign conjecture found in the primary-source investigation. That smaller target led to the written Hardy-sign argument.

The negative finding is narrow: the three inspected statements did not supply the requested estimate. It did not prove that such an estimate is impossible or exclude every other approach. Neither this discarded route nor the later auxiliary result proves RH.

Source provenance: the applicability audit was frozen on September 13, 2026 at 10:41:45 UTC; its acceptance and the cycle summary were committed in `2cd029b338ed03661ce46f667af875e6652b0681`. Exact source identifiers and hashes are in the bundle manifest and coordination evidence record. This public summary omits internal routing details.