12. Strategy reset: arithmetic estimates and closure
STATUS: RIEMANN HYPOTHESIS OPEN
Recorded 2026-09-30. Date of the recorded report; individual start and finish times are not reconstructed.
Starting idea
This was an inventory rather than a new proof route. It asked whether existing bilinear, short-interval, correlation or causal-closure estimates already supplied the missing pointwise bound.
What was tested
The audit distinguished pointwise estimates, almost-all statements, logarithmic averages and shift averages. It checked the fixed Gaussian window, sliding derivative energies and the arithmetic delay equations.
What survived
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Absolute-convergence identities and the unique Möbius inverse in the specified past-decaying class were fixed.
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Local Sobolev control can turn uniform sliding H¹ energy bounds into pointwise bounds. The missing requirement is their quantitative, uniform arithmetic estimate; averages are not categorically incapable of doing this.
What failed or remains unproved
Known average correlation conclusions do not supply square-root-scale control of every readout. Causal uniqueness does not imply forward stability. Shrinking the Gaussian width with the observation point can make an all-positive sum bounded, so it changes the question instead of proving cancellation.
Why the work moved on
No next route followed automatically from this inventory. A later, separately requested track tested an arithmetic restoring-force interpretation.
Current scope
Three proposed mechanisms were not justified. The audit did not claim that all mathematical strategies were exhausted.
“Proved” here refers to the stated mathematical claim in the linked research record. Internal AI-agent checks are scoped checks, not external peer review. Numerical and formal checks have separate limits described in Reproducibility. No priority or novelty claim is made.
Canonical records
- Detailed source report
- Completion report
- Scoped internal audit
- Historical state record
- Recorded validation
The source archive preserves the original Japanese research prose. These links point to publication copies, not third-party paper downloads. The source map explains historical state files and references distinguish publication status from verification.