15. A common variational parent?
STATUS: RIEMANN HYPOTHESIS OPEN
Recorded 2026-09-30. Date of the recorded report; individual start and finish times are not reconstructed.
Starting idea
The actual Weil ground state and a prolate proxy both appear near the arithmetic kernel. Could one variational principle force them to agree?
What was tested
The work fixed the pullback Q(Eh), its induced metric E*E, and the difference between the prolate h₀/h₄ zero-integral mixture and a usual concentration ground state. It tested energy excess, residuals and gaps.
What survived
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For a simple ground state with positive gap Δ, Rayleigh excess gives an angle bound controlled by (R_B − e₀)/Δ. Transferring it to Fourier transforms on expanding support also costs a weighted norm factor.
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The known global arithmetic radical is infinite dimensional. Exact radical identities do not make a finite prolate proxy an exact null vector.
What failed or remains unproved
No common-parent identity or sufficient excess-to-gap decay was proved. A near-zero energy cannot select a unique vector from a large radical. A large upper-bound ratio is not a lower bound on actual distance. The finite high-precision diagnostics are not interval certificates or a theorem about all cutoffs.
Why the work moved on
The next track examined how finite cutoffs split that degeneracy and whether rates or path history select a direction.
Current scope
An exact variational dictionary and sufficient estimates retained; full ground comparison remains open.
“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.