Target: the standard Riemann Hypothesis, every zero of zeta in 0 < Re(s) < 1 has Re(s) = 1/2. Proof and disproof are equally acceptable. This checkpoint explores the central logarithmic moment route. It does not replace that target with finite matrix positivity.
Scope: this directory, its case-log entry, and generated index if changed. No paid services, extra agents, recurring jobs, or edits to core mathematics. Use the existing local Python environment. Source base: origin/main 783307c8. The session-list tool is unavailable in this runtime; git worktrees were inspected.
id: central_moments
question: Can theta-integral structure prove all central logarithmic moment matrices positive, or produce a negative witness?
frontier: no all-orders positivity argument has been established in this attempt
proposed_attack: derive the moment recurrence, compare direct derivatives and theta quadrature, and challenge positivity transfer with exact controls
dead_routes:
- finite positive matrices alone do not imply the infinite family
- prior concavity-only theta shortcuts do not supply real-rootedness
required_oracles:
- exact rational arithmetic for control matrices
- independent derivative and quadrature evaluations
- ordinary proof with explicit dependencies and external review still pending
kill_conditions:
- a positive symmetric measure with nonreal transform zeros passes the proposed finite sufficiency test
- independent numerical routes disagree beyond their stated precision target
agents_may:
- derive identities and bounds
- run bounded local experiments
- preserve unresolved obligations
agents_may_not:
- assume RH or the desired infinite positivity
- claim novelty from an incomplete literature search
- promote finite numerical signs into a uniform theorem