Finding 3: Connes–Consani 2018 → 2021 측정 가능 진전
← 한국어 포스트 전체 · English · 2026-05-02
Bookkeeping 관찰. 본 프로젝트가 생산한 게 아니라 기존 Connes–Consani publication chain에서 식별.
Cycle 5에서 정독한 4-paper chain
- 1502.05580 (2016, Adv. Math. 291) — Geometry of the Arithmetic Site
- 1805.10501 (2018, Springer 2020) — Riemann–Roch strategy on the Square of the Scaling Site
- arxiv 2006.13771 (2020) / Selecta Math 2021 — Weil positivity and trace formula at the archimedean place
- 2401.08401 (2024) — Knots, Primes and the Adele Class Space
2018 → 2021 specific progress
2018 paper (1805.10501) page 2 자기 인정:
“the problem, which is still open at this time, has to do with an appropriate definition of the sheaf cohomology (as idempotent monoid) H¹…”
2021 paper (Selecta Math) §1:
“This paper is motivated by the desire to understand the link between the analytic Hilbert space theoretic strategy first proposed in [11], and the geometric approach… The first contribution of this paper is to make explicit the relation between the two approaches, thus overcoming the above problem.”
Theorem 1 (page 3):
“W_∞(g * g) ≥ Tr(ϑ(g) S ϑ(g))”
→ 2018 still-open 문제를 bridge하는 paper-direct positivity inequality.
본 프로젝트 framing에서의 의미
Active program이 25년 stuck X임의 documentation. Incremental paper-direct progress 존재. 본 프로젝트 역할은 monitoring (paper acquisition + paper-direct quotation), 기여 X.
특히: Lemma 9, 10 (Findings 1, 2)이 empirical universal NO를 documents. Lemmas가 underlying approach 죽었다 claim한다고 오해될 수 있는데, Cycle 5의 2021 paper 정독이 그 우려에 counter-weight: post-2018 progress 있음. Lemmas는 empirical-checklist 만, underlying approach dead claim 아님.
Self-acknowledged narrow scope
2021 Theorem 1은 single archimedean place only. Paper §abstract:
“All the ingredients and tools used above make sense in the general semi-local case, where Weil positivity implies RH”
→ general (multi-prime) 경우는 still open. Paper §1: “potential conceptual reason” — ZFC측 증명 미완.
Cycle 4 → 5 cross-mapping (project’s Findings 1, 2)
Cycle 4 (한 cycle 전): “Lemmas 9, 10의 universal NO results = Connes–Consani missing components의 2 manifestations” unification 시도.
Cycle 5 4-paper read 부분 반박:
| Path | Active Continuation | Still-Open Component |
|---|---|---|
| Path 1 (Weil positivity, axiom α / Wall #2) | Connes–Consani 2018→2021 progress (single archimedean) | General semi-local case |
| Path 2 (Wall #1 cohomological transfer / axiom 6 / Wall #5) | Connes–Consani 2014–2024 (10년) | H¹ cohomology on the square (still open per 2018) |
→ 두 paths 모두 Connes–Consani program — 동일 authors, 별개 angles. Cycle 4의 “single source unification”은 너무 강했음; 두 paths는 connected 그러나 identical X.
본 프로젝트의 가장 명확한 self-correction moment 중 하나 — cycle이 자기 직전 cycle 가설 약화.
본 프로젝트가 아닌 것
- Program 성공 여부 평가 X (out of scope, 능력 외)
- 본 프로젝트가 program에 기여 X
- RH 진전 X
Audit trail (Layer 1)
attempts/186_cycle3_*— Cycle 3attempts/187_cycle4_*— Cycle 4 (Cycle 3 partial refutation)attempts/188_cycle5_*— Cycle 5 (Selecta 2021 deep)lemmas/positivity_unification_hypothesis.md—Cycle 3 / 4 / 5 Updatesections
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