Finding 2: Wall #2 ∫E(t)dt unconditional bound — 4/4 universal NO
← 한국어 포스트 전체 · English · 2026-05-02
경험적 관찰, 정리 아님. Finding 1과 동일 logical structure.
Statement
Newman–de Bruijn forward heat flow 관련 4 paper-direct candidates 중, unconditional + constructive + RH-independent ∫_0^Λ E(t)dt bound 미발표.
Source: lemmas/lemma2_wall2_axiom_alpha_ceiling.md.
Audit table
| # | Paper | axiom α strict | Paper-direct anchor |
|---|---|---|---|
| 1 | Polymath15 (de Bruijn–Newman upper) | NO | Λ ≤ 0.22 conditional (3-tool combination, Theorem 1.1). Unconditional bound 미부여. |
| 2 | Rodgers–Tao 2020 (Λ ≥ 0 unconditional) | NO | “far from optimal” (paper §1.5). ∫_{Λ/2}^0 E(t)dt — backward only control. |
| 3 | Platt–Trudgian 2021 | NO | Λ ≤ 0.2 via numerical RH up to H = 3·10¹²; theoretical bound X. |
| 4 | Newman 1976 | NO | Λ ≤ 0 ⟺ RH equivalence. Definition only, abstract. |
4/4 universal axiom α strict NO.
Falsifier search (5+ 인접 분야)
- Bombieri–Lagarias 1999 (Λ ≥ 0 lower bound only) — falsifier 아님
- Selberg method (Wall #3) — 직접 무관, falsifier 아님
- Bourgain–Gamburd–Sarnak expander — heat semigroup 형식 유사, integrated bound 형태 X, falsifier 아님
- Otto’s calculus / Wasserstein gradient flow — 시간 대칭, falsifier 아님
- Concentration compactness — forward control X, falsifier 아님
- Free probability R-transform — Wall #6 axis, falsifier 아님
→ paper-direct no falsifier (5+ 분야).
Specialist Δ (Lemma 7 anchored)
- Tao + Conrey: Polymath15 §6 “this is the limit of the present method” + Iwaniec phrase “extra little tiny bit”
- Tao (hard analysis): Rodgers-Tao 2020 §1.5 “far from optimal” + time-asymmetry essential
- Logician (S9): Lagarias 2002 (RH Π_1) anchor
Caveats
- Empirical NO만 (4/4 + 5 falsifier 분야). Necessary universal NO 미증명.
- 5년 무진전 (Rodgers–Tao 2020 → 2025) empirical fact, obstacle 증명 X.
- ZFC-independence 배제 X.
- Newman 1976 equivalence는 abstract — axiom α의 constructive form이 ZFC에서 증명 가능한지 미정.
Falsifier (lemma 폐기 조건)
다음 4 항목 모두 만족하는 paper:
- Unconditional ∫_0^Λ E(t)dt explicit upper bound — paper-direct quote
- RH 가정 부재 — paper-direct verification
- Constructive form (abstract equivalence X) — paper-direct
- Fine-tuning parameter 부재 — paper-direct
→ lemma 폐기.
Cross-reference: Finding 1과 동일 구조
Lemma 9 (Wall #5, axiom 6) + Lemma 10 (Wall #2, axiom α)는 동일 logical structure, 다른 wall:
- 4-specialist 합의 axiom 정의
- Paper-direct audit table
- Falsifier search across adjacent fields
- 명시 falsifier criterion
- Empirical NO ≠ Necessary NO 경고
Cycle 2의 의도적 “cycle 1 형식 직접 재사용”. 검증된 codification template의 generalizability 증거.
Audit trail (Layer 1)
lemmas/lemma2_wall2_axiom_alpha_ceiling.mdattempts/185_cycle2_*attempts/028_*,106_*,113_*,132_*,161_*,173_*
반박
Unconditional + constructive ∫E(t)dt upper bound paper가 있다면 x2ever.han@gmail.com.
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