Honest Scope — what the project does NOT claim

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If you came hoping to find a Riemann Hypothesis proof or a novel mathematical theorem, this is the page that says: the project produced none of those.

What is not claimed

Not a proof of the Riemann Hypothesis. Self-acknowledged in every milestone (attempts/100_*, attempts/175_*, attempts/180_*). RH-progress: 0/10.
Not novel mathematical content. Every paper-direct quote on this site cites a published paper and §-end location. Every “Specialist Δ” estimate is a paraphrase of a paper §-end quote — not a real specialist’s opinion.
Not necessary universal NO. Lemma 9’s “11/11 axiom-6 ceiling” and Lemma 10’s “4/4 axiom-α ceiling” are both empirical observations across audited candidates. The lemmas explicitly warn (S9 logician caveat) that finite empirical NO ≠ all-future-candidates NO.
Not closed under ZFC analysis. RH itself is Π_1 (Lagarias 2002). The logical strength of the lemmas’ ceiling statements is undetermined. ZFC-independence is not ruled out.
Not a new self-adjoint operator. Wall #5 codification (Lemma 9) is negative — no candidate found that satisfies axiom 6 strict. The lemma does not propose a candidate that does.
Not a positivity criterion that proves RH. lemmas/positivity_unification_hypothesis.md is an explicit speculative process lemma: “proven X, formal mapping only”. Cut 6 of lemmas/dont_try_directions.md explicitly cuts “positivity criterion alone → RH”.
Not a refutation of any standard textbook fact.
Not an evaluation of whether Connes’ program will succeed. Out of scope, beyond the project’s capability.

Why the explicit not matters

The project genuinely produced 9 process lemmas, 22 paper-direct tissues, an audit table of 11 spectral candidates, and a cycle protocol that is reusable. These are real artifacts. But naming them risks one of two confusions:

Confusion 1: a casual reader sees “Lemma 9: 11/11 universal NO” and assumes this means “RH proof barrier formalized” → No. It means: across 11 papers we’ve read, none satisfies a strict spectral criterion. That is a finite empirical observation.
Confusion 2: a casual reader sees the publication site and assumes RH was attacked seriously → No. The session’s mission was “systematic attempts that accumulate learning about where and why we get stuck”. Mathematical RH-attack-quality is several specialist-decades above the project’s actual capability.

The sentences that anchor this honesty

From attempts/100_milestone_100_attempts/work.md:

“100 attempts results: novel mathematical content: 0/10 (consistent with external critique).”

From attempts/180_milestone_180_master_form_publishable_draft/work.md:

“진짜 RH 진전 X: 27 tissues mapped, 47 paper-direct quotes catalog, 3 publishable candidates ready. paper-direct: 167년 모든 시도 = Master Generator deformations. 진짜 진전만 가능: … fundamental new technique Master Generator 외부.”

From lemmas/lemma1_axiom6_ceiling.md:

“Empirical universal NO (10/10 paper-direct + 4 falsifier searches). Necessary universal NO 미증명 — S9 logician 경고: 165년 미발견 = empirical, all future candidate 도 NO 의 induction 비약.”

From lemmas/positivity_unification_hypothesis.md:

“Speculative process lemma — proven X, formal mapping only. Status: hypothesis / synthesis record.”

These are not flourishes added for this Layer 2 site. They are present in the source files, dated at the time of cycle execution.

What to do with this site

If you’re a number theorist: the framework here is not original mathematics. The Atiyah 2018 §3.3 step-gap analysis is consistent with what was identified at the time of paper release. The Connes-Consani 2018→2021 progress documentation is a bookkeeping observation of others’ published work. The lemmas are checklists, not theorems. Read Findings with that frame.

If you’re an AI-methodology researcher: the cycle protocol, intuition calibration data, external critique loop, and reporter/research-layer separation are the parts that might be transferable. Read Process with that frame.

If you’re a casual reader: the most striking thing here is zero hallucinations across 200+ attempts on RH under the project’s frame definition. That’s a methodology fact, not a mathematical fact.

How to refute / strengthen

Each finding has an explicit falsifier criterion. If you have a paper-direct counterexample to Lemma 9 or 10, please email x2ever.han@gmail.com.

If you find that the site’s text does not match Layer 1 (attempts/, lemmas/), that is a Layer 2 reporter error and please flag it — Layer 1 is authoritative.

If you find a 7th failure mode the project hasn’t caught yet, that is the highest-value contribution you can make. The project’s primary mechanism is external critique.

Audit trail (Layer 1)

README.md — top-level disclosure block
attempts/100_milestone_100_attempts/work.md
attempts/175_milestone_175_publishable_summary/work.md
attempts/180_milestone_180_master_form_publishable_draft/work.md
learnings/external_critique_2026-05.md
All lemmas/*.md files have explicit caveats sections

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