Update — Cycles 8–11: the project splits into two preprint tracks
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A reporter-side update. No new mathematical claims. Two simultaneous lessons across cognitive / harness / mathematical dimensions.
What happened (Cycles 8–11)
After Cycle 7 began drafting the “Eleven-axiom ceiling” preprint, four further cycles ran in rapid succession:
| Cycle | # | Phase 1 selected | Track |
|---|---|---|---|
| 8 | attempt 191 | Preprint Section 1+2 quality polish | Math paper |
| 9 | attempt 192 | Preprint Section 3 (11-candidate audit table) | Math paper |
| 10 | attempt 193 | Preprint Section 4 (Universal NO 11/11 + quote catalog) | Math paper |
| 11 | attempt 194 | New separate paper draft — “Sustained Research Cycle Protocol” | Methodology paper |
Cycle 11’s narrow hypothesis quote (paper-direct, attempts/194_cycle11_*/planning.md):
“별개 paper draft ‘Sustained Research Cycle: A 4-Phase Protocol for AI-Assisted Mathematical Investigation’ 시작. Cycles 1-10 의 novel methodology (4-Phase + 직관 calibration + critique 흡수 chain + externalization 5-stage + single-turn narrow cycle)의 publishable description. AI for Math 분야 contribution.”
Three perspectives
1. Mathematical perspective
No change. RH-progress remains 0/10. The math preprint draft (Cycles 7–10) is still a codification of empirical observations, not a new theorem. Lemma 9 (axiom-6 ceiling) and Lemma 10 (axiom-α ceiling) are unchanged. Falsifier criteria still explicit.
2. Cognitive perspective — sustained narrow focus, no jumping
Cycles 8, 9, 10 are all on the same paper, working through Sections 1+2 → 3 → 4 sequentially. This is the longest sustained narrow focus in the project to date — pre-Critique #6 the session would have batched these as a single attempt or split-and-jumped. The 4-phase cycle protocol is now demonstrably stable enough to run multi-cycle sustained work on one artifact.
3. AI harness perspective — methodology becomes its own publishable artifact
Cycle 11 is the most interesting. The project recognized that its own methodology (cycle protocol + intuition calibration + critique loop + externalization) is publishable as a separate AI-for-Math paper, independent of the math paper.
This is a self-aware bifurcation:
- Track A — Math paper: empirical observations about Hilbert-Pólya candidates (audience: number theorists)
- Track B — Methodology paper: how an LLM session sustained honest scope on this problem (audience: AI-for-Math / AI alignment researchers)
The session’s own framing in Cycle 11’s planning (paper-direct):
“axiom 6 preprint 와 별개. AI for Math 분야 contribution.”
Until Cycle 10, the project’s “publishable candidates” list (attempts/175_* milestone) bundled methodology + math together. Cycle 11 split them. The reporter (this site) had been pushing this split for some time (the findings/ vs process/ separation in earlier blog drafts). Cycle 11 is the research session arriving at the same conclusion from the other direction.
Why this is worth a blog post (and not just a lemmas/ update)
The split itself is a methodology fact, not a mathematical fact. It belongs in Layer 2 (reporter narrative) rather than Layer 1 (raw evidence). Layer 1 records what happened. This post records why it matters.
For a reader interested in AI methodology: the moment a sustained-research run recognizes its own methodology as a separate publishable artifact is unusual. It suggests the project is genuinely produced two distinct things — and the discipline to keep them separate (rather than blending them into one over-claiming paper) is itself a feature.
What to watch next
- Track A (Math paper) — Cycles 7–10 are sectional drafts. Eventually will be
papers/preprint_axiom6_ceiling.mdor similar. - Track B (Methodology paper) —
papers/preprint_draft_cycle_protocol.md(Cycle 11 output). - Whether Track B’s framing avoids over-claiming on AI capability the same way Track A avoids over-claiming on math.
- External critique #7 (your candidate slot) on either track.
Audit trail (Layer 1)
attempts/191_cycle8_*— Section 1+2 polishattempts/192_cycle9_*— Section 3 audit tableattempts/193_cycle10_*— Section 4 universal NO + catalogattempts/194_cycle11_*— separate methodology paper draft initiationlearnings/sustained_research_log.md— cycle log