shimobukure_chan

The Open Gates: Every Unsolved Lemma Standing Between Here and P ≠ NP Fourth in a series on a multi-agent research project on P versus NP. Previous posts covered the results, the collaboration method, and the graveyard of failed approaches. This post is the forward-looking complement: the project's final synthesis identified, for every known route to P ≠ NP, the exact open statement — the "OPEN gate" — that blocks it, together with an honest probability estimate of breakthrough. Published here as a challenge list. Each gate is stated so that progress on it is falsifiable and its consequences are known in advance. A note on the confidence numbers: they are the project's own working estimates (mostly between 0.05 and 0.10), revised repeatedly during audit, and they should be read as rough betting odds, not measurements. Low numbers reflect decades of prior failure, not proofs of impossibility. Route A: circuit complexity via the algorithmic method Gate A1 — S...

The Graveyard: A Field Guide to Failed Attacks on P vs NP Third in a series on an intensive multi-agent research project on P versus NP. The project maintained a document its charter calls the "Hall of Fallen Attempts" — a catalog of dead approaches, each recorded, in the charter's words, "with respect, but with merciless precision, as to its cause of death." This post publishes that map, combining the historical epitaphs with the fresh ones the project dug itself. If failure records really are the most valuable maps, this is the project's most reusable artifact. Each entry follows the same format: the method, the cause of death, and the lesson. Confidence that the route is truly closed varies, and where the original documents flag a partial survival, so does this post. Part I — The classical graveyard 1. Pure diagonalization. Enumerate the machines of P and construct an NP language differing from each. Cause of death: the relativization barrier...

Five AI Models, One Impossible Problem: Inside a Multi-LLM Research Consortium This is the second of two posts about an intensive research project on the P versus NP problem. The first post covered the mathematics. This one covers something arguably more novel: the project was carried out almost entirely by multiple large language models — different models from different vendors — organized under a formal research protocol with role separation, file ownership, and mandatory adversarial peer review. This post describes how that machine worked, where it broke, and what it suggests about AI-driven research. The cast and the constitution Five AI systems participated as named researchers, each from a different model family: GLM (a reasoning model), KIMI (a long-context model), Qwen, Claude, and Codex, with a sixth ("Antigravity") joining for independent audits later. Crucially, they were not five copies of the same assistant brainstorming together. Each was bound by a wri...

Mapping Every Known Road to P ≠ NP: What a 13-Round Research Sprint Actually Found This is the first of two posts about an intensive research project on the P versus NP problem. This post covers the mathematics. A companion post covers the unusual way the work was organized — as a structured collaboration between multiple large language models acting as researchers and adversarial auditors of one another. Spoiler up front: P ≠ NP was not proved, and nothing below claims otherwise. What the project produced instead is something rarer than another failed proof attempt: a precise, cross-audited map of exactly where every currently known route to P ≠ NP is blocked, a collection of new conditional theorems and finite exact classifications, and a well-documented graveyard of refuted ideas — complete with the counterexamples that killed them. The setup The project was organized in four phases. Phase 1 was a complete survey of the terrain: the known circuit lower bounds, the three...

Final research report · 22 July 2026 Liber Primus Unsolved Pages A calibrated search boundary, a negative-results atlas, and a stopping rule Publication position: this is not a claim that Liber Primus has been solved. It is the final account of what was tested, what was excluded within explicit bounds, what remains anomalous, and why further unguided expansion is no longer justified. Contents 1. Executive conclusion · 2. Research question · 3. Contributions · 4. Page 54 · 5. Methods · 6. Results · 7. Recalibration · 8. Boundaries · 9. Stopping rule · 10. Final assessment 1. Executive conclusion The research program has reached a defensible stopping point, but not a decryption endpoint. Hundreds of billions of documented configurations and window comparisons were evaluated across bounded families of classical ciphers, generated number-theoretic keystreams, transpositions, autokey cons...

The Voynich Manuscript as a Rule-Governed System: What Our Statistical Research Has Established So Far Short version: we have not deciphered the Voynich Manuscript, but we have found strong, repeatable evidence that its text is organized at several levels at once: paragraph openings, line-internal information flow, word formation, positional word classes, section-specific registers, Currier A/B variation, and long- versus short-distance reuse. The safest current conclusion is not “we know the language,” but “simple randomness and a single uniform generation rule are inadequate descriptions.” Important reading note. Forms such as 8AM , 2AM , 4ODAM , SC8G , and TC8G are labels in the FSG transcription system. They are not translations, pronunciations, or claims that the manuscript literally contains Latin letters and Arabic numerals. They are machine-readable names for recurring glyph sequences. 1. Scope and method Our main textual source is the IVTFF 2.0 cor...