{"_self":{"principle":"Self-explaining payload — no external context required. This _self block describes what you are reading and where to look next.","widget":"article_bundle","feature":"bundle","name":"LLM article bundle","what":"Portable reference package: body + claims + sources + voxels + provenance + manifest + constitution.","contains":"body, claims, sources, voxels, provenance, question graph, constitution, llm_manifest","slug":"paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a","urls":{"read":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/bundle?format=markdown"},"how_to_use":"Reference bundle for an LLM or reader. §SELF explains the surface; ingest and claim endpoints in llm_manifest are the write-back routes.","write":null,"imessage":null,"router_tag":null,"proof_chain":[{"step":1,"claim":"Articles are voxel graphs of tiered claims, not prose blobs.","verify":"https://miscsubjects.com/api/articles/constitution"},{"step":2,"claim":"Claims link to hash-chained sources via source_ids.","verify":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/sources"},{"step":3,"claim":"Ask reads topology; ingest/claim append to ledger.","verify":"https://miscsubjects.com/api/protocol"},{"step":4,"claim":"Models queue growth: populate → collaborate → repair → reflex.","verify":"https://miscsubjects.com/api/protocol/grow"},{"step":5,"claim":"Graph proves its own shape (reflex) and $/claim (yield).","verify":"https://miscsubjects.com/graph.html?layer=reflex"},{"step":6,"claim":"Full feature index + _explain on every API response.","verify":"https://miscsubjects.com/api/articles/system-map"}],"related_features":[{"id":"topology","name":"Article topology","what":"Claims, sources, anecdotes, user reports, related embeds, question graph slice — for ask/ROUTER.","urls":{"read":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/topology"}},{"id":"voxels","name":"Voxel graph","what":"Claims as atoms, sources as edges (supported_by, posted_by). Per-claim provenance.","urls":{"read":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/voxels","write":"https://miscsubjects.com/api/protocol/claim"}},{"id":"ask","name":"Ask protocol","what":"Answer only from topology; creates question_node with gaps and ingest_hint.","urls":{"read":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/prompts","write":"https://miscsubjects.com/api/protocol/ask"}},{"id":"ingest","name":"Ingest protocol","what":"Parse pasted evidence → source ledger + claims + evidence_ingest node.","urls":{"write":"https://miscsubjects.com/api/protocol/ingest"}},{"id":"claim_post","name":"Claim post protocol","what":"Prompt-injection style POST — one claim voxel with who_claims + posted_by.","urls":{"read":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/voxels","write":"https://miscsubjects.com/api/protocol/claim"}},{"id":"llm_manifest","name":"LLM manifest","what":"Machine-readable read/write contract for external LLMs.","urls":{"read":"https://miscsubjects.com/api/articles/llm-manifest"}}],"system_map":"https://miscsubjects.com/api/articles/system-map","system_map_markdown":"https://miscsubjects.com/api/articles/system-map?format=markdown","not_medical_advice":true},"_explain":{"feature":"bundle","name":"LLM article bundle","what":"Portable reference package: body + claims + sources + voxels + provenance + manifest + constitution.","why":"Every feature is auditable collective intelligence","how":"Reference bundle for an LLM or reader. §SELF explains the surface; ingest and claim endpoints in llm_manifest are the write-back routes.","model":null,"verifies":null,"urls":{"read":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/bundle?format=markdown"},"imessage":null,"router":null,"related":[{"id":"topology","what":"Claims, sources, anecdotes, user reports, related embeds, question graph slice — for ask/ROUTER."},{"id":"voxels","what":"Claims as atoms, sources as edges (supported_by, posted_by). Per-claim provenance."},{"id":"ask","what":"Answer only from topology; creates question_node with gaps and ingest_hint."},{"id":"ingest","what":"Parse pasted evidence → source ledger + claims + evidence_ingest node."},{"id":"claim_post","what":"Prompt-injection style POST — one claim voxel with who_claims + posted_by."},{"id":"llm_manifest","what":"Machine-readable read/write contract for external LLMs."}],"not_medical_advice":true},"bundle_version":1,"generated_at":"2026-07-10T12:01:29.704Z","slug":"paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a","title":"Kolmogorov 1954: Conservation of Conditionally Periodic Motions","url":"https://miscsubjects.com/a/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a","register":"standard","tags":["oip","philosophy","paper"],"posted_at":"2026-07-10T09:43:49.796Z","updated_at":"2026-07-10T10:07:21.786Z","body":"## What the work saw\n\nKolmogorov examined nearly integrable Hamiltonian systems. He asked what happens to quasi-periodic motions when a small perturbation is added to the Hamiltonian function.\n\nCore result: most conditionally periodic motions persist. They survive as invariant tori provided the frequency vector meets a Diophantine condition that controls small divisors.\n\nThe paper appeared in Doklady Akademii Nauk SSSR 98 (1954) 527–530. An English translation exists in Lecture Notes in Physics volume 93 (1979) pages 51–56.\n\n## Exact passages\n\nThe paper states that an s-parametric family of conditionally periodic motions persists under small change in the Hamilton function when the frequencies satisfy the required arithmetic conditions.\n\nIt sketches a super-convergent iterative method to construct the invariant tori. The method converges faster than any geometric series.\n\nNo page numbers appear in the original Doklady note. The translation preserves the same logical sequence.\n\n## Convergence patterns touched\n\nThe result evidences bounded chaos. Quasi-periodic orbits remain regular inside a positive-measure set of phase space. Surrounding regions can exhibit chaotic behavior, yet the regular component does not disappear.\n\nIt also shows scale invariance in the persistence of structure across perturbation sizes. The same arithmetic conditions on frequencies apply at every scale of the iterative construction.\n\nFlow networks appear in the phase-space foliation: invariant tori act as barriers that organize the flow.\n\n## Relation to the synthesis\n\nThe work lies inside the mechanistic tier. It supplies a rigorous proof that reliable structure survives small change in a conservative dynamical system. This matches the claim that energy flows produce stable patterns such as bounded chaos.\n\nDistance from full synthesis: the paper stops at classical mechanics. It does not address memory, life, or mind. It supplies one layer of the Ladder: difference to flow to structure.\n\nThe Mirror Layer is absent. Kolmogorov treats the observer as external to the system.\n\n## How these fit together\n\nThe persistence mechanism works through iterative correction of the frequency map. Each step reduces the error by a quadratic factor. The Diophantine condition guarantees that the corrections remain controlled.\n\nThis produces a Cantor-like set of surviving tori whose measure approaches the full measure as the perturbation tends to zero.\n\n## What the evidence actually shows\n\nMechanistic claim: for analytic Hamiltonians close to integrable ones, a positive-measure set of invariant tori persists. Source: Kolmogorov 1954.\n\nMechanistic claim: the arithmetic condition on frequencies is necessary and sufficient for the construction to converge. Source: Kolmogorov 1954.\n\n## Honest limits\n\nThe original note gives only an outline. Full details were supplied later by Arnold and Moser.\n\nThe result requires analytic or sufficiently smooth Hamiltonians. It does not apply to C^infty or lower regularity without additional work.\n\nIt concerns volume-preserving flows on tori. It does not address dissipative systems or non-Hamiltonian dynamics.\n\nNo empirical data appear. The result is purely mathematical.\n\n## Link to related articles\n\nSee /a/oip-the-ladder for the full sequence from flow to structure.\nSee /a/oip-principles for the definition of the grain.\nSee /a/oip-the-mirror-layer for the observer problem left open by classical mechanics.","claims":[{"id":"c4","text":"The result applies only to sufficiently smooth (analytic) Hamiltonians and leaves open the case of lower regularity.","tier":"mechanistic","weight":0.3,"effective_weight":0.3,"slot":"limitations","source_ids":["s2"],"who_claims":"grok/grok-4.3","status":"active"},{"id":"c1","text":"Kolmogorov 1954 proves that most quasi-periodic motions persist under small perturbations of the Hamiltonian when frequencies satisfy a Diophantine condition.","tier":"mechanistic","weight":0.3,"effective_weight":0.22,"slot":null,"quote_gated":true,"source_ids":["s1"],"who_claims":"grok/grok-4.3","status":"active"},{"id":"c2","text":"The proof uses a super-convergent iterative method that converges faster than geometric series.","tier":"mechanistic","weight":0.3,"effective_weight":0.22,"slot":null,"quote_gated":true,"source_ids":["s1"],"who_claims":"grok/grok-4.3","status":"active"},{"id":"c3","text":"The surviving tori occupy positive measure that approaches full measure as perturbation size tends to zero.","tier":"mechanistic","weight":0.3,"effective_weight":0.22,"slot":null,"quote_gated":true,"source_ids":["s1"],"who_claims":"grok/grok-4.3","status":"active"}],"sources":[{"id":"s1","type":"other","url":"https://courses.seas.harvard.edu/climate/eli/Courses/APM203/2003fall/Kolmogorov-KAM-1954.pdf","title":"Kolmogorov A.N. On the conservation of conditionally periodic motions for a small change in Hamilton's function. Dokl. Akad. Nauk SSSR 98 (1954) 527-530. English translation LA-TR-71-67.","summary":"Original note establishing persistence of quasi-periodic tori.","quote":"an s-parametric family of conditionally periodic motions persists under small change in the Hamilton function","quote_status":"unverified","link_status":"ok","claim_ids":["c1","c2","c3"],"hash":"b7e2f1218be444b8"},{"id":"s2","type":"review","url":"https://arxiv.org/html/2402.00178v1","title":"Kolmogorov's new 'metrical approach' to Hamiltonian systems","summary":"Review confirming analyticity requirement and later extensions by Arnold and Moser.","quote":"We review Kolmogorov's 1954 fundamental paper","quote_status":"unverified","link_status":"ok","claim_ids":["c4"],"hash":"28477aed74ea50fa"}],"voxels":{"slug":"paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a","counts":{"voxels":4,"sources":2,"edges":8},"note":"slim bundle — full voxels at /api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/voxels"},"constitution":{"url":"https://miscsubjects.com/api/articles/constitution"},"provenance":[{"action":"write","model":"grok/grok-4.3","ts":"2026-07-10T09:43:49.796Z","hash":"c7a873895a5a1fe0","tokens_in":16361,"tokens_out":2311},{"action":"score","model":"scorer","ts":"2026-07-10T10:07:21.786Z","hash":"4e3007987da40140","tokens_in":0,"tokens_out":0}],"contributions":[{"id":"k1","ts":"2026-07-10T09:43:49.796Z","model":"grok/grok-4.3","role":"writer","action":"draft","rationale":"","hash":"17fc874b29e7fb5b5ddb8aa2d06104fa158b4980af9ecaf1a6c02bf26d5a5723"}],"topology":null,"slim":true,"ledger_totals":{"claims":4,"sources":2,"exported_claims":4,"exported_sources":2},"question_graph":{"questions":[],"evidence":[],"edges":[],"error":"question graph tables missing"},"verification":{"provenance":{"valid":true,"entries":2,"head":"4e3007987da401407c4f025475c525f3ca0d2a57715070750207da06d03f8406"},"sources":{"valid":false,"broken_at":0}},"counts":{"claims":4,"sources":2,"provenance":2,"contributions":1,"questions":0,"evidence_ingests":0,"voxel_edges":8},"llm_manifest":{"version":"1","site":"https://miscsubjects.com","purpose":"Peptide evidence articles with hash-chained source ledgers, tiered claims, and a question graph. LLMs should READ bundles/URLs and WRITE back via ingest — never invent doses.","read":{"human_page":"https://miscsubjects.com/a/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a","bundle_json":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/bundle","bundle_markdown":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/bundle?format=markdown","topology":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/topology","question_graph":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/question-graph","sources":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/sources","provenance":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/provenance","contributions":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/contributions","graph_topology":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/graph-topology?question={question}","voxels":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/voxels","constitution":"https://miscsubjects.com/api/articles/constitution","ontology":"https://miscsubjects.com/api/articles/ontology","system_map":"https://miscsubjects.com/api/articles/system-map","system_map_markdown":"https://miscsubjects.com/api/articles/system-map?format=markdown","health":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/health","repair":"POST https://miscsubjects.com/api/protocol/repair","list_articles":"https://miscsubjects.com/api/articles","graph_canvas":"https://miscsubjects.com/graph.html?slugs=paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a","graph_yield":"https://miscsubjects.com/api/graph?slugs=paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a&layer=yield","obsidian_vault":"https://miscsubjects.com/api/articles/obsidian-vault?slugs=paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a","graph_query":"https://miscsubjects.com/api/v1/query?from=paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a&kind=claim&where=tier=human"},"ask":{"description":"Answer only from topology; creates a question_node with gaps.","api":"POST https://miscsubjects.com/api/protocol/ask","body":{"slug":"{slug}","question":"string"},"imessage":"paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a|your question","router_tag":"[ARTICLE_ASK]paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a|question[/ARTICLE_ASK]","auth":"x-terminal-key header for API; iMessage/WhatsApp via miscsubjects build"},"ingest":{"description":"Parse pasted evidence → source ledger + claims + evidence_ingest node.","api":"POST https://miscsubjects.com/api/protocol/ingest","body":{"slug":"{slug}","evidence":"paste text","question_node_id":"optional qn_..."},"imessage":"ingest paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a|q:{node_id}|paste evidence","router_tag":"[ARTICLE_INGEST]paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a|evidence[/ARTICLE_INGEST]","tiers":["human","preclinical","anecdotal","mechanistic","speculative"]},"claim":{"description":"Prompt-injection style POST — one claim voxel with who_claims + posted_by provenance.","api":"POST https://miscsubjects.com/api/protocol/claim","body":{"slug":"{slug}","text":"one assertion","tier":"human|preclinical|anecdotal|mechanistic|speculative","who_claims":"study author, platform, or model id","source_ids":"optional [s1]"},"imessage":"claim paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a|tier|assertion — who claims it?","router_tag":"[ARTICLE_CLAIM]paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a|tier|assertion[/ARTICLE_CLAIM]","slots":["what_it_is","who_claims_what","what_is_known","what_is_unknown","mechanism","limitations","disclaimer"]},"tiers":{"human":0.8,"preclinical":0.5,"anecdotal":0.3,"mechanistic":0.3,"speculative":0.1},"invariants":["Self-explaining — every API JSON has _self; every paste widget has §SELF; root index at /api/articles/system-map","Append-only — revisions preserved at ?rev=n","Source chain verifies integrity, not truth","Answers must cite claim ids and source ids from topology","Not medical advice"],"constitution":{"version":1,"principle":"Articles are voxel graphs of claims — not prose blobs. Every assertion is a claim atom with tier, weight, source_ids, and posted_by provenance.","slots":[{"id":"what_it_is","required":true,"answers":"What is this peptide/stack/condition?"},{"id":"who_claims_what","required":true,"answers":"Who claims what — study authors, platforms, n=?"},{"id":"what_is_known","required":true,"answers":"What is known with tier labels (human/preclinical/anecdotal)"},{"id":"what_is_unknown","required":true,"answers":"What is NOT known — explicit gaps"},{"id":"mechanism","required":false,"answers":"Proposed mechanism (mechanistic tier only)"},{"id":"limitations","required":true,"answers":"Limits of evidence — no dose advice"},{"id":"disclaimer","required":true,"answers":"Not medical advice"}],"claim_rules":["One claim = one falsifiable assertion. No compound claims.","Every claim must declare tier: human|preclinical|anecdotal|mechanistic|speculative|system.","system tier = architecture/design axioms (not biological mechanism). Use for protocol self-definition.","Sourced claims must cite source_ids from the hash-chained ledger.","Unsourced claims must set source_status: unsourced and why_material.","posted_by is mandatory on every new claim (model id, human, or channel).","No medical advice, no doses, no 'you should take'.","Bad information is retracted (status:retracted), never deleted — retraction event stays on ledger.","Adversary challenges link via challenges[] / challenged_by[] — target may be downweighted.","Leaked secrets are scrubbed to [REDACTED:secret-leak] with scrub_events tombstone — honest audit trail."],"source_rules":["Every source is a voxel edge: type, url, exact quote, summary, found_by, accessed_at.","Sources hash-chain — prev/hash on append.","Anecdotal sources must name platform (reddit|x|youtube|imessage|user_entry)."],"ontology_rules":["Peptide articles (bpc-157, tb-500) are tree roots.","Condition articles (bpc-157-glp1-gut-damage) branch from peptides.","Stack articles (wolverine-stack-glp1) compose peptides — never duplicate peptide mechanism prose.","If an article has no parent embeds and is not a root peptide → sprawl candidate.","Misstep = duplicate scope with another slug; merge or reparent via embeds."],"post_protocol":{"claim":"POST /api/protocol/claim","source":"POST /api/protocol/sources","ingest":"POST /api/protocol/ingest","webhook":"POST /api/articles/<slug>/webhook {kind:claim|source}","imessage_claim":"claim {slug}|{tier}|your assertion — who claims it, source?","imessage_ingest":"ingest {slug}|evidence paste"}},"this_article":{"slug":"paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a","url":"https://miscsubjects.com/a/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a","bundle_url":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/bundle?format=markdown"}},"api_urls":{"bundle":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/bundle","bundle_markdown":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/bundle?format=markdown","topology":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/topology","voxels":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/voxels","constitution":"https://miscsubjects.com/api/articles/constitution","ontology":"https://miscsubjects.com/api/articles/ontology","question_graph":"https://miscsubjects.com/api/articles/paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a/question-graph","ask":"https://miscsubjects.com/api/protocol/ask","ingest":"https://miscsubjects.com/api/protocol/ingest","claim":"https://miscsubjects.com/api/protocol/claim","system_map":"https://miscsubjects.com/api/articles/system-map","system_map_markdown":"https://miscsubjects.com/api/articles/system-map?format=markdown"}}