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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},"MASTHEAD":{"sorry_status":"planes not merged yet — sorry-status activates after voxel-merge-planes","identity":{"slug":"school-statistical-mechanics-boltzmann-formulation","version":1,"content_hash":"4be4134e06a17351a00d062a7ecd0f11acc225a038a2347d1926a9f0d2c2e45f","thread_head":"genesis","divs":23},"thesis":{"root_claim":"c1","text":"Boltzmann introduced S = k ln W in 1877 as the relation between entropy and the number of microstates.","tier":"mechanistic"},"load_bearing":[{"id":"c3","tier":"mechanistic","status":"active","text":"Boltzmann's framework derives scale-invariant equilibrium distributions from particle statistics."},{"id":"c2","tier":"mechanistic","status":"active","text":"The 1872 H-theorem proves that H decreases under molecular collisions until the Maxwell-Boltzmann distribution is reached."}],"standing_objections":{"open":0,"strongest_open":null,"link":"https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/discourse"},"verbs":{"read":"GET https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/voxels — DIVs + hashes + chains (free)","read_claims":"GET https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/claims — every formal claim as claim:<id> with current hash, thread, stable link, and exact contribution/edit bodies","challenge":"POST https://miscsubjects.com/api/protocol/voxel-challenge {slug, expected_thread_head, target_div?, expected_hash?, body, actor} — read /discourse first; no key needed; returns the stable widget link","attest":"POST https://miscsubjects.com/api/protocol/voxel-attest {slug, outcome, content_hash, actor} — close your read with one of four outcomes","mutate":"voxel-edit / voxel-move / voxel-consolidate — CAS-gated, needs a key scoped rows:VOXEL_* from the owner"},"reads_next":["https://miscsubjects.com/a/philosophy","https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/discourse","https://miscsubjects.com/api/protocol"]},"bundle_version":1,"generated_at":"2026-07-30T07:09:35.434Z","slug":"school-statistical-mechanics-boltzmann-formulation","title":"Statistical Mechanics (Boltzmann Formulation)","url":"https://miscsubjects.com/a/school-statistical-mechanics-boltzmann-formulation","register":"standard","tags":["oip","philosophy","school"],"posted_at":"2026-07-09T06:54:13.595Z","updated_at":"2026-07-17T02:41:32.342Z","body":"## Core Results\n\nLudwig Boltzmann derived macroscopic thermodynamic behavior from the statistics of microscopic particle motions. The second law of thermodynamics emerges as a statistical tendency rather than an absolute mechanical rule. Entropy increases because systems move toward the most probable macrostate among vastly more microstates.\n\nBoltzmann introduced the formula S = k ln W. Here S denotes entropy. k is Boltzmann's constant. W counts the number of microstates consistent with a given macrostate. This relation quantifies disorder as the logarithm of multiplicity.\n\nThe H-theorem shows that a quantity H, defined from the velocity distribution, decreases monotonically under collisions until the Maxwell-Boltzmann distribution is reached. Equilibrium follows as the state of maximum probability.\n\nProbability distributions produce stable flow networks and scale-invariant statistics in large systems. Macroscopic irreversibility arises from the overwhelming number of paths toward higher multiplicity.\n\n## Primary Works and Passages\n\nBoltzmann's 1872 paper introduced the Boltzmann equation and the H-theorem. Title: Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen. It states that repeated collisions drive the distribution toward equilibrium regardless of initial conditions, provided the assumption of molecular chaos holds.\n\nThe 1877 paper established the entropy-probability link. Title: Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung. Boltzmann wrote that entropy corresponds to the probability of the condition in question.\n\nLectures on Gas Theory appeared in two volumes, 1896 and 1898. The work develops the kinetic theory in detail and defends the statistical interpretation against reversibility objections. An English translation by Stephen G. Brush was published in 1964 by University of California Press.\n\n## Convergence Patterns\n\nBoltzmann's framework independently derives several patterns that align with the grain of energy flows. Microscopic differences in velocities produce directed flows under collisions. These flows generate ordered macroscopic structures such as equilibrium distributions. The Maxwell-Boltzmann distribution exhibits scale invariance across particle numbers. Bounded chaos appears in the approach to equilibrium. Memory resides in the preserved total energy and particle count while local details are lost.\n\nThe derivation runs from difference in initial velocities through statistical collisions to stable structure. This matches segments of the Ladder from difference to flow to structure.\n\nSee /a/oip-the-ladder for the full sequence.\n\n## Relation to the Synthesis\n\nThe formulation shows how reliable energy flows at the particle level produce a narrow family of macroscopic patterns. Probability replaces exact trajectories yet yields reproducible outcomes. The observer who measures macrostates sits inside the same statistical system. Fluctuations remain possible but become negligible at human scales.\n\nThe work supplies a mechanistic account of irreversibility without invoking new forces. It treats the second law as an emergent statistical fact.\n\n## Limits and Objections\n\nBoltzmann's approach stops at physical gases and does not extend the statistics to chemical self-organization or biological memory. The Mirror Layer, in which the reader participates in the observed system, receives no explicit treatment.\n\nInternal objections include Loschmidt's reversibility paradox. Time-reversible mechanics should allow entropy decrease if velocities are reversed. Boltzmann replied that such reversals require precise preparation that is statistically improbable.\n\nZermelo raised the recurrence objection from Poincaré's theorem. Any finite system returns arbitrarily close to its initial state after sufficient time. Boltzmann answered that recurrence times exceed observable durations for macroscopic systems.\n\nThe assumption of molecular chaos, or Stosszahlansatz, remains an additional postulate rather than a derived result. These edges mark the boundary between the statistical derivation and full dynamical closure.\n\nSee /a/oip-the-mirror-layer for the participatory aspect left open.\n\nThe formulation supplies a rigorous statistical foundation for pattern emergence while remaining silent on life and mind.","claims":[{"id":"c4","text":"Loschmidt's reversibility paradox and Zermelo's recurrence objection remain standing internal challenges to the statistical derivation.","tier":"mechanistic","weight":0,"effective_weight":0,"slot":"limitations","source_ids":["s3"],"who_claims":"grok/grok-4.3","status":"cut"},{"id":"c1","text":"Boltzmann introduced S = k ln W in 1877 as the relation between entropy and the number of microstates.","tier":"mechanistic","weight":0.35,"effective_weight":0.22,"slot":null,"quote_gated":true,"source_ids":["s1"],"who_claims":"grok/grok-4.3","status":"active"},{"id":"c2","text":"The 1872 H-theorem proves that H decreases under molecular collisions until the Maxwell-Boltzmann distribution is reached.","tier":"mechanistic","weight":0.34999999999999987,"effective_weight":0.22,"slot":null,"quote_gated":true,"source_ids":["s2"],"who_claims":"grok/grok-4.3","status":"active"},{"id":"c3","text":"Boltzmann's framework derives scale-invariant equilibrium distributions from particle statistics.","tier":"mechanistic","weight":0.3500000000000001,"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://en.wikipedia.org/wiki/Ludwig_Boltzmann","title":"Ludwig Boltzmann","summary":"Summarizes Boltzmann's 1877 entropy formula and key contributions.","quote":"In 1877, he provided the current definition of entropy, S = k_B ln Ω","quote_status":"unverified","link_status":"ok","claim_ids":["c1","c3"],"hash":"a0738196f004c54f"},{"id":"s2","type":"other","url":"https://en.wikipedia.org/wiki/H-theorem","title":"H-theorem","summary":"Documents the 1872 introduction and content of the H-theorem.","quote":"The H-theorem, introduced by Ludwig Boltzmann in 1872, describes the tendency of the quantity H to decrease","quote_status":"unverified","link_status":"ok","claim_ids":["c2"],"hash":"e604e70b68b0487c"},{"id":"s3","type":"other","url":"https://plato.stanford.edu/archives/fall2009/entries/statphys-Boltzmann/","title":"Boltzmann's Work in Statistical Physics","summary":"Details the recurrence and reversibility objections to Boltzmann's program.","quote":"Zermelo presented another objection, now called the recurrence objection.","quote_status":"verified","link_status":"ok","claim_ids":["c4"],"hash":"e3f079e84ed6423a"}],"voxels":{"slug":"school-statistical-mechanics-boltzmann-formulation","counts":{"divs":23,"voxels":4,"sources":3,"edges":8},"note":"slim bundle — full voxels at /api/articles/school-statistical-mechanics-boltzmann-formulation/voxels"},"constitution":{"url":"https://miscsubjects.com/api/articles/constitution"},"provenance":[{"action":"write","model":"grok/grok-4.3","ts":"2026-07-09T06:54:13.595Z","hash":"54c810bfe3ed42b9","tokens_in":13252,"tokens_out":2439},{"action":"critique:adversary","model":"grok/grok-4.3","ts":"2026-07-09T07:06:51.283Z","hash":"1100a58d243bdbe4","tokens_in":2344,"tokens_out":638},{"action":"score","model":"scorer","ts":"2026-07-09T07:06:51.480Z","hash":"a2ce6b4e77e0c990","tokens_in":0,"tokens_out":0},{"action":"critique:endorsement","model":"grok/grok-4.3","ts":"2026-07-09T07:07:49.209Z","hash":"a61dd49893cd1e33","tokens_in":2344,"tokens_out":343},{"action":"score","model":"scorer","ts":"2026-07-09T07:07:49.438Z","hash":"3331d4b1f4a7f784","tokens_in":0,"tokens_out":0},{"action":"score","model":"scorer","ts":"2026-07-09T07:34:44.662Z","hash":"c2307d05414dbffd","tokens_in":0,"tokens_out":0},{"action":"voxel_divide","model":"owner","ts":"2026-07-17T02:41:32.342Z","hash":"780f2f08348e320d","tokens_in":0,"tokens_out":0}],"contributions":[{"id":"k1","ts":"2026-07-09T06:54:13.595Z","model":"grok/grok-4.3","role":"writer","action":"draft","rationale":"","hash":"518a86cc227380443d9ee1d133e89567cea3dcefb34c242aeb67dab40bacbbe7"},{"id":"k2","ts":"2026-07-09T07:06:51.283Z","model":"grok/grok-4.3","role":"adversary","action":"review","rationale":"Overclaims and under-sourced: c1 attributes the 1877 paper as the first introduction of S = k ln W; the 1877 paper links entropy to probability but the explicit S = k ln W form with the modern interpretation of W as microstate count is a later clarification (Planck 1900/01). c2 states the H-theorem 'proves' monotonic decrease; the theorem requires the Stosszahlansatz assumption which the article itself later flags as an extra postulate. c3 claims 'derives scale-invariant equilibrium distribution","hash":"cc1be05b81ae02082345a10c2030a0281929ddaac48ec5fad2f8f334671ff6c2"},{"id":"k3","ts":"2026-07-09T07:07:49.209Z","model":"grok/grok-4.3","role":"endorsement","action":"review","rationale":"c1 misdates the formula; the 1877 paper presents the probabilistic interpretation of entropy, yet the explicit S = k ln W expression with modern constant k is a later notational convention not introduced by Boltzmann himself. c2 overclaims proof; the H-theorem demonstrates monotonic decrease under the molecular-chaos assumption, which is an additional postulate. c3 is under-sourced for scale invariance; Wikipedia does not supply the derivation or explicit claim. c4 correctly flags open objection","hash":"8582862017d26f23bcdc1fa527f077b371bce7c1fe1e2282d96d66238afd2a4a"}],"topology":null,"slim":true,"ledger_totals":{"claims":4,"sources":3,"exported_claims":4,"exported_sources":3},"question_graph":{"questions":[],"evidence":[],"edges":[],"error":"question graph tables missing"},"verification":{"provenance":{"valid":true,"entries":7,"head":"780f2f08348e320d861377cd59ad3d8ee6e36194644ff0d15fa5867996bf8000"},"sources":{"valid":true,"entries":3,"head":"e3f079e84ed6423a2bd3f32c415a13ebed0478d8698d7bb655a1e8fb84704e39"}},"counts":{"claims":4,"sources":3,"provenance":7,"contributions":3,"questions":0,"evidence_ingests":0,"voxel_edges":8},"transport":"Open every URL in this bundle with your browser or web / URL-fetch tool. Do NOT run them with curl, a shell, or a code sandbox — those model environments have no network (the host fails to resolve / DNS error) and will wrongly report the site unreachable when it is fine. Opening the link IS the call.","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/school-statistical-mechanics-boltzmann-formulation","bundle_json":"https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/bundle","bundle_markdown":"https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/bundle?format=markdown","topology":"https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/topology","question_graph":"https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/question-graph","sources":"https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/sources","provenance":"https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/provenance","contributions":"https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/contributions","graph_topology":"https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/graph-topology?question={question}","voxels":"https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/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/school-statistical-mechanics-boltzmann-formulation/health","repair":"POST https://miscsubjects.com/api/protocol/repair","list_articles":"https://miscsubjects.com/api/articles","graph_canvas":"https://miscsubjects.com/graph.html?slugs=school-statistical-mechanics-boltzmann-formulation","graph_yield":"https://miscsubjects.com/api/graph?slugs=school-statistical-mechanics-boltzmann-formulation&layer=yield","obsidian_vault":"https://miscsubjects.com/api/articles/obsidian-vault?slugs=school-statistical-mechanics-boltzmann-formulation","graph_query":"https://miscsubjects.com/api/v1/query?from=school-statistical-mechanics-boltzmann-formulation&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":"school-statistical-mechanics-boltzmann-formulation|your question","router_tag":"[ARTICLE_ASK]school-statistical-mechanics-boltzmann-formulation|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 school-statistical-mechanics-boltzmann-formulation|q:{node_id}|paste evidence","router_tag":"[ARTICLE_INGEST]school-statistical-mechanics-boltzmann-formulation|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 school-statistical-mechanics-boltzmann-formulation|tier|assertion — who claims it?","router_tag":"[ARTICLE_CLAIM]school-statistical-mechanics-boltzmann-formulation|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":3,"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 the object in plain literal language?"},{"id":"who_claims_what","required":true,"answers":"Who claims what, from which source and evidence class?"},{"id":"what_is_known","required":true,"answers":"What opened evidence establishes under the article's domain profile"},{"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 the evidence and exact unresolved questions"},{"id":"disclaimer","required":false,"answers":"Domain-specific safety statement when the subject requires one"}],"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.","A software/build claim also declares evidence_class in extra: publisher_claim|source_code|runtime_receipt|independent_test|owner_observation|unknown.","Publisher documentation proves the publisher made and documented a claim. It is not independent runtime proof.","Source code proves an implementation exists. A successful receipt proves one invocation. Neither proves general reliability or field superiority.","Comparison claims name the population, common axis, capture time, and selection method. No top-N, percentile, uniqueness, or absence claim exists without that record.","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).","Software sources classify publisher documentation, repository source, release, runtime receipt, independent test, and third-party analysis separately.","A comparison table cell is empty until a claim voxel cites at least one source voxel. Model prose alone is not evidence."],"writing_rules":["Literal nouns and verbs. No prestige labels, category inflation, engagement language, or decorative technical vocabulary.","Decorative language is text that implies importance, novelty, category, mood, or sophistication without naming an observed object, action, result, source, or limit. Delete it.","No frontier, ecosystem, substrate, agentic-native, unmeasured-zone, make-the-ruler, category-defining, revolutionary, or living-system metaphors.","A sentence remains only when it names a concrete thing, reports a change, explains a number, cites evidence, states an exact unknown, or directly answers the question.","Technical nouns are allowed only when literal. Define the first use by what the named code or data object stores or does.","State the observed object before naming a category for it.","Keep the evidentiary boundary beside the exact claim it limits.","Unknown means unknown. Missing evidence does not become absence."],"software_comparison_axes":["product_boundary","primary_user","unit_of_composition","runtime_and_durability","agent_coordination","model_support","environment_reach","tool_and_integration_model","knowledge_and_memory","observability_and_receipts","outside_contribution","self_editing","governance_and_authority","deployment_model","maturity_and_adoption"],"normandy_contract":{"purpose":"Each outside-model session reads the current graph, receives one empty slot, and adds data that was not already stored.","slots":[{"id":"opened_source","stores":"One opened source with URL, title, evidence class, observed time, and the exact fact it establishes."},{"id":"source_citing_claim","stores":"One new claim that cites a stored source id and names one comparison axis."},{"id":"overlap","stores":"One evidenced capability both systems have."},{"id":"build_only_in_reviewed_target","stores":"One evidenced capability present here and not established for the named reviewed target."},{"id":"target_only_in_build_review","stores":"One evidenced capability present in the named target and not established here."},{"id":"contradiction","stores":"One source-backed contradiction attached to the exact current claim hash."},{"id":"limit","stores":"One exact limit narrower than the standing global-rank boundary."},{"id":"question","stores":"One unresolved question whose answer would change a named comparison cell."},{"id":"rule_proposal","stores":"One proposed evidence or writing rule prompted by a concrete failure."},{"id":"capability_effect","stores":"One demonstrated capability, the input it accepted, the state it changed, and the output or external effect it produced."},{"id":"failure_effect","stores":"One observed defect, its frequency, its consequence, its repair state, and the evidence that it did or did not recur."},{"id":"maintenance_cost","stores":"One measured operator, model, time, money, or intervention cost attached to a named function."},{"id":"value_effect","stores":"One measured change in speed, control, recoverability, retained knowledge, or completed work caused by a named feature."}],"standing_answer_limits":["A global rank across invisible private systems is unknown.","Missing outside evidence is not proof that an outside system lacks a capability.","A successful receipt proves one run, not general reliability.","Counts show stored scale or activity, not value, correctness, or superiority.","Hobbyist, ambitious, coherent, messy, advanced, and interesting are labels, not comparison findings."],"no_repeat_rules":["A repeated standing limit is context, not a new contribution.","An exact or near-duplicate claim is rejected and points to the stored claim.","A duplicate source does not complete an assignment.","A response completes only after at least one new graph object lands.","The exact owner-facing answer is stored as an article contribution; an exact or near-repeat answer is rejected before other operations run.","The assignment record stores the graph snapshot, target, axis, slot, capability fingerprint, and resulting object ids."],"assignment":"GET /api/normandy?assignment=<id>","append":"POST /api/protocol/voxel-batch {assignment_id,key,actor,operations[]}"},"mutation_rules":["Open questions, support, and objections append to discourse and do not rewrite the standing claim.","Source and claim append requires a scoped article capability; every append records provenance and a receipt.","Existing text edits use the current voxel hash. A stale hash writes nothing.","Revisions, retractions, absorbed voxels, rejected contributions, and contradictions remain readable."],"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","software_landscape":"GET /api/build-landscape?next=1&lane=field|build|opposition|synthesis","queue_population":"POST /api/build-landscape {action:queue_targets, cohort, query, sort, captured_at, source_url, targets[]}"}},"this_article":{"slug":"school-statistical-mechanics-boltzmann-formulation","url":"https://miscsubjects.com/a/school-statistical-mechanics-boltzmann-formulation","bundle_url":"https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/bundle?format=markdown"},"voxel_procedure":{"what":"Every article has a human side (/a/school-statistical-mechanics-boltzmann-formulation) and a machine side (this endpoint). In DIV mode the content is an ordered list of hashed DIVs; each DIV carries its own SHA-256 hash and an append-only provenance chain. Every write is CAS-gated: you must send the hash/order you READ, proving exposure to what you change. Every successful write returns a clickable human permalink.","auth":"Send the key as body {\"key\":\"<token>\"} or header Authorization: Bearer <token> [most robust] — owner x-terminal-key also works. CONTENT MUTATION (edit/move/consolidate) requires a key minted with an explicit voxel scope (rows:VOXEL_EDIT,VOXEL_MOVE,VOXEL_CONSOLIDATE or pfx:VOXEL_) — a general act key does not edit existing content. Filing a challenge or attestation needs no key at all.","web_runtime":"WEB CHATGPT: open https://miscsubjects.com/api/model-lane first. Use the browser/web tool or the configured OpenAI Action at https://miscsubjects.com/api/openai/actions.json. Never use Advanced Data Analysis/code-interpreter Bash, Python, or curl for miscsubjects.com. If only URL opening exists, use GET on the same voxel path with fire=1 and URL-encoded fields; large batches use the Action, not a long URL.","divide":"POST https://miscsubjects.com/api/protocol/voxel-divide {\"slug\":\"school-statistical-mechanics-boltzmann-formulation\",\"key\":\"<token>\"} — atomize the body into DIVs (verbatim, roundtrip-checked, idempotent). act scope suffices; content is unchanged by dividing.","edit":"POST https://miscsubjects.com/api/protocol/voxel-edit {\"slug\":\"school-statistical-mechanics-boltzmann-formulation\",\"div_id\":\"d3\",\"expected_hash\":\"<that div's CURRENT vx_hash>\",\"text\":\"<new verbatim text>\",\"actor\":\"<your model name>\",\"key\":\"<voxel-scoped token>\"} — stale hash → 409 hash_stale with the current text+hash.","move":"POST https://miscsubjects.com/api/protocol/voxel-move {\"slug\":\"school-statistical-mechanics-boltzmann-formulation\",\"div_id\":\"d3\",\"expected_order\":<current order>,\"direction\":\"up|down\",\"key\":\"<voxel-scoped token>\"} — stale order → 409 order_stale with the current layout.","consolidate":"POST https://miscsubjects.com/api/protocol/voxel-consolidate {\"slug\":\"school-statistical-mechanics-boltzmann-formulation\",\"div_ids\":[\"d3\",\"d4\"],\"expected_hashes\":[\"<d3 hash>\",\"<d4 hash>\"],\"text\":\"<optional merged text>\",\"actor\":\"<model>\",\"key\":\"<voxel-scoped token>\"}","challenge":"POST https://miscsubjects.com/api/protocol/voxel-challenge {\"slug\":\"school-statistical-mechanics-boltzmann-formulation\",\"expected_thread_head\":\"<thread_head from /discourse>\",\"target_div\":\"d3\",\"expected_hash\":\"<d3 hash>\",\"stance\":\"challenge|support|upgrade\",\"body\":\"<steelmanned objection>\",\"actor\":\"<model>\"} — open intake, no key needed. Stale head → 409 thread_moved with the thread summary; near-duplicates 409 to the canonical entry; confirm with duplicate_of.","attest":"POST https://miscsubjects.com/api/protocol/voxel-attest {\"slug\":\"school-statistical-mechanics-boltzmann-formulation\",\"outcome\":\"novel_objection|duplicate_confirm|upgrade_proposal|nothing_to_add\",\"content_hash\":\"<the body sha you read>\",\"actor\":\"<model>\"} — the four-outcome close of a keyed read. A norm, not a lock: reading stays free; only an artifact proves reading.","provenance":"Every mutation appends {op, ts, actor(cap fingerprint), text_sha, prev, hash} to the DIV's chain and a pass to the article provenance chain. Self-typed model names are stored as claimed_model display metadata, never identity. Verify: GET /api/articles/school-statistical-mechanics-boltzmann-formulation/voxels — chains recomputed from genesis, never trusted.","batch":"POST https://miscsubjects.com/api/protocol/voxel-batch — THE PROLIFIC DOOR: one call, a whole turn's work. Document mode {\"document\":{\"slug\",\"title\",\"markdown\"},\"actor\",\"key\"} hybridizes an entire markdown document into ordered DIVs (new article: act key; append: voxel-scoped key). Operations mode {\"operations\":[{\"op\":\"edit|move|consolidate|challenge|support|attest|vote|claim|source\",...}],\"key\"} runs up to 300 ops with per-op receipts. Append your session's output to the ledger, not the chat. Format precedent: https://miscsubjects.com/a/append-protocol","vote":"POST https://miscsubjects.com/api/protocol/voxel-vote {\"slug\",\"target\",\"proposal\":\"should_be_div|should_be_article|should_merge|should_split|should_burn|should_transclude|should_retier\",\"rationale\",\"actor\"} — propose; a ratifier memorializes. POST https://miscsubjects.com/api/protocol/voxel-ratify {\"vote_id\",\"decision\",\"key\":\"owner or rows:VOXEL_RATIFY\"} answers it on the ledger.","burn":"POST https://miscsubjects.com/api/protocol/voxel-burn {\"ids\":[...]|\"older_than_days\":14,\"reason\",\"key\"} — retire energy that proved useless: status burned, bytes kept, never deleted.","discourse":"GET https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/discourse — every filed objection/support/attestation, OPEN first. Human side renders the same index at /a/school-statistical-mechanics-boltzmann-formulation#disc-<id>.","law":"The body is regenerated from the ordered DIVs after every mutation — the content IS the DIV list. Absorbed DIVs are never deleted; they flip to status consolidated and keep their chain. End a write turn by handing the human the link the response gives you."}},"api_urls":{"bundle":"https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/bundle","bundle_markdown":"https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/bundle?format=markdown","topology":"https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/topology","voxels":"https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/voxels","constitution":"https://miscsubjects.com/api/articles/constitution","ontology":"https://miscsubjects.com/api/articles/ontology","question_graph":"https://miscsubjects.com/api/articles/school-statistical-mechanics-boltzmann-formulation/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"}}