{"_self":{"principle":"Self-explaining payload — no external context required. This _self block describes what you are reading and where to look next.","widget":"article_topology","feature":"topology","name":"Article topology","what":"Claims, sources, anecdotes, user reports, related embeds, question graph slice — for ask/ROUTER.","contains":"claims, sources, anecdotes, question_graph slice","slug":"logical-economics","urls":{"read":"https://miscsubjects.com/api/articles/logical-economics/topology"},"how_to_use":"Claims, sources, anecdotes, user reports, related embeds, question graph slice — for ask/ROUTER.","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/logical-economics/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":"ask","name":"Ask protocol","what":"Answer only from topology; creates question_node with gaps and ingest_hint.","urls":{"read":"https://miscsubjects.com/api/articles/logical-economics/prompts","write":"https://miscsubjects.com/api/protocol/ask"}},{"id":"graph_topology","name":"Cross-article graph","what":"Merged claims/sources across condition+stack slugs for one question.","urls":{"read":"https://miscsubjects.com/api/articles/logical-economics/graph-topology?question=..."}},{"id":"question_graph","name":"Question graph","what":"Ask nodes (questions + gaps) and evidence_ingest nodes (pasted model output).","urls":{"read":"https://miscsubjects.com/api/articles/logical-economics/question-graph","write":"https://miscsubjects.com/api/protocol/ask"}},{"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/logical-economics/voxels","write":"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","not_medical_advice":true},"_explain":{"feature":"topology","name":"Article topology","what":"Claims, sources, anecdotes, user reports, related embeds, question graph slice — for ask/ROUTER.","why":"Every feature is auditable collective intelligence","how":"Claims, sources, anecdotes, user reports, related embeds, question graph slice — for ask/ROUTER.","model":null,"verifies":null,"urls":{"read":"https://miscsubjects.com/api/articles/logical-economics/topology"},"imessage":null,"router":null,"related":[{"id":"ask","what":"Answer only from topology; creates question_node with gaps and ingest_hint."},{"id":"graph_topology","what":"Merged claims/sources across condition+stack slugs for one question."},{"id":"question_graph","what":"Ask nodes (questions + gaps) and evidence_ingest nodes (pasted model output)."},{"id":"voxels","what":"Claims as atoms, sources as edges (supported_by, posted_by). Per-claim provenance."}],"not_medical_advice":true},"slug":"logical-economics","title":"Logical economics: the least reasoning energy that makes an action correct enough for its consequence","register":"standard","tags":["logical-economics","assurance","error-rate","common-cause-failure","pricing"],"updated_at":"2026-07-30T05:19:58.302Z","body_excerpt":"Most deployments today use model expense as a proxy for correctness: send everything to the biggest model, spend tokens indiscriminately, and hope. There is no stated relationship between compute spent and risk removed.\n\nThe primitive is three lines:\n\n```\nSYSTEM PROMPT\n  MODEL AUDITABLY REASONING OVER A DECISION\n    DECISION OR ACTION\n```\n\nEverything else — panels, gates, receipts, anchors — is implementation of those three lines. And the question that matters is not how to maximise assurance. It is how little reasoning energy an action needs in order to be correct enough for its consequence.\n\n## The equation\n\n```\nE* = argmin_E [ C(E) + P_wrong(E, K) x L ]\n\nE        reasoning energy: channels, families, passes, recitation depth, thresholds\nK        task complexity\nC(E)     compute cost of that configuration\nP_wrong  MEASURED probability that the assembly emits a wrong answer undetected\nL        consequence of a wrong action\n\nsubject to:  marginal cost of additional audit  <  marginal reduction in expected loss\n```\n\nThe ledger term is what makes this tractable: recording the reasoning costs nothing extra once every invocation already passes through the same architecture. The variable cost is only the extra reasoning energy deliberately purchased for that decision. So the optimisation is real and it is per-action, not per-system.\n\nThe only unknown in that equation is P_wrong. Everything else is a price or a policy. Below is P_wrong, measured, for one task class.\n\n## The control law, and the five things it can decide\n\n```\n(R, K, e)  ->  E*  ->  { APPROVE | NEGATE | NO_ACTION | DISPUTE | ESCALATE }\n\nR   consequence: the loss exposure of a wrong action\nK   logical complexity of the task\ne   permitted wrongful-action rate\nE*  minimum sufficient reasoning energy: channel count, channel class, training-family\n    diversity, independent passes, required clause recitation, confidence floor,\n    verification depth\n```\n\nThe gate does not emit a verdict. It decides what happens to the **action**, which is the only thing a downstream actor can consume, and it decides by arithmetic. Every outcome below was produced by the live row, each with a receipt anyone can open:\n\n| decision | the condition that produces it | action authorised | receipt |\n|---|---|---|---|\n| **APPROVE** | unanimous AFFIRM, identical clause citations, enough distinct training families, no malformed finding, stated confidence at or above the floor | yes | [inv_df97ytym64](https://miscsubjects.com/receipt/inv_df97ytym64) |\n| **NEGATE** | unanimous DENY on the same terms — the action is refused, not deferred | no | [inv_p16tspdf3v](https://miscsubjects.com/receipt/inv_p16tspdf3v) |\n| **NO_ACTION** | unanimous CANNOT_CONCLUDE — a required record is missing, so nothing is authorised and nothing is refused | no | [inv_vnyq5o2ve5](https://miscsubjects.com/receipt/inv_vnyq5o2ve5) |\n| **DISPUTE** | the only failing test is a stated confidence below the supplied floor, **and the caller explicitly opted in with `require_confidence`** — see below | no | [inv_bhbpezra76](https://miscsubjects.com/receipt/inv_bhbpezra76) |\n| **ESCALATE** | any verdict divergence, clause-citation divergence, malformed finding, too few channels, or too little training-family diversity | no | [inv_agl1v89k7v](https://miscsubjects.com/receipt/inv_agl1v89k7v) |\n\n**Stated confidence is recorded and does not gate authorisation.** The DISPUTE receipt above was produced while it did. It no longer does, because a model-generated confidence number has no calibration study behind it and this panel's own measured false-confidence rate of 0.214 to 0.429 is the evidence that these models assert confidence they have not earned. Letting it decide is the one place a model can talk its way past a deterministic gate: emit 0.99. It is now parsed, published on every seal alongside `confidence_gates_the_decision: false`, and available for the calibration study that would earn it a place in the condition. Re-run today, three ","ranking":"safety-first (interaction_risk/limitations), then quote-gated effective_weight","claims":[{"id":"c1","text":"The primitive is a system prompt, a model reasoning auditably over a decision, and the decision or action; the optimisation problem is to spend the least reasoning energy that makes an action correct enough for its consequence, E* = argmin over E of C(E) + P_wrong(E,K) times L.","tier":"argued","section":"equation","interaction_risk":false,"status":"active","source_ids":["s2"],"retracted_at":null,"retraction_reason":null,"challenged_by":[],"effective_weight":0.1,"quote_gated":false},{"id":"c2","text":"On a 14-item boundary-weighted task class, the mean undetected-wrong rate falls from 0.314 at one channel to 0.178 at two, 0.136 at three, 0.100 at four and 0.071 at five, while the emit rate falls from 0.972 to 0.429 — so the second channel is the steepest reduction per unit cost and the fifth is the shallowest.","tier":"measured","section":"table","interaction_risk":false,"status":"active","source_ids":["s1"],"retracted_at":null,"retraction_reason":null,"challenged_by":[],"effective_weight":0.1,"quote_gated":false},{"id":"c3","text":"The best achievable undetected-wrong rate stops improving beyond two channels at 0.071 because one item — P07, where all five channels answered DENY against a declared correct verdict of CANNOT_CONCLUDE — survives every configuration; whether that is common-cause model failure or a contestable ground-truth label is published as an open question, because DENY is defensible under clause 3 and CANNOT_CONCLUDE under clause 4 of the same rule set.","tier":"measured","section":"floor","interaction_risk":false,"status":"active","source_ids":["s1"],"retracted_at":null,"retraction_reason":null,"challenged_by":[],"effective_weight":0.1,"quote_gated":false},{"id":"c4","text":"Redundancy cannot detect correlated wrongness because unanimity is what the gate takes as permission to emit; the only instrument that found the floor item was a known-answer probe with the answer declared in advance.","tier":"argued","section":"floor","interaction_risk":false,"status":"active","source_ids":["s1","s2"],"retracted_at":null,"retraction_reason":null,"challenged_by":[],"effective_weight":0.1,"quote_gated":false},{"id":"c5","text":"At fixed channel count and cost, a cross-family pair emits fewer wrong answers than a same-family pair — 0.169 against 0.214 — and same-family adjudicators agree 0.893 of the time against 0.714 cross-family, so diversity rather than count is the lever.","tier":"measured","section":"diversity","interaction_risk":false,"status":"active","source_ids":["s1"],"retracted_at":null,"retraction_reason":null,"challenged_by":[],"effective_weight":0.1,"quote_gated":false},{"id":"c6","text":"The table's emit rates are upper bounds because the live gate additionally requires identical clause citations across channels, a test this suite's output shape cannot express.","tier":"demonstrated","section":"limits","interaction_risk":false,"status":"active","source_ids":["r1","s2"],"retracted_at":null,"retraction_reason":null,"challenged_by":[],"effective_weight":0.1,"quote_gated":false},{"id":"c7","text":"Every rate rests on fourteen observations in one task class under one rule set, so the defensible reading is ordinal rather than to the third decimal, and no distribution-free bound in the conformal sense has been computed.","tier":"argued","section":"limits","interaction_risk":false,"status":"active","source_ids":["s1"],"retracted_at":null,"retraction_reason":null,"challenged_by":[],"effective_weight":0.1,"quote_gated":false},{"id":"c8","text":"For any decision whose permitted error is below the measured floor of a task class, the table's answer is not to deploy the assembly, which is stated before anything ships rather than after a loss.","tier":"argued","section":"policy","interaction_risk":false,"status":"active","source_ids":["s1"],"retracted_at":null,"retraction_reason":null,"challenged_by":[],"effective_weight":0.1,"quote_gated":false},{"id":"c9","text":"The gate produces five outcomes by arithmetic — APPROVE, NEGATE, NO_ACTION, DISPUTE, ESCALATE — and all five were exercised on the live row with a public receipt each; only APPROVE authorises an action, and NO_ACTION is kept distinct from NEGATE because withholding for a missing record and refusing under the rule carry different consequences.","tier":"demonstrated","section":"control-law","interaction_risk":false,"status":"active","source_ids":["g_approve","g_negate","g_no_action","g_dispute","g_escalate"],"retracted_at":null,"retraction_reason":null,"challenged_by":[],"effective_weight":0.1,"quote_gated":false},{"id":"c10","text":"Adjacent work holds one side each: difficulty-based routing optimises the accuracy-compute frontier, cost-aware cascades escalate on model uncertainty, conformal calibration targets an error rate on the act decision, and IEC 61508 assigns integrity levels at design time; none allocates auditable reasoning expenditure per action from consequence and complexity together and then gates the material action on the resulting record.","tier":"argued","section":"novelty","interaction_risk":false,"status":"active","source_ids":["s2"],"retracted_at":null,"retraction_reason":null,"challenged_by":[],"effective_weight":0.1,"quote_gated":false},{"id":"c11","text":"Stated confidence is recorded on every seal and does not gate authorisation unless a caller explicitly opts in, because no calibration study exists for these models' stated confidence and the panel's measured false-confidence rate of 0.214 to 0.429 is the evidence against trusting it.","tier":"demonstrated","section":"control-law","interaction_risk":false,"status":"active","source_ids":["g_dispute"],"retracted_at":null,"retraction_reason":null,"challenged_by":[],"effective_weight":0.1,"quote_gated":false},{"id":"le_c2","text":"The loop is executable in one call: action and action class in, and R, K, epsilon, the configuration, the execution, the seal and the bounded act derived and recorded, with the caller unable to supply the risk, the complexity, the permitted error, the thresholds or the configuration.","tier":"demonstrated","section":"loop","interaction_risk":false,"status":"active","source_ids":["loop_row"],"retracted_at":null,"retraction_reason":null,"challenged_by":[],"effective_weight":0.1,"quote_gated":false},{"id":"le_c3","text":"On the two live runs where all three channels conformed and returned the same verdict, the gate still refused because the channels cited different clause sets, and no bound assembly has ever reached APPROVE.","tier":"measured","section":"loop","interaction_risk":false,"status":"active","source_ids":["loop_A_approve_at"],"retracted_at":null,"retraction_reason":null,"challenged_by":[],"effective_weight":0.1,"quote_gated":false},{"id":"le_c4","text":"At a clinical epsilon of 0.02 the allocator executes nothing, because the measured floor for the only characterised task class is 0.071, so the refusal happens before any model call.","tier":"demonstrated","section":"loop","interaction_risk":false,"status":"active","source_ids":["loop_row"],"retracted_at":null,"retraction_reason":null,"challenged_by":[],"effective_weight":0.1,"quote_gated":false},{"id":"le_c5","text":"Ten adversarial submissions — forged model, forged family, forged verdict, duplicated record, mismatched rule set, mismatched artifact, lowered thresholds, replayed finding, a non-adjudication record and nonexistent ids — all failed closed, and the battery surfaced two real loader defects that were fixed rather than worked around.","tier":"demonstrated","section":"adversarial","interaction_risk":false,"status":"active","source_ids":["loop_row"],"retracted_at":null,"retraction_reason":null,"challenged_by":[],"effective_weight":0.1,"quote_gated":false},{"id":"le_c6","text":"Observed shape conformance constrains configuration selection: the configurations reaching the measured 0.071 floor all depend on a channel that has never emitted the required output shape, so the cheapest viable configuration sits at 0.214 and no tighter epsilon can be served.","tier":"measured","section":"loop","interaction_risk":false,"status":"active","source_ids":["loop_row"],"retracted_at":null,"retraction_reason":null,"challenged_by":[],"effective_weight":0.1,"quote_gated":false}],"sources":[{"id":"s1","type":"live_surface","url":"https://miscsubjects.com/a/adjudication-probe-report-eu-ai-act","title":"The 14-item suite and the 70 findings this table is computed from","summary":"Four rates per model, the agreement estimators, and every probe item with its declared correct verdict and the reason.","claim_ids":[],"hash":"0f902444b3ffc7517689c427b6a57ac4950d33d55bf37fa80fb8f1b5f011344b"},{"id":"s2","type":"live_surface","url":"https://miscsubjects.com/api/directory/SEAL_PANEL","title":"The gate whose behaviour the table simulates","summary":"Unanimity, identical clause citations, and channel diversity counted by training family. 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