The Math · Derivation
How every 1-in-N figure is built: outcome-space partition × cascade discount × multiplier ladder. No analyst overlay. Plus the corpus-level LUCK TEST — 92…
The 1-in-N improbability derivation
How JYOTINT computes the odds that a sealed call landed by chance: an outcome-space partition × a cascade exponent × a capped multiplier ladder, published as a repeatable derivation with no analyst-in-the-loop fudge. The logic behind every '1-in-N' figure on the record.
The locked master formula: N = partition floor (a sourced outcome-space partition whose bin weights sum to 1.00; the floor is 1/weight on the called bin) × PCP (public-consensus penalty, credited only where zero named public callers are on record, cap 10×) × CP (conjunction premium, cap 2.5×) × DH (domain hardness, calibrated to published forecast-skill literature, cap 3×) × LT (lead-time premium, calibrated to documented horizon decay, cap 3×) × AW (analyst-window premium, cap 2×). Correlated cascade descendants are exponent-discounted (e = 0.2) so one mechanism is never double-counted; every multiplier is capped, so there is no unbounded fudge; the rubric locks at issue time — no retcon. The same N feeds both SITA's Improbability axis (log-scaled 0–100) and Information Yield's bits (log₂N): one engine, three downstream numbers. Worked example (Starship IFT-2): partition floor 45 × PCP 10 × CP 2.5 × DH 3 ≈ 1-in-3,375 → 11.7 bits if confirmed, zero if not. Per-call one_in_n values: /api/v1/info-yield.json.
The luck test, corpus-level: under strict clustered scoring, 51 of 68 independent event-groups landed as called; the pre-registered break-even for the record’s claims is ≥65%, with falsification conditions stated before the test; the sittings ledger is 23/23. Full data: /api/v1/luck-test.json — significance with base-rate floors, never a skill trophy; a base-rate baseline still ties the headline Brier by construction.
The headline numbers this math sits under: the aggregate Brier is 0.0958 (launch-only subset 0.036); the could-it-be-luck significance is p≈2.2×10−⁵ (≈ 1-in-44,843) at a coin-flip floor per event; Information Yield runs a median 6.8 bits of against-consensus surprise per call, and the SITA decision-value profile a median of 71. The record sits on the Bitcoin-anchored seal manifest (manifestHash c5878fa3d9de…) — 104 sealed records, of which 92 are closed and graded into the Brier.