The Math Ledger

I.The money identity and the hold-time term

The founding inequality frame law

Required-edge scaling in hold time design

A 14-day hold must earn ~14× the per-day edge of a 1-day flip to deserve the same capital. Turnover and sizing become one optimization; capital mechanically flows to the shortest hold clearing the sealed bar. The 14-day cap itself is a reasoned default awaiting the accrual curve (Build 1).

II.The Konstant value function, ported

v_fast implemented (home domain) port: design

The port is a feature adapter, not a rewrite: field→wallet (later entity), severity→normalized informedness (markout-derived), recurrence→cross-window persistence, embedding→behavioral fingerprint. The orphan term's pillar-independence is the load-bearing property: map o_i[d] to a tracker-visibility vector (d = each leaderboard, sold list, public recipe flag) and the term reads literally: high informedness × high persistence × invisible to every product.

The operational orphan definition design — census-refined

The visibility dimensions are concretely enumerable from the 103-source census. First-ever measurement of an orphan set = syncopation-port Build 5.

Fingerprint injection hypothesis (H-FINGERPRINT)

Wallet behavioral fingerprints (markets, timing, sizing, category mix) in a content-addressed structure so entity continuity survives address rotation; enters v_fast through the sanctioned redundancyMatrix override — injection, never modification of the patent path. Weight calibration teacher in our domain = realized markout (Konstant's nightly LLM teacher, upgraded: settlements don't hallucinate).

III.Interaction math and the symmetry fact

Pairwise uplift / Shapley interaction implemented, formally checked

The symmetry fact (the arc's sharpest catch): uplift is symmetric in i and j — an arithmetic identity. No windowing scheme can extract direction from the value function. Who-triggers-whom must come from a temporal-precedence layer outside v(S), entering the Konstant code only at its two sanctioned injection points: typed relationships and the redundancy override.

The trigger primitive design

Decision episodes (same entity/market/direction, sessionized) are the grain; chain-true fills are the atom — because WS-feed direction inference is only ~59% accurate vs on-chain truth measured (census, Dubach). Alert channels are mediator super-nodes inside the graph, never exogenous clocks: leader→alert→crowd is the copy-contagion chain.

IV.Settlement math (the settle half)

Exact Shapley on ratio KPIs implemented, externally reviewed

Complementary-contribution sampling for n>20 (CC_N(S) = U(S) − U(N\S), size-stratified); Owen values for grouped players — the estimator family the unit-of-signal ablation will use: wallet-history vs category vs flow feature groups compete for markout-prediction credit, and the winning group is the unit design, first post-gate build.

The June external review verified fixes in every file read

15 defects (3 critical): anti-conservative CC variances, future-leaking top-N segment maps, interpolated conformal quantiles, ratio-game singular denominators. Fixes are landed in each file opened so far; worker T8 is verifying all 15 plus the 164 math commits the reviewer never saw.

V.The serve half, honestly labeled

Additive amortizer v̂ poc — "validated with ZERO real data" (its own header)

The gradient frontier poc — sound math, projection band only

The correction this review forced: the "hierarchical partial-pooling Bayesian surrogate whose posterior variance is the band" exists in prose, not code; in its home harness the promotion gate refused every candidate (champion: carry_forward). "Size by the calibrated gradient" is re-labeled: gradient-sized (RMSE band + FLOOR 8) works today; calibrated-gradient-sized is a build. Docs describing the destination as the present is the failure mode this ledger exists to prevent.

Conformal calibration implemented, exemplary honesty (home domain)

VI.Identification and the null ladder design, pre-registered

Every pair gets a four-way label — exogenous-response / candidate-contagion / pre-clock-informed / unidentified — never collapsed. The claim standard is Granger-class predictive triggering, never "causes." Positive control before discovery: if the method can't detect the copy-bots we know exist (published ~1.8s lags), it has no business claiming orphan leaders — the port halts nearly free.

VII.The alert-echo experiment design (E-ALERT-ECHO), sealed 65/40/30

Second-order consumption of sold signals: a sold edge decays for its subscribers as it sells; as our input it grows with subscriber count. Doctrine, in the owner's words: "we don't buy edges — but we might buy other people's edges to use as input signal to create an edge."

VIII.Open mathematical questions

The unit of signal — wallet vs entity vs market-type vs flow vs event; group-Shapley credit decides design. H-ROTATION — attractor wallets manufacturing follower flow then harvesting it from fresh addresses; detection = rising trigger-out that goes quiet + timing-correlated counter-side size + entity linkage hypothesis. The accrual curve / taker cost gate — both were anchored on CALL-017's +3.01c, and the scale verdict (2026-08-11) mooted them: at 230,977-wallet power the persistence does not scale — trade-weighted crude decile +0.02c n.s. vs eligible-rest −0.84c (informed wallets stop losing, they don't win), and none of the refined selections (orphan-invisibility, v_fast composite, DPP diverse) recover it; all paired-lift CIs negative measured, 2.7M/73.5M trades, clustered. The +3.01c reproduces exactly on its own 300 markets — real on the slice, an artifact at scale. Family closed at the own-entry estimand, pending the chain-built cross-check now running. Wash-aware denominators — up to ~60% of weekly volume is wash at peaks; no volume-derived quantity is meaningful without the entity pre-pass measured (census, Columbia).

IX.Structured strategies — the joint payoff is the object

The synthesis the full-width results forced (2026-08-11): the venue's MARGINS are efficient; its JOINTS are not. Marginal calibration — null at 531M trades. Informed-wallet persistence — null at 230k wallets. Copy-crowd reaction — real phenomenon, negative economics. The one family that survived full-window scale is the interaction object: combo joint probabilities overpriced +2.64pp against the correlation-adjusted product of their own marginals. Where the marginals are right and the joint is wrong, the mispricing lives in the dependence structure — precisely the term Precise's interaction math prices and additive attribution cannot. Next family dispatched accordingly: the within-event Dutch-book court (EVENT-SUM — do mutually-exclusive outcome books sum to 1?).

The altitude shift (2026-08-10): stop pricing single directional bets, price structured multi-leg positions the way an options desk does. This is not a detour from the math — it is the math's native home, because a multi-leg payoff is an interaction object, exactly what Shapley/Shapley-Taylor computes. The first clear signal of the arc is one of these — and it survived the full window (2026-08-11): combo-YES priced +2.638pp above the correlation-adjusted fair joint measured, CI [+2.539,+2.736], N=399,867 combos, 0 mis-oriented, 62k untouched confirmations; the structured hedge-leg trade nets +5.18c/combo after modeled costs at the 5pp pre-trade screen CI [+4.75,+5.61], 11.8k rows, dose–response +2.6→+5.2→+7.1c as the screen deepens. The July-1 +5.44pp point (N=3,822) was the discovery slice; the full-window number is the one that stands.

The menu, each a joint-payoff object: combo dispersion (maker-provide Combo-NO / leg-hedge — re-shaped by the execution court) arc complete, SHELF-001; correlation trades (isolate and trade the combo-implied correlation) design; favorite–longshot spreads — CLOSED by the full-width calibration court (08-11): 531M trades, 12/13 bands show NO familywise miscalibration; the venue's margins are efficient; the one nominal signal (0–2c longshots, −0.21c) failed its preregistered negative control and was refused promotion null, full corpus; portfolio baskets neutral to the market factor, long the specific edge, sized by the Precise gradient design.

X.Why this is AdTech (and every attribution vertical)

The structured-strategy math is not analogous to media attribution — it is media attribution, on a fast-settling instrument. A conversion is a joint outcome of correlated touchpoints, exactly as a combo is a joint of correlated legs. Read the map straight:

The through-line: the edge lives in the correlation term that additive/independence-assuming attribution gets wrong. Polymarket combos are the cheapest place to prove the interaction-aware method that AdTech (and insurance, credit, clinical-arm attribution) needs but can't validate in under a quarter.

XI.Patentable Precise methodology — the orphan-detection analog

Konstant patents the structural methods (v_fast, orphan, syncopation, DPP): "find the high-value thing the standard tracker misses." The Precise analog is a contribution method: find the credit the standard attribution mis-prices. The combo result is its reduction-to-practice. Candidate claims (technical articulation only — filing, ownership, and legal scope are the founder packet's, not this page):

Candidate 1 is the one that rhymes with orphan detection and it already has a worked example on a real instrument. The novelty to defend is the gap-as-detector-plus-gradient-sized-harvest, sealed and calibrated — not "using Shapley," which is prior art.

Prior-art scan result web-verified, 2026-08-10: the broad ideas are occupied — Shapley marginal credit (US8775248B1), comparing attribution models on the same path (US8788339B2), Shapley-vs-last-click for correlated channels (Nisar & Yeung), marginal-derivative allocation (US8417564B2), counterfactual-with-CI + bid adjustment (US10977697B2), impact-optimized execution (US8571967B1), and Sellforte runs the whole loop commercially. Candidate 1: CROWDED (0.82) — but a narrow residue is open: no source claims the precise ordered protocol — the signed interaction-vs-additive GAP as a repeated detector statistic + a cluster-exchangeable conformal gate + gap-gradient sizing with actor-impact + sealed settlement + explicit refusal states. That specific protocol, not "Shapley attribution," is the defensible claim. Candidate 2: CROWDED (0.80) — defensible only if it binds the same sealed settlement game to the served model, the analytic derivative, a derivative-specific refusal, and a pre-action reproducibility receipt. Candidate 3: OCCUPIED (0.92) — US8412617B1 already discloses remove-own-impact/simulate-alternative-impact; rescuable only if our own action changes the coalition value function itself and the Shapley settlement is recomputed on that action-indexed game. Honest takeaway: there is a patentable Precise method, but it's the narrow sealed-detector protocol, not the concept.