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 — when does the +3.01c materialize (front-loaded vs linear); decides fund-vs-footnote Build 1, in flight. The taker cost gate — does >2c survive spread + fee + trade+1 haircut Build 2 / CALL-018. 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).