01
Initialisation 𝒜₀
On an empty ledger each process routes an immediate marketable order at ℓ = 0 and persists the realised fill — not the requested quote — as the lattice origin.
Market Weaver X instantiates two orthogonal, path-dependent inventory processes on a single underlying: each a discretely monitored, adverse-excursion-triggered accretion scheme on a fixed-mesh price lattice, carrying a piecewise-constant affine notional schedule and an absolute first-passage liquidation barrier on its aggregate mark-to-market. No state-space filtering. No directional forecast of the drift term. A purely endogenous, signal-free control law.
The control law is invariant to the drift μ of the underlying. State transitions are driven exclusively by realised adverse excursion relative to the extremal fill, and each cycle terminates on an absolute P&L first-passage event.
On an empty ledger each process routes an immediate marketable order at ℓ = 0 and persists the realised fill — not the requested quote — as the lattice origin.
Each adverse excursion of one lattice quantum Δκ beyond the extremal fill admits exactly one increment. Λ⁺ references the offer and Λ⁻ the bid, so the half-spread never contaminates Δκ.
Notional follows a non-geometric step function, affine in the tranche index and never multiplicative: q(ℓ) = q₀ + η·⌊ℓ / τ⌋
When the aggregate mark-to-market of the ledger, inclusive of swap carry, first crosses the absolute barrier Θ, the entire inventory is unwound together and the process re-initialises at ℓ = 0.
Λ⁺ may carry forty open tranches while Λ⁻ completes five full liquidation cycles. Neither process can observe, enumerate or unwind the other's inventory.
Accretes one tranche each time the offer declines one full lattice quantum below the infimum of its fill prices.
The exact reflection: accretes one tranche each time the bid rises one full lattice quantum above the supremum of its fill prices.
Identical closed form to the production controller. Perturb the parameters to observe the convexity of cumulative notional in ℓ, and the worst-case mark-to-market at terminal accretion.
At initialisation both ledgers are rebuilt from the live position book before any order is routed. A book of 22 Λ⁺ and 7 Λ⁻ tranches is recovered as exactly that — no spurious ℓ = 0, no index reset.
At most one increment per process per quote-arrival event. After every confirmed fill the book is re-read and the extremal anchor and trigger node κ(ℓ+1) are recomputed before any further increment is admissible.
When the underlying traverses several lattice nodes discontinuously, accretion proceeds one node per event with full re-evaluation between — never a burst of orders into a thin book.
If 17 of 20 tranches unwind and 3 are rejected, the cycle is not deemed terminated: the ledger stays in a re-entrant CLOSING state and retries until its cardinality is exactly zero.
Λ⁺ spacing is measured offer-to-offer and Λ⁻ bid-to-bid, so the spread cannot compress Δκ. The lattice anchors to the extremal fill, not the most recent one.
Netting accounts collapse opposing exposure into one net position. This is detected at initialisation, and the bilateral mode refuses to run there without an explicit override.
The control law is invariant with every overlay latent. Activated overlays are evaluated strictly before any accretion, and the microstructure gate never inhibits a liquidation.
Ledger cardinality, aggregate MTM, volume-weighted average cost, the next trigger node κ(ℓ+1) and every overlay state, streamed from the controller every few seconds.
Enter the telemetry plane