Ledger
plain-language theorem explainer
The structure supplies a carrier type equipped with optional state and tick bookkeeping fields for recognition specifications. Modules handling observable projections reference it to maintain canonical states without extra overhead. The declaration is a direct structure definition that composes the carrier with defaulted Option fields.
Claim. A ledger consists of a type $C$ serving as carrier, an optional element of $C$ as state, and an optional map from $C$ to natural numbers as tick function, all with default none values.
background
In the RecogSpec.Core module the structure provides a minimal carrier for states used in observable payloads. It draws on the tick definition from Constants, which sets the fundamental RS time quantum with one octave equal to eight ticks. The sibling Bridge structure extends the same carrier to add equivalence relations over ledgers.
proof idea
The declaration is a structure definition that introduces the carrier field together with defaulted optional state and tick components.
why it matters
This definition establishes the base carrier for ledger-based bookkeeping in recognition specifications and supports the Bridge sibling for units equivalence. It incorporates the fundamental tick quantum that aligns with the eight-tick octave in the forcing chain. No downstream theorems are recorded yet.
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