LedgerSnapshot
LedgerSnapshot packages a discrete tick index with a nonnegative real defect to represent a ledger state at one moment. Researchers deriving the arrow of time from Recognition Science ledger updates cite it as the basic state object. The construction is a direct record type carrying the tick, defect value, and the single inequality constraint.
claimA LedgerSnapshot consists of a tick index $t$ (an element of the atomic Tick type) together with a defect value $d$ satisfying $d = J(x)$ for some $x > 0$ and $d ≥ 0$.
background
The TimeEmergence module identifies time with the ledger tick counter rather than a continuous manifold. A Tick is the atomic unit of temporal progression, ordered by its natural-number index; the ordering instances are defined directly on the index field. The defect field is supplied by the defect functional from LawOfExistence, which equals the J-cost and satisfies defect_nonneg for positive arguments.
proof idea
Direct structure definition that records the three fields: the Tick, the real defect, and the nonnegativity witness. No lemmas or tactics are invoked; the declaration simply bundles the components with the imported defect_nonneg constraint.
why it matters in Recognition Science
LedgerSnapshot supplies the state type for arrow_of_time, DefectMonotone, before, and the past/future constructions that establish F-006. It anchors the claim that time emerges as tick count and that the arrow of time coincides with monotonic defect decrease, linking directly to the eight-tick octave and the T0–T8 forcing chain.
scope and limits
- Does not introduce a continuous time parameter.
- Does not encode spatial coordinates or voxel data.
- Does not specify the evolution rule for defect between consecutive ticks.
- Does not prove defect monotonicity; that property is stated separately in DefectMonotone.
formal statement (Lean)
64structure LedgerSnapshot where
65 tick : Tick
66 defect : ℝ
67 defect_nonneg : 0 ≤ defect
68
69/-- Temporal ordering: snapshot A is before snapshot B iff its tick index is smaller. -/