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IndisputableMonolith.Foundation.TimeEmergence

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The TimeEmergence module defines the discrete tick as the atomic unit of temporal progression in the Recognition Science ledger. Time advances only through these indivisible steps rather than continuously. It supplies the basic objects and irreversibility properties that downstream work on orbits and dynamics requires. The module is built from upstream constants and the Law of Existence.

claimThe tick $T$ is the atomic unit of temporal progression with time quantum satisfying $T_0 = 1$ tick. Temporal advance occurs in discrete recognition steps; an epoch is a finite sequence of ticks and the arrow of time is the induced irreversible ordering.

background

The module imports Constants (defining the RS time quantum as one tick), Cost, DimensionForcing (establishing D=3), and LawOfExistence (x exists precisely when defect(x)=0). It introduces the tick as the ledger's indivisible temporal atom, epochs as ordered collections of ticks, DefectMonotone, and RecognitionStep together with the irreversibility property recognition_irreversible.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

It supplies the temporal primitives required by TimeAsOrbit (which identifies the tick sequence with the Lawvere natural-number object under successor) and by VariationalDynamics (which defines the ledger update map from state at tick t to state at t+1). The module thereby bridges the Law of Existence to the emergence of discrete time.

scope and limits

used by (2)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (4)

Lean names referenced from this declaration's body.

declarations in this module (19)