IndisputableMonolith.Foundation.TimeEmergence
The TimeEmergence module introduces discrete time in Recognition Science by defining the ledger tick as the atomic unit of temporal progression. Time advances only in discrete steps tied to recognition events rather than flowing continuously. Researchers deriving spacetime structure from the forcing chain would cite it when linking constants and the Law of Existence to temporal discreteness. The module consists of definitions and imports that organize the discrete-time primitives for later use.
claimThe atomic time unit is the tick satisfying $\tau_0 = 1$ tick, with temporal progression occurring via discrete recognition steps where an entity exists precisely when its defect vanishes.
background
The module imports the RS time quantum $\tau_0 = 1$ tick from Constants. It draws on the Law of Existence, which states that $x$ exists if and only if defect$(x) = 0$. DimensionForcing supplies the spatial setting with $D = 3$ forced by the framework. The local theoretical setting is the emergence of time from recognition processes in the ledger after the existence and dimension results are in place.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
It supplies the temporal primitives that TimeAsOrbit uses to identify Tick as the Lawvere natural-number object forced by recognition. VariationalDynamics relies on it to formalize the ledger update rule from state$(t)$ to state$(t+1)$. The module advances the forcing chain by discretizing time after the Law of Existence and dimension results.
scope and limits
- Does not derive continuous time from any background manifold.
- Does not compute epoch lengths or tick counts.
- Does not address relativistic transformations of ticks.
- Does not connect ticks to specific mass or coupling formulas.
used by (2)
depends on (4)
declarations in this module (19)
-
structure
Tick -
structure
Epoch -
def
epoch_length -
theorem
epoch_length_eq -
def
tick_within_epoch -
structure
LedgerSnapshot -
def
before -
structure
DefectMonotone -
def
arrow_of_time -
theorem
arrow_well_defined -
structure
RecognitionStep -
theorem
recognition_irreversible -
def
present -
def
past -
def
future -
theorem
past_is_fixed -
theorem
time_is_discrete -
theorem
minimal_temporal_resolution -
theorem
time_emergence_certificate