module module high

`IndisputableMonolith.Archaeology.PotterySerialFromJCost`

This module defines per-style popularity at scaled time s = t/τ as 1/(1 + J(s)) for s > 0, drawing on the J-cost from Recognition Science. Archaeologists modeling artifact popularity curves would cite these definitions. The module consists of definitions plus basic nonnegativity and bound lemmas with no complex proofs.

claim$popularity(s) = 1/(1 + J(s))$ for $s > 0$, where $s = t/τ$ and $J$ is the J-cost function.

background

The module imports Constants, which sets the fundamental RS time quantum τ₀ = 1 tick, and Cost, which supplies the J-cost. It introduces scaled time s = t/τ and the popularity function popularity s = 1/(1 + J(s)) for s > 0. This places the definitions in the Archaeology domain of the Recognition Science framework.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

This module supplies the popularity function that feeds PotterySerialCert and related certificates within the same module. It applies the J-cost to archaeological modeling and connects to the RS forcing chain through the imported Cost and Constants modules.

scope and limits

Does not derive numerical values for specific pottery styles.
Does not connect to empirical archaeological datasets.
Does not extend the model to artifact types other than pottery.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (13)

def popularity L44
theorem popularity_peak L49
theorem Jcost_nonneg_of_pos L55
theorem popularity_nonneg L67
theorem popularity_pos L78
theorem popularity_le_one L85
def adjacencyGap L98
theorem adjacencyGap_eq L100
theorem adjacencyGap_pos L117
theorem adjacencyGap_band L122
structure PotterySerialCert L131
def potterySerialCert L139
theorem pottery_serial_one_statement L150