module module moderate

`IndisputableMonolith.Ecology.ExtinctionCascadeFromLedgerBankruptcy`

The module establishes definitions for extinction cascades in ecology triggered by ledger bankruptcy, anchored at the life-ignition rung Z_life = φ^19. It provides predicates and iteration functions for modeling cascade propagation on rung-based ecosystems. Theoretical ecologists applying Recognition Science to biodiversity would cite these for linking financial-style ledgers to species loss. Content consists of definitions and basic monotonicity properties.

claimDefines $Z_{life} := ϕ^{19}$ as life-ignition rung, IsBankrupt as antimono predicate on ecosystems, and cascadeStep, cascadeIterate as operators propagating bankruptcy steps from totalRung.

background

The module sits in the Ecology domain and imports Constants, where τ₀ is the RS time quantum equal to 1 tick. It introduces Z_life = φ^19 (cf. AbiogenesisFirstCrossing) as the rung threshold for life ignition on the phi-ladder. Sibling definitions cover Ecosystem, totalRung with positivity, IsBankrupt and its antimono property, plus cascadeStep and cascadeIterate for iterative propagation.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

Supplies foundational objects for ecological applications of Recognition Science, extending the phi-ladder and constants into biodiversity modeling via ledger bankruptcy. It positions Z_life = φ^19 as the entry point for life-related phenomena. No downstream theorems are recorded yet.

scope and limits

Does not simulate numerical extinction outcomes or time evolution.
Does not connect definitions to empirical species data.
Does not invoke the forcing chain T0-T8 or Recognition Composition Law.
Does not derive mass formulas or alpha-band constants.

depends on (1)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import

declarations in this module (24)

def Z_life L71
theorem Z_life_pos L73
theorem Z_life_gt_one L77
structure Ecosystem L85
def totalRung L97
theorem totalRung_pos L100
def IsBankrupt L112
theorem isBankrupt_antimono L121
def cascadeStep L137
theorem cascadeStep_subset L141
theorem cascadeStep_card_le L147
def cascadeIterate L154
theorem cascadeIterate_zero L159
theorem cascadeIterate_succ L162
theorem cascadeIterate_subset L165
theorem cascadeIterate_subset_initial L170
theorem cascadeIterate_card_monotone L178
def recoveryTime L187
theorem recoveryTime_pos L189
theorem recoveryTime_strict_mono L193
theorem deep_cascade_recovery_lower L204
structure ExtinctionCascadeCert L214
def extinctionCascadeCert L241
theorem extinction_cascade_one_statement L262