module module high

`IndisputableMonolith.Ethics.Virtues.Independence`

This module defines the four categories of ethical transformation in the Recognition Science framework. It introduces VirtueCategory as the classification structure and EffectSignature for operational impacts, together with concrete signatures for ten listed virtues. Researchers formalizing ethics or extending foundational systems would cite it to organize virtue-based transformations. The module consists solely of definitions with no proofs.

claimThe module establishes four categories of ethical transformation, with core objects $VirtueCategory$ and $EffectSignature$, together with signatures $loveSignature$, $compassionSignature$, $sacrificeSignature$, $justiceSignature$, $temperanceSignature$, $humilitySignature$, $wisdomSignature$, $patienceSignature$, $prudenceSignature$, and $forgivenessSignature$.

background

The module resides in the Ethics domain of the Recognition Science mirror and imports only Mathlib. It supplies the local theoretical setting by organizing ethical virtues into four transformation categories that extend the broader framework beyond its physical derivations. Key definitions introduced are VirtueCategory for grouping ethical concepts and EffectSignature for capturing their effects, as declared among the sibling names.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

This module supplies the categorical structure for ethical virtues that larger Ethics-domain constructions rely upon. It fills the definitional step for the four categories of ethical transformation, providing the base objects before any application in parent theorems or extensions of the Recognition Science chain. No downstream theorems are recorded, yet the module supports formalization of ethical concepts alongside the T0-T8 forcing chain and RCL.

scope and limits

Does not prove any theorems about the virtues or their interactions.
Does not connect the categories to physical constants, the phi-ladder, or J-cost.
Does not specify mathematical relations or composition rules among the virtue signatures.
Does not detail integration with the core Recognition Composition Law or eight-tick octave.

declarations in this module (35)

inductive VirtueCategory L21
structure EffectSignature L29
def loveSignature L36
def compassionSignature L37
def sacrificeSignature L38
def justiceSignature L39
def temperanceSignature L40
def humilitySignature L41
def wisdomSignature L42
def patienceSignature L43
def prudenceSignature L44
def forgivenessSignature L45
def gratitudeSignature L46
def courageSignature L47
def hopeSignature L48
def creativitySignature L49
def allSignatures L51
theorem allSignatures_length L59
theorem Relational_ne_Systemic L63
theorem Relational_ne_Temporal L66
theorem Relational_ne_Facilitative L69
theorem Systemic_ne_Temporal L72
theorem Systemic_ne_Facilitative L75
theorem Temporal_ne_Facilitative L78
theorem sig_ne_of_cat_ne L83
theorem sig_ne_of_idx_ne L86
theorem all_signatures_distinct L95
def SignatureIndependent L102
def SignatureSetMinimal L105
def SignatureSetComplete L108
theorem all_signatures_minimal L113
theorem signatures_complete L116
theorem signatures_non_redundant L119
theorem all_virtues_independent L132
theorem virtue_signatures_minimality_complete L177