IndisputableMonolith.Core.Recognition
The Core.Recognition module organizes the foundational recognition primitives by importing the base Recognition module that establishes T1. Researchers deriving physics constants and the forcing chain from the single functional equation would cite this module as the entry point for core definitions. It contains no proofs and functions purely as an organizational layer that exposes the recognition axioms to downstream code.
claimT1 (MP): Nothing cannot recognize itself, serving as the base for the Recognition Composition Law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$ and the subsequent forcing chain.
background
The module imports Mathlib and IndisputableMonolith.Recognition. The upstream Recognition module supplies T1 (MP): Nothing cannot recognize itself. This axiom initiates the derivation of all physics from one functional equation, with the J-cost function defined as $J(x) = (x + x^{-1})/2 - 1$ and the phi-ladder constructed from the self-similar fixed point.
proof idea
This is a definition module with no proofs. It consists solely of imports that re-export the core recognition structure from the base Recognition module, providing namespace access without additional lemmas or tactics.
why it matters in Recognition Science
The module supplies the core recognition foundation imported by the ComputationBridge scaffold in Complexity.ComputationBridge, which explores a hypothetical ledger-style P vs NP framework. It directly anchors T1 and feeds the certificate chain steps that produce the eight-tick octave and D = 3 dimensions.
scope and limits
- Does not contain theorem proofs or sorry statements.
- Does not implement the full forcing chain T0-T8 or physical constants.
- Does not resolve P vs NP questions; those remain in downstream exploratory scaffolds.
- Does not define mass formulas or the alpha band.