IndisputableMonolith.Foundation.GlobalCoIdentityConstraint
The GlobalCoIdentityConstraint module defines the canonical fractional-part projection from reals to the unit interval and assembles theorems on uniqueness and existence of global phases under the co-identity constraint. Researchers working on the GCIC paper or the Consciousness layer would cite it for phase consistency results. The module imports graph rigidity and reduced phase potential to construct the objects without internal proofs.
claimThe canonical projection $frac:ℝ→[0,1)$ satisfies $frac(x)=x-⌊x⌋$. The global co-identity constraint requires that the reduced phase potential $J̃_b(δ)=cosh(λ⋅d_ℤ(δ))−1$ vanishes on a connected graph if and only if the phase field is constant modulo integers, with $λ=ln b$ and $d_ℤ$ the distance to the nearest integer.
background
This module sits in the Foundation domain and supplies the Global Co-Identity Constraint (GCIC) machinery. It re-states the fractional-part projection locally to avoid import cycles with the Consciousness layer. Upstream, Constants supplies the RS time quantum τ₀=1 tick. GraphRigidity proves that the ratio energy C_G[x]=Σ J(x_v/x_w) vanishes if and only if x is a constant positive field. ReducedPhasePotential defines the reduced phase-mismatch potential J̃_b(δ)=cosh(λ⋅d_ℤ(δ))−1 induced by the discrete scaling quotient.
proof idea
This is a definition module, no proofs. It imports Mathlib, Cost, Constants, GraphRigidity, and ReducedPhasePotential to define wrapPhase together with the GCIC theorems on global phase uniqueness, existence, and independence of basepoint and path.
why it matters in Recognition Science
The module supplies the global phase uniqueness and existence results that feed the Consciousness layer. It fills in GCIC paper Result 1 on graph rigidity and Section IV on the reduced phase potential. It supports phase consistency in the Recognition Science framework by ensuring fields satisfy the co-identity constraint independently of path or basepoint.
scope and limits
- Does not address infinite or disconnected graphs.
- Does not derive new physical constants or mass formulas.
- Does not prove theorems inside the Consciousness module.
- Does not handle non-positive or zero fields.
depends on (4)
declarations in this module (14)
-
def
wrapPhase -
theorem
wrapPhase_bounds -
theorem
wrapPhase_add_int -
theorem
wrapPhase_eq_of_int_diff -
theorem
gcic_global_phase_unique -
theorem
gcic_existence_of_global_phase -
theorem
gcic_global_phase_independent_of_basepoint -
theorem
gcic_global_phase_independent_of_path -
def
lam_canonical -
theorem
lam_canonical_ne_zero -
theorem
gcic_canonical -
structure
GlobalCoIdentityConstraintCert -
def
gcicCert -
theorem
gcic_one_statement