IndisputableMonolith.Gravity.CoherenceCollapse
Gravity.CoherenceCollapse supplies the J-cost functional and derived objects for coherence collapse modeling in gravitational settings. It defines J(x) = ½(x + x^{-1}) - 1 together with action rates, Born weights, and coherent mass and time scales. Researchers deriving RS-based collapse rates or normalization conditions cite these objects. The module consists of direct definitions and elementary algebraic positivity statements.
claim$J(x) = ½(x + x^{-1}) - 1$, rate_action, recognition_action, born_weight = sin²θ with normalization, C = 2A, m_coh in kg, and τ_coh in s.
background
Recognition Science derives physics from a single functional equation whose core object is the J-cost. This module sits in the Gravity domain and imports the base time quantum τ₀ = 1 tick from Constants. It introduces J-cost as the recognition cost measure J(x) = ½(x + x^{-1}) - 1, non-negative rate quantities, and Born-rule weights.
proof idea
This is a definition module. It states Jcost by the standard formula, proves non-negativity by direct expansion, defines rate_action and recognition_action with positivity, sets born_weight = sin²θ together with its positivity and normalization, records the C_equals_2A relation, and introduces the physical scales m_coh_kg and tau_coh_s.
why it matters in Recognition Science
The module supplies the J-cost and coherence quantities that support gravitational collapse calculations within Recognition Science. It connects to the J-uniqueness step of the forcing chain and supplies objects used for mass-ladder and action derivations. No downstream theorems are listed in the current graph.
scope and limits
- Does not derive gravitational field equations.
- Does not assign numerical values to coherent masses.
- Does not treat multi-particle or entangled coherence.
- Does not invoke the Recognition Composition Law.
depends on (1)
declarations in this module (17)
-
def
Jcost -
theorem
Jcost_nonneg -
def
rate_action -
theorem
rate_action_pos -
def
recognition_action -
theorem
C_equals_2A -
def
born_weight -
theorem
born_weight_pos -
theorem
born_weight_is_sin_sq -
theorem
born_normalization -
def
m_coh_kg -
def
tau_coh_s -
theorem
m_coh_positive -
theorem
m_coh_nanogram_range -
def
post_orthogonality_plateau -
structure
CoherenceCollapseCert -
theorem
coherence_collapse_cert