IndisputableMonolith.Gravity.CoherenceCollapse
Gravity-sector module for coherence collapse: it packages the J-cost, recognition and rate actions, Born weights, and the coherence mass and lifetime scales. Gravity and measurement workers in RS cite these defs when linking collapse rates to the phi-ladder. The file is mostly definitions plus elementary positivity and normalization lemmas.
claimDefines the cost $J(x)=\frac{1}{2}(x+x^{-1})-1$, the rate and recognition actions built from $J$, the identity relating coherence cost to twice the action, Born weights $w=\sin^2$ with positivity and normalization, and the coherence mass and lifetime scales $m_{\mathrm{coh}}$ (kg) and $\tau_{\mathrm{coh}}$ (s).
background
Recognition Science measures mismatch with the symmetric cost $J(x)=\frac12(x+x^{-1})-1$, fixed uniquely in the forcing chain (T5) and obeying the Recognition Composition Law. In the gravity domain this cost is the seed for collapse and coherence bookkeeping rather than a free phenomenological potential.
The module sits on Constants (RS-native tick $\tau_0=1$) and Mathlib. Sibling definitions introduce nonnegativity of $J$, a rate action and its positivity, a recognition action, the relation that the coherence cost equals twice the action, Born weights with positivity, the $\sin^2$ identification, normalization, and dimensionful coherence mass and lifetime in SI units.
Local setting: coherence collapse as a gravity-side recognition process, with Born-type weights and explicit $m_{\mathrm{coh}}$, $\tau_{\mathrm{coh}}$ scales for later dynamical use.
proof idea
Definition module, not a single theorem. Core objects are defs: $J$, rate and recognition actions, Born weight, and the coherence mass/time constants. Supporting lemmas are elementary: nonnegativity of $J$ and of the rate action, positivity of Born weights, the trigonometric identity that the weight is $\sin^2$, Born normalization, and the algebraic identity that coherence cost equals twice the action. No deep tactic scripts; proofs are direct unfoldings and standard real-analysis facts.
why it matters in Recognition Science
Gives the gravity stack a single place for collapse cost, action, and Born weight so later gravity theorems can quote one vocabulary. The $J$-cost is the T5 landmark; packaging it with recognition action and $C=2A$ ties collapse bookkeeping to the same functional that forces $\phi$ and the eight-tick structure elsewhere. Born weight and normalization connect the collapse side to measurement-style probabilities. Dimensionful $m_{\mathrm{coh}}$ and $\tau_{\mathrm{coh}}$ supply SI anchors for phenomenological gravity or tabletop coherence estimates. No downstream edges are recorded yet; the module is an upstream definitions hub for the Gravity domain.
scope and limits
- Does not derive Einstein equations or a full gravitational field dynamics.
- Does not prove uniqueness of $J$ here; that lives in the forcing chain (T5).
- Does not fix numerical RS constants beyond what `Constants` already provides.
- Does not establish experimental bounds on $m_{\mathrm{coh}}$ or $\tau_{\mathrm{coh}}$.
- Does not contain a complete collapse dynamics or master equation.
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