χTopic tag
#metastability
5 documents indexed here. Mathematical objects, methods, systems, and recurring technical questions.
ℓNotes
5- Notes
Fruit
Low-conductance clusters as the basic unit of cohesive existence. Cheeger conductance, the fruit definition with threshold θ, and Theorems A (Energy Isolation) and D (Metastability).
- Notes
Main Theorems A–H
Complete statements and full proofs of the eight core theorems of RelationWorld Theory — energy isolation, door finiteness, self-interpretation, metastability, curvature localisation, spectral stability, door stability, and flow stability.
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Part II · Main Theorems A–H (summary)
A condensed statement of the eight main theorems of RelationWorld Theory with one-paragraph proof ideas and their logical dependencies. Full proofs live in the research archive.
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Theorem D — Metastability
The expected escape time from a fruit under the lazy walk is at least 1/(2 theta), via the Cheeger inequality and the Sinclair–Jerrum spectral bound.
- Notes
T7-Enhanced — Non-Idempotent Metastability Advantage
At a non-idempotent closure fixed point with operator norm < 1, the closure Hessian contribution is strictly positive definite (n/n positive eigenvalues). For idempotent closure, only n-k of n eigenvalues are positive. The mathematical payoff of SCC's deliberate non-idempotence commitment.