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Pith / Derivations

Derivations from first principles

Every entry below begins from the Recognition Science primitives (ledger, tick, voxel, cost composition law) and ends at a measurable consequence. Each step is a clickable Lean theorem; every empirical claim carries a named falsifier. 222 published of 246 tracked.

Domains: All Applied 7 Biology & medicine 1 Consciousness & ethics 11 Fundamental constants 23 Cosmology 37 Gravity 32 Mathematics & foundations 29 Particle physics 55 Quantum mechanics 27
Tiers: All Applied 23 Derived 148 Foundational 51

Recently published

Consciousness & ethics

Sigma-equilibration, ethics, virtue, consent, and awareness as recognition-cost consequences.

Derivation Tier Status Anchors Predictions
Consciousness Bandwidth
Awareness throughput is a recognition-bandwidth quantity 		Derived THEOREM 1 0
Consent Interface from J-Cost
Consent is the J-cost-minimizing protocol for joint recognition 		Derived THEOREM 1 0
Extraction is Thermodynamically Unstable
Net-extraction strategies cannot persist; equilibration always wins 		Derived THEOREM 1 0
Love as the Unique Equilibrating Virtue
Among virtues that drive sigma to zero, love is the unique stable target 		Derived THEOREM 1 1
Moral Debt as Accumulated Imbalance
Unredressed recognition imbalance forms a ledger of moral debt 		Derived THEOREM 1 0
Recognition Bandwidth Saturation
Every physical system has a finite recognition bandwidth; saturation drives observable effects 		Derived THEOREM 3 0
Stake Graph
The graph of who has a stake in a recognition event is forced by event topology 		Derived MODEL 1 0
Virtue Generators from J-Cost
The classical virtues are J-cost generators of recognition equilibration 		Derived THEOREM 4 0
Virtues Form a Finite Lattice
All possible virtue combinations live in a finite, enumerable lattice 		Derived THEOREM 4 0
Recognition Cost Model for Ethics
All ethical evaluations reduce to a recognition cost J(stakes) 		Foundational THEOREM 1 0
Sigma Equilibration as Drive
The drive to equilibrate recognition imbalance is the basis of ethical action 		Foundational THEOREM 2 0

How to read these pages

Pith derivations are a hybrid of narrative explanation and machine-checked proof. Anything tagged THEOREM is backed by a Lean 4 proof in the canonical Recognition library; the corresponding declarations are linked inline. A tag of HYPOTHESIS means the claim is empirically falsifiable but not yet formally derived; a MODEL tag means the claim is a definitional choice. OPEN is reserved for active gaps.

Direct URL: https://pith.science/derivations/<slug>. JSON form: https://pith.science/derivations/<slug>.json. Search: https://pith.science/derivations/search.json?q=.... No nav link by design. Cite a derivation by its stable URL plus the version number printed at the top of the page.