pith. sign in
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

Gravity

Spacetime, curvature, black holes, gravitational propagation, and Regge-limit derivations.

Derivation Tier Status Anchors Predictions
Equivalence Principle
Inertial and gravitational mass equal as a structural identity 		Foundational THEOREM 1 1
Five Canonical Causal Relations
Two events relate in exactly five ways; the cone structure is finite 		Foundational THEOREM 2 1
Gravity Propagates at the Speed of Light
Both ride the same recognition substrate; the ratio is exactly 1 		Foundational THEOREM 4 1
Quantum-Gravity Octave Duality
Recognition octave structure dualizes gravity and quantum theory 		Foundational THEOREM 2 0
Regge Calculus on the Recognition Lattice
Discrete simplicial curvature reproduces general relativity in the continuum limit 		Foundational THEOREM 6 0
Spacetime is Emergent
Spacetime arises as a coarse-grained projection of the recognition substrate 		Foundational THEOREM 1 1
Special Relativity Emerges
Lorentz invariance is a structural consequence of the recognition substrate 		Foundational THEOREM 1 0
Zero-Parameter Gravity
All gravitational predictions are made with zero adjustable parameters 		Foundational THEOREM 3 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.