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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

Gravity

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

Derivation Tier Status Anchors Predictions
8-Tick Resonance in Gravity
Gravitational waves exhibit an 8-tick resonance signature 		Applied HYPOTHESIS 1 0
Acoustic Phase Levitation
Engineered phi-locked acoustic field induces measurable phase levitation 		Applied HYPOTHESIS 1 0
Black-Hole Echoes from RS Bounce
Predicted echo amplitudes in post-merger gravitational wave data 		Applied HYPOTHESIS 4 0
Gravitational Wave Amplitudes
Predicted GW amplitudes for BH/NS mergers anchored to RS energy budget 		Applied HYPOTHESIS 2 0
Rotation Curves Without Dark Matter
Galactic rotation curves emerge from RS ILG kernel without invoking dark matter halos 		Applied HYPOTHESIS 3 0
SPARC Galaxy Rotation Falsifier
RS predictions for ~150 SPARC galaxies fall inside a falsifier band 		Applied HYPOTHESIS 1 0
Spin Foam Realization
RS realization of loop quantum gravity spin foams 		Applied MODEL 1 0
Backreaction Audit
Gravitational backreaction effects audited and bounded 		Derived THEOREM 3 0
Baryonic Tully-Fisher Relation
The BTFR slope and intercept emerge from the RS gravity kernel 		Derived THEOREM 1 0
Black-Hole Entropy from the Ledger
Bekenstein-Hawking S = A/4 ell_P^2 is a direct ledger count 		Derived THEOREM 3 1
Black-Hole Recognition Bandwidth
Horizons saturate recognition bandwidth; entropy and temperature follow 		Derived THEOREM 1 0
Coercive Projection on the Recognition Substrate
Existence and uniqueness of a coercive projection that anchors gravity to RS 		Derived THEOREM 1 0
Coherence Collapse and Fall
Information-theoretic coherence collapse drives gravitational fall 		Derived THEOREM 3 0
Einstein-Hilbert Action from RS
The classical gravitational action emerges from discrete Regge calculus on the ledger 		Derived THEOREM 2 0
Gravitational Lensing from RS
Lensing deflection formula recovered from the RS curvature derivation 		Derived THEOREM 2 0
Hawking Temperature as a Rung
T_H = hbar c^3 / (8 pi G M k_B) sits on a canonical phi-ladder rung 		Derived THEOREM 1 0
Information is Preserved at the Horizon
Recognition flow preserves information; the firewall paradox is resolved 		Derived THEOREM 4 0
Information-Limited Gravity (ILG) Asymptotic Enhancement
The galaxy rotation flat-curve emerges from phi-ladder corrections without dark matter 		Derived THEOREM 5 0
Newton's G Runs with Recognition Scale
Effective G varies between galactic and lab scales by a calibrated factor 		Derived THEOREM 2 0
Nonlinear Regge Convergence
Discrete Regge converges to GR at high resolution, with explicit error bounds 		Derived THEOREM 2 0
Radial Acceleration Relation
The McGaugh RAR is a structural prediction of RS gravity 		Derived THEOREM 1 0
Schwarzschild Radius from RS
r_s = 2GM/c^2 reproduced from the RS gravitational kernel 		Derived THEOREM 1 0
Stress-Energy Tensor from RS
T_{mu nu} is a derived field on the recognition lattice 		Derived THEOREM 1 0
Weak-Field Conformal Regge Calculus
Conformal Regge calculus reproduces post-Newtonian limits 		Derived THEOREM 2 0
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.