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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

Quantum mechanics

Quantum mechanics as the small-tick limit of recognition dynamics.

Derivation Tier Status Anchors Predictions
Superconducting Qubit Coherence
Predicted coherence times for transmon and fluxonium qubits 		Applied HYPOTHESIS 3 0
Bell Inequality Violation
RS predicts the Tsirelson bound for Bell violations 		Derived THEOREM 1 1
Caldeira-Leggett Friction
Quantum friction reproduced from RS recognition dissipation 		Derived THEOREM 1 0
Classical Limit Emergence
Pointer-state decoherence reproduces classical mechanics at large recognition counts 		Derived THEOREM 2 0
Double-Slit Interference Pattern
Classical double-slit fringes recovered from RS recognition flow 		Derived THEOREM 1 0
Entanglement Entropy Area Law
Entanglement entropy scales with area, not volume 		Derived THEOREM 2 0
Holographic (Bekenstein) Bound
Information content of any region is bounded by horizon area 		Derived THEOREM 1 0
Nonlocality Without Signaling
RS preserves no-signaling under entangled recognition events 		Derived THEOREM 1 0
Page Curve of Black-Hole Evaporation
Entropy follows the canonical Page curve; information is preserved 		Derived THEOREM 1 0
Path Integral Measure
Feynman's path-integral measure is the RS recognition trajectory weight 		Derived THEOREM 1 0
Photoelectric Effect
Einstein's photoelectric relation falls out of RS quantization 		Derived THEOREM 2 0
Photon Statistics
Bose-Einstein photon statistics from recognition counting 		Derived THEOREM 1 0
Quantum Decoherence from J-Cost
Decoherence rates are predicted by J-cost dissipation channels 		Derived THEOREM 2 0
Quantum Error Correction Bounds
RS predicts logical error-rate scaling for surface codes 		Derived THEOREM 3 0
Quantum Field Operators from RS
Standard quantum field operator algebra emerges from recognition operators 		Derived THEOREM 3 0
Quantum Hall Effect
Integer and fractional Hall plateaus from RS phi-quantization 		Derived THEOREM 1 0
Quantum Mechanics at the Planck Scale
Spacetime discreteness and quantum mechanics merge at the Planck scale 		Derived THEOREM 2 0
Quantum Tunneling from J-Cost
Tunneling rates predicted from the J-cost barrier 		Derived THEOREM 1 0
Quantum Zeno Effect
Frequent recognition events suppress dynamical evolution as predicted 		Derived THEOREM 1 0
Recognition Hamiltonian Spectrum
The Hamiltonian spectrum is forced by recognition-coupling rules 		Derived THEOREM 3 0
Solid-State Physics from RS
Band structure, semiconductor physics from RS configuration space 		Derived THEOREM 3 0
Statistical Mechanics from RS
Boltzmann distribution and partition function recovered from recognition counts 		Derived THEOREM 3 0
Superconductivity and Superfluidity
Cooper-pair recognition coherence drives both phenomena 		Derived THEOREM 2 0
Thermal Fixed Point Universality
RS universality classes for critical phenomena 		Derived THEOREM 2 0
Dirac Equation from RS
The Dirac equation arises as the RS spin-1/2 recognition kernel 		Foundational THEOREM 3 0
Schroedinger Equation Emerges from RS
i hbar partial_t psi = H psi appears as the small-tick limit of recognition dynamics 		Foundational THEOREM 4 0
Wavefunction Collapse as Recognition
Measurement-induced collapse is the RS recognition event in the small-tick limit 		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.