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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

Particle physics

Standard-Model masses, gauge couplings, mixing matrices, and representation counts.

Derivation Tier Status Anchors Predictions
Sterile Neutrino Exclusion
Eg parametric exclusion of an eV-scale sterile neutrino 		Applied HYPOTHESIS 1 0
String Theory from J-Cost
If strings exist, RS forces specific compactification structure 		Applied MODEL 3 0
Supersymmetry is Spontaneously Broken at the RS Scale
RS predicts a specific SUSY breaking pattern; sparticle masses lie above the EW scale 		Applied MODEL 1 0
W-Mass Anomaly Structure
RS prediction for the W-mass anomaly relative to Standard-Model expectations 		Applied HYPOTHESIS 1 0
alpha_QED Running with Energy
The QED coupling runs predictably from low to high energy 		Derived THEOREM 3 0
alpha_s Two-Loop Running
The strong coupling runs through canonical RS thresholds at two loops 		Derived THEOREM 4 0
Baseline Numerical Mass Predictions
Concrete numerical predictions for the full Standard-Model spectrum 		Derived THEOREM 1 0
Baseline RS Mass Predictions
Closed-form mass predictions and their consistency lemmas 		Derived THEOREM 1 0
Charged Lepton Ladder
Electron, muon, tau placed at rungs 27, 32, 37 on phi-ladder 		Derived THEOREM 2 3
CKM Quark Mixing Matrix
All four CKM angles and the CP phase emerge from the cube topology 		Derived THEOREM 2 1
Coherence Exponent for the Mass Yardstick
The exponent that ties the yardstick to phi^5 emerges from the cost-composition law 		Derived THEOREM 1 0
Electron Mass on the Phi-Ladder
m_e is forced at rung 27 of the phi-ladder with proved positivity 		Derived THEOREM 4 1
Electroweak Symmetry Breaking
Higgs vacuum expectation value emerges; no fine tuning 		Derived THEOREM 2 0
Electroweak VEV is Not a Free Parameter
v lives on a specific phi-ladder window; the Higgs mechanism dissolves the hierarchy puzzle 		Derived THEOREM 6 1
Family Mass Ratios Are Proved
Inter-generation mass ratios are exact phi-power identities 		Derived THEOREM 1 0
Gap-Function Forcing
The Z-dependent gap correction is structurally forced; no free parameter 		Derived THEOREM 1 0
Gauge Boson Verification
Cross-check of W, Z masses against RS phi-ladder 		Derived THEOREM 1 0
Higgs EFT Bridge
Higgs effective field theory parameters live on canonical phi-rungs 		Derived THEOREM 3 0
Higgs EFT Low-Energy Limit
The Higgs EFT reduces to canonical SM-Higgs in the low-energy limit 		Derived THEOREM 1 0
Higgs Observable Skeleton
All Higgs observable predictions in one structure 		Derived THEOREM 1 0
Higgs-Yukawa Bridge
Yukawa couplings sit on phi-ladder positions that reproduce fermion masses 		Derived THEOREM 2 0
J-Cost Perturbation Closes the Mass Sub-Leading Terms
The 88-lemma perturbative expansion sets sub-leading mass corrections 		Derived THEOREM 2 0
Longitudinal Vector Scattering Unitarity
RS preserves unitarity in WW->WW scattering at high energy 		Derived THEOREM 1 0
Mass Anchor Policy
Rules that fix mass anchors and their gap windows 		Derived MODEL 3 0
Muon/Electron Mass Ratio
The dimensionless ratio m_mu/m_e is bracketed by the RS phi-ladder spacing 		Derived THEOREM 1 1
Neutrino Mass Hierarchy
Normal hierarchy is forced; inverted hierarchy is excluded 		Derived THEOREM 1 0
Neutrino Yardstick and Hierarchy
Neutrino masses share a yardstick that fixes the normal hierarchy 		Derived THEOREM 3 0
Particle Physics Depth from RS
Hierarchical particle physics emerges from RS recognition layers 		Derived THEOREM 1 0
Pion Mass Spectrum
Charged and neutral pion masses sit at canonical light-quark rungs 		Derived THEOREM 1 0
PMNS Neutrino Mixing Matrix
Three mixing angles plus CP phase forced by RS Q3 representations 		Derived THEOREM 4 1
Proton Mass
QCD binding plus quark rungs give the proton mass within the RS gap window 		Derived THEOREM 2 1
Quark Coordinate Reconciliation
Quark masses and mixing reconcile across reference frames 		Derived THEOREM 1 0
Quark Mass Ladder
Up, down, strange, charm, bottom, top quarks at canonical phi-rungs 		Derived THEOREM 3 0
Radioactive Decay Types
Alpha, beta, gamma decays fall out as RS recognition channels 		Derived THEOREM 1 0
Renormalization Group Transport
Couplings, masses and operators transport along the RG flow consistently 		Derived THEOREM 2 0
Standard Model Group Structure
SU(3)xSU(2)xU(1) emerges as the unique gauge structure from RS 		Derived THEOREM 2 0
Standard-Model Mass Hierarchy
The qualitative ordering m_e < m_u < m_d < ... is forced 		Derived THEOREM 1 0
Strong CP and the Theta Vacuum
The CP-violating theta_QCD is forced to be statistically zero 		Derived THEOREM 1 0
Strong Force from RS
QCD confinement at low energy emerges as an RS color-binding bound 		Derived THEOREM 3 0
Symmetry Breaking Pattern
All Standard-Model symmetry breakings reduce to RS recognition steps 		Derived THEOREM 1 0
Three Gauge Couplings Run Consistently
alpha_QED, alpha_W, alpha_s run with calibrated thresholds 		Derived THEOREM 2 0
Topological Defects
RS classifies stable topological defects in field theory 		Derived THEOREM 3 0
Top Quark MSbar Mass
Top-quark MSbar mass with phi-ladder + RGE corrections inside CODATA bracket 		Derived THEOREM 1 1
Torsion Forcing in the Mass Sector
The torsion-driven correction is the canonical fix for heavy quark closure 		Derived THEOREM 1 0
Weak Force from RS
Charged- and neutral-current weak interactions emerge with the canonical mediator masses 		Derived THEOREM 2 0
Weak Gauge Coupling
g_2 emerges from the RS gauge sum; alpha_W is bracketed 		Derived THEOREM 1 0
Weinberg Angle sin^2 theta_W
The electroweak mixing angle is fixed by the RS gauge ratio 		Derived THEOREM 3 1
Why Three Fermion Generations
The Q3 partition forces exactly three families 		Derived THEOREM 2 1
W, Z, H Masses on the Phi-Ladder
Electroweak gauge and Higgs masses sit at canonical phi-rungs 		Derived THEOREM 2 3
W/Z Mass Ratio
The W to Z mass ratio is the cosine of the Weinberg angle 		Derived THEOREM 1 1
All Three Gauge Couplings Proved
alpha_em, alpha_W, alpha_s emerge from one recognition framework 		Foundational THEOREM 1 0
Mass Spectrum on the Phi-Ladder
All Standard-Model masses follow m = yardstick * phi^{rung - 8 + gap(Z)} 		Foundational THEOREM 4 2
Q3 Representation Structure
All Standard-Model representations sit in the Q3 partition lattice 		Foundational THEOREM 1 0
Spinor Structure Forces D = 3
Two-component spinors are the unique RS-compatible structure 		Foundational THEOREM 6 0
Yang-Mills Mass Gap
A mass gap exists for the RS-derived Yang-Mills theory 		Foundational THEOREM 2 2

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.

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