Framework Catalog

Two reference artifacts in one place: the Periodic Table of Primes — a 5-tier hierarchy of primes generated from division algebra dimensions, all mapped to physical constants — and the Crystallization Catalogue — 17 types describing how one dynamical principle manifests across all of physics.

Hover over grid cells for decomposition details. Click mapped primes or type cards to expand. Use confidence filters to navigate by derivation status.

Periodic Table of Primes

Framework dimensions 11 generate primes at five tiers of algebraic complexity. Ten Tier 2 primes (a² + b²) are each mapped to physical constants; higher tiers govern mass ratios, mixing angles, and cosmological observables.

Master Pattern
Observable = Prime(algebraic_structure) × Fraction(scale_selector)
Tier 1Structural
Tier 2Framework
Tier 3Triple-Sum
Tier 4Four-Square
Tier 5Additive / Non-Framework
1
dim(R)
2
dim(C)
3
Im(H)
4
dim(H)
7
Im(O)
8
dim(O)
11
n_c
1
dim(R)
2
5
10
17
50
65
122
2
dim(C)
5
8
13
20
53
68
125
3
Im(H)
10
13
18
25
58
73
130
4
dim(H)
17
20
25
32
65
80
137
7
Im(O)
50
53
58
65
98
113
170
8
dim(O)
65
68
73
80
113
128
185
11
n_c
122
125
130
137
170
185
242
Stage 1 (early)
Stage 2 (precision)
Stage 3 (derived)
Non-prime
PrimeFormConstantPrecisionStage
21² + 1²Binary structureExact1
51² + 2²Fermion representations0.0%1
132² + 3²Neutrino mixing0.23%1
171² + 4²Lepton mass ratio1.1%1
532² + 7²Strong coupling0.02%2
733² + 8²Koide angle0.006%2
979² + 4²Weak mixing angle3.75 ppm2
10910² + 3²Recombination redshift0.018%3
1137² + 8²Glueball mass0.004%2
1374² + 11²Fine structure constant0.27 ppm3

Crystallization Catalogue

Seventeen types of crystallization (C1-C17), all governed by a single order parameter and a shared potential. From the Big Bang to neutrino oscillations, each process is a different channel of the same tilt-reduction mechanism. Click any type card to see its formula, experimental signatures, known gaps, and falsification criteria.

17
Types
69
SymPy Scripts
723
Tests
98.5%
Pass Rate

Order Parameter: ε

Ground state: ε* = α² ≈ 10⁻⁵

ε 0
Pure Crystal
No physics. Pre-Big-Bang.
ε ≪ ε*
Near-Symmetric
Inflation era
ε ≈ ε*
Ground State
Normal physics (our universe)
ε > ε*
Excited
High-energy processes
ε → 0
De-crystallization
Black hole singularity

Unifying Function

g(φ) = 1 − φ²/μ²
C1Drives inflation: V(φ) = V₀ g(φ)
C3Mexican hat: W = −a g(φ)|ε|² + b|ε|⁴
C4Decoherence: Γ_dec = 4a g(φ) Γ
C7Spectral index: n_s from g″/g

17 Crystallization Types

C1Cosmic Crystallization
derivation
ForwardUniverseAllPotential-driven
ε = 0->ε = ε*

The Big Bang as nucleation from pristine crystal to imperfect ground state.

C2Symmetry Breaking
theorem
ForwardUniverse–ParticleAll→RCHOSymmetry
SO(11)->SO(4)×SU(3)

SO(11) breaks through exactly one forced chain into spacetime × internal.

C3Tilt Dynamics
derivation
Forward+OscAllAllPotential
Tilt fluctuations->Equilibrium at ε*

Tilt matrix settles via Mexican hat potential with shared g(φ) function.

C4Quantum Measurement
derivation
ForwardQuantumAllNoise-driven
Superposition->Eigenstate

Born rule derived from Fubini-Study geometry: P(k) = |c_k|².

C5Black Holes
conjecture
ReverseAstrophysicalR-dominantPotential
ε = ε*->ε → 0

De-crystallization: tilt returns to zero at singularity (reverse of Big Bang).

C6Forces / Boundaries
derivation
ForwardParticle–AstroC or OBoundary
Vacuum fluctuations->Reduced modes

Gauge forces as boundary-induced crystallization. Beta coefficients exact.

C7Cosmological Phases
conjecture
ForwardCosmologicalSequentialPotential
Post-inflation->Phase transitions

Sequential crystallization through EWSB, QCD, BBN, recombination epochs.

C8Photon Emission
derivation
ForwardQuantum/ParticleC (EM)Emission
Higher tilt->Lower tilt + photon

Photon emission as C-channel crystallization: α = 1/N_I = 1/137.

C9Mass Freezing
conjecture
StaticParticleMixedSymmetry
Massless->Massive particles

Particle masses freeze via EWSB. 15 = 1+2+4+8 fermions, 3 = Im(H) generations.

C10Weak Decay
framework-constrained
ForwardParticleH (weak)Emission
Parent particle->Daughter(s) via W/Z

H-channel flavor-changing crystallization. Z couplings test sin²θ_W = 28/121.

C11Pair Creation
framework-constrained
BothParticleC or mixedEmission
Energy/photons->Particle-antiparticle pair

Reversible crystallization: tilt structure created or dissolved in matched pairs.

C12Hadronization
conjecture
ForwardParticleO (strong)Boundary
Free quarks/gluons->Color-singlet hadrons

O-channel confinement: color charges form singlet bound states.

C13Nuclear Binding
standard-relabeled
ForwardNuclearMixed (O+C+H)Multi-channel
Free nucleons->Bound nucleus

Residual O-channel interaction between color-singlet nucleons with Coulomb repulsion.

C14Neutrino Oscillation
conjecture
OscillatoryParticleHPrecession
Flavor α->Detected as flavor β

H-channel flavor precession between Im(H) generation directions.

C15Gravitational Waves
standard-relabeled
ForwardAstrophysicalREmission
Accelerating mass->GW emission; merger

R-channel tilt wave emission from accelerating mass. No GW echoes predicted.

C16Baryogenesis
speculation
ForwardCosmologicalMixed (H+O+C)Asymmetric
Symmetric plasma->Baryon excess (η ~ 6×10⁻¹⁰)

Asymmetric crystallization producing net matter over antimatter. Least developed type.

C17Structure Formation
framework-constrained
ForwardCosmologicalR-dominantPotential
Uniform post-recombination->Galaxies, clusters, cosmic web

R-channel gravitational clustering seeded by primordial perturbations from C1.

Composability Chains

Crystallization types compose into physical processes. Each chain reads left to right.

Universe History
C1->
C2->
C7->
C3
Big Bang → symmetry breaking → cosmological phases → tilt dynamics
Quantum Measurement
C4->
C8
Collapse selects eigenstate → photon emission
Stellar Collapse
C1->
C7->
C3->
C5
Forward crystallization → black hole de-crystallization
Collider Process
C8->
C6->
C4->
C8
Inject → confine → collapse → emit
EWSB
C2->
C9->
C8
Eigenvalue partitioning → mass freeze → Higgs emission
Particle Creation
C7->
C9->
C8
Phase transition → mass freeze → emission
Neutrino Propagation
C10->
C14->
C10
Weak production → flavor oscillation → weak detection
Binary Merger
C15->
C5->
C15
GW inspiral → merger/BH → ringdown radiation
Galaxy Formation
C7->
C17->
C13->
C8
Cooling → clustering → nuclear burning → starlight
Hadron Physics
C11->
C12->
C6
Pair creation → hadronization → confinement forces

Gap Tracker

Critical (4)

Landau coefficients c₁, c₂ magnitudes
C2
V₀ not derived (inflation amplitude A_s)
C1
Individual particle masses not derived
C9
CMB peak heights not fully derived
C7

High Priority (6)

b₂ < 0 sign: mechanism is conjecture
C2
g(φ) quadratic form assumed, not derived
C3
QCD string tension formula (HRS=6)
C6
Ω_m mechanism unknown
C7
CKM/PMNS matrix not derived
C10C14
n_c/Im_H gauge coupling mechanism unknown
C6

Falsified Claims

Predictions that were tested and failed. Intellectual honesty requires tracking these.

η* = 337 Mpc
Actual: 280 Mpc
S198falsified
c_s = 3/7
Actual: 1/√3
S198falsified
Λ from V(ε*): wrong sign
Actual: Sign convention error
S199resolved S230

Resolved Gaps

Previously-open questions that have been addressed with verified derivations.

c₃ > 0: dynamic curvature derivation
S2077/8 PASS
b₂ ≠ 0: degenerate minima contradiction
S20710/10 PASS
Noise structure: Fubini-Study geometry
S169PASS
ℓ₂ peak: baryon loading φ_odd = 3/11
S1990.4%
Coset space: Gr(4,11) gives 28 Goldstones
S195PASS

Related pages

Division Algebras
Interactive guide to R, C, H, O and how their dimensions generate all key numbers.
Derivation Chains
Trace the logical steps from axioms to predictions.
Prediction Explorer
Browse all 45+ predictions with filters and precision data.