Explore the Framework

Four views into the same structure: domain health across 12 physics areas, the algebraic building blocks, the recursive gap tower, and 50 individual predictions you can filter and verify.

Framework Status by Domain

Health dashboard across 12 physics domains — prediction counts, experiments, and confidence levels.
50
Predictions
32
Confirmed
4
Pending
13
Falsified
B-
Grade
25-40%
P(genuine)
Showing 12 of 12 domains

Status categories

Strong — sub-10 ppm
Testable — awaiting test
Active — ongoing
Developing — percent-level
Structural — math only
Open — unresolved

Periodic Table of Primes & Crystallization Catalogue

5-tier prime hierarchy from division algebra dimensions, plus 17 crystallization types governing all of physics.

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.

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. Click any type card to expand.

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

Perspective Mathematics: The Recursive Gap Tower

What happens when perspective examines its own blind spot? A finite tower terminating at Im(C) — 185/185 tests PASS.

The Recursive Gap Tower

A perspective on an 11-dimensional space sees 4 dimensions and misses 7. But that 7-dimensional blind spot can itself be examined by a new perspective, producing a smaller blind spot. This recursion terminates when the gap shrinks to dimension 1 — too small for any perspective to exist.

Step through the cascade, or click any level for details. All 512 possible towers from dim=11 terminate at gap dimension 1. The specific cascade 7 -> 3 -> 1 traces the imaginary parts of the division algebras in reverse.

Step 3/3
Level 0: The Crystal
dim11-4(dim(H))=7(Im(O))
4 dimensions accessible (spacetime)7 dimensions hidden (Im(O) — octonion imaginaries)
Level 1: The First Blind Spot
dim7-4(dim(H))=3(Im(H))
4 dimensions accessible3 dimensions hidden (Im(H) — quaternion imaginaries)
Level 2: The Second Blind Spot
dim3-2(dim(C))=1(Im(C))
2 dimensions accessible1 dimension hidden (Im(C) — the imaginary unit i)
Terminal: Im(C)
dim = 1NO PERSPECTIVE POSSIBLE

Dimension 1 is below the threshold for perspective (Corollary 1.8: need dim >= 2). No further examination is possible. This single direction — Im(C), spanned by the imaginary unit i — is permanently inaccessible.

4 + 4 + 2 + 1 = 11(accessible + terminal = n_c)
7 + 3 + 1 = 11(Im(O) + Im(H) + Im(C) = n_c)

The Irreducible Element: Im(C)

The tower terminates at a 1-dimensional subspace. It is not just "a copy of R" — it is Im(C), the imaginary axis of the complex numbers, carrying five independent algebraic properties. Each is verified computationally.

Click any property for its proof sketch and physical consequence.

Click any property above to see its proof and physical consequence.

The Self-Knowledge Paradox

The mathematics establishes a precise paradox:

Necessary

Without Im(C), unitarity, uncertainty, and interference all collapse simultaneously. No quantum mechanics is possible. Perspective cannot function.

Inaccessible

Dimension 1 is below the threshold for perspective (need dim >= 2). No perspective in any tower can examine Im(C). Structurally impossible.

Non-Removable

Removing Im(C) doesn't weaken the framework — it destroys it entirely. There is no intermediate state. All or nothing.

The one direction perspective can never access is the one direction without which perspective cannot exist. This holds for all perspectives, all towers, all starting dimensions >= 2.

Epistemic Boundary

Not all results carry equal confidence. The framework explicitly classifies each claim. Theorems are computationally verified. Derivations have gaps. Conjectures are plausible but unproven. 185/185 tests PASS across 7 scripts.

THEOREMP.1Symmetry Breaking
THEOREMTHM_04B0All 512 towers terminate at dim=1
THEOREM3.2-3.6Five properties of Im(C)
THEOREMTHM_04B1Permanent inaccessibility + necessity
THEOREM4.5Non-removability (all-or-nothing)
DERIVATION2.6Division algebra cascade (rank selection)
DERIVATIONTHM_04B2The seed: Im(C) + CCP forces n_c=11
DERIVATION2.13Top-down = bottom-up identification
CONJECTURETower BInfinite meta-theory tower (Godel)
CONJECTURE2.12Maximality at meta-levels
Confidence Hierarchy
Terminal gap has dim = 1>Terminal gap is Im(C)>Specific cascade is 7 -> 3 -> 1

Each layer depends on all previous layers plus additional assumptions. The outermost claim is the most robust; the innermost is the most assumption-dependent.

Verification

185/185 PASS
recursive_gap_tower.py
38/38 PASS
Tower, 512 paths, cascade
imc_irreducible_element.py
67/67 PASS
Five properties, seed
imc_necessity_consequences.py
46/46 PASS
QM necessity proofs
+ 4 more scripts
34/34 PASS
Evaluation, self-model, rank
Speculative theoretical framework. Not peer-reviewed. Amateur work with AI assistance. The mathematical theorems are computationally verified; the physical interpretation is what needs external scrutiny.

Prediction Explorer

Browse all 50 predictions — filter by tier, domain, status, or blind prediction flag.
Sort:
Showing 50 of 50 predictions

Understanding the tiers

Tier 1 — sub-10 ppm
Tier 2 — 10-10k ppm
Tier 3 — percent-level
Falsified — documented failures

More to explore

Division Algebras
Interactive guide to R, C, H, O and how their dimensions generate all key numbers.
Derivation Chains
Trace any prediction back to its axioms step by step.
Framework Status
Compact overview of domain health and verification counts.