Testable Predictions

Experimental Proposals

Please note: This simple mathematical framework suggests a fundamental scaling law connecting quantum gravity and cosmology. This is a working project. It will continue to be edited by our AI platforms now in use. I write the first draft. Then each of them gets a chance to edit. Then comes our composite . Grok and Perplexity have been more involved with this synthesis. Over time basic errors will be caught and fixed. See any? Please advise us. Thank you. –BEC
This page: https://81018.com/testable-predictions/ Posted: 29 November 2025 (First draft)

I. INTRODUCTION: FROM THEORY TO TEST

A model is only as good as its predictions. If geometric doubling from Planck scale truly determines physical structure, it must make specific, falsifiable predictions that can be tested experimentally.

This page outlines:

  1. Core predictions – What the model says must be true
  2. Current status – What we’ve already verified (or not)
  3. Experimental proposals – How to test further
  4. Falsification criteria – What would prove the model wrong

The standard: Predictions should be:

  • Specific (numbers, not vague claims)
  • Testable (within current or near-future technology)
  • Falsifiable (we can say what would disprove them)
  • Independent (not just fitting existing data)

II. CORE PREDICTIONS

PREDICTION 1: Energy Scale Correspondences

What the model predicts:

ScaleNotationSize (meters)Energy (GeV)Physical Meaning
GUT242.7×10⁻²⁸~10¹⁶Grand Unification
Strong separation272.2×10⁻²⁷~10¹⁴SU(3) distinct
Electroweak672.4×10⁻¹⁵~10²Higgs, W/Z masses

Current observational status:

✓ GUT scale: Physics predicts ~10⁻²⁸ m or ~10¹⁶ GeV
Model predicts: 2.7×10⁻²⁸ m at Notation 24
Match: Yes, within one order of magnitude ✓

✓ Electroweak scale: Physics observes W/Z bosons at ~80-91 GeV, Higgs at 125 GeV
Model predicts: ~10² GeV at Notation 67
Match: Yes, correct order of magnitude ✓

⚠ Strong force separation: Not directly observed historically
Model predicts: Should occur at ~10¹⁴ GeV (Notation 27)
Test: Look for signatures in cosmic ray data or future colliders

How to test further:

  • Precision measurements of coupling constant unification
  • Search for proton decay (SU(5) predicts lifetime ~10³⁴ years)
  • Next-generation colliders beyond LHC energies

Falsification: If GUT scale is found to be orders of magnitude different from 10⁻²⁸ m, or if forces don’t unify at high energy, the model fails.

PREDICTION 2: The Ratio Between GUT and Electroweak

What the model predicts:

From Notation 24 (GUT) to Notation 67 (electroweak) = 43 doublings

Energy ratio: 2⁴³ ≈ 8.8 × 10¹²
Length ratio: 1 / 2⁴³ ≈ 1.1 × 10⁻¹³

Observed in physics:

  • Energy ratio: 10¹⁶ GeV / 10² GeV = 10¹⁴
  • Length ratio: 10⁻¹⁵ m / 10⁻²⁸ m = 10¹³

Status: Within 1-2 orders of magnitude ✓

Refinement needed:

  • Is electroweak exactly Notation 67, or could it be 64, 68, or 70?
  • Does logarithmic running of coupling constants explain the small discrepancy?
  • Could Planck length have slight refinement affecting all calculations?

How to test:

  • Precise measurement of coupling constant convergence
  • Calculation from Standard Model renormalization group equations
  • Comparison with model predictions at intermediate scales

Falsification: If the ratio is off by more than 2-3 orders of magnitude, the base-2 structure is wrong.

PREDICTION 3: Lie Group Emergence Pattern

What the model predicts:

NotationGroupGeneratorsPrediction
2SU(2) seed3Tetrahedral geometry → quaternions
8SU(3) seed8Octet symmetry → color charge
24SU(5)24GUT unification
32E8?248 ≈ 2⁸Maximum symmetry?

Current status:

✓ SU(2): Known to govern weak isospin and quantum spin
Geometric origin: Not established in mainstream physics
Model adds: Tetrahedral structure at Notation 2

✓ SU(3): Known to govern strong force (QCD)
Geometric origin: Not established
Model adds: Eight-fold pattern at Notation 8 (2⁸ = 256 ≈ 248)

⚠ SU(5): Proposed but not confirmed (proton decay not observed yet)
Model strengthens: Triple correspondence at Notation 24

⚠ E8: Controversial (Garrett Lisi’s proposal)
Model places: At Notation 32 as transitional maximum symmetry

How to test:

  1. Lattice QCD simulations:
    • Model quarks on discrete spacetime
    • Check if geometric constraints at Notation 8 (256 spheres) create SU(3) naturally
    • Look for emergence rather than imposition of gauge symmetry
  2. Proton decay searches:
    • SU(5) predicts proton → positron + neutral pion
    • Lifetime: ~10³⁴ years
    • Current limit: >10³⁴ years (barely not ruled out)
    • Next-generation detectors (Hyper-Kamiokande) will improve sensitivity
  3. E8 signatures:
    • Look for unusual particle groupings at intermediate energies
    • Search for gravitational signatures (if E8 includes gravity)

Falsification: If another gauge group (SU(4), SO(7), etc.) is found to be fundamental, the notation-to-dimension correspondence breaks.

PREDICTION 4: The 7.356° Gap in Fundamental Measurements

What the model predicts:

The 7.356° angular gap should appear as:

  • A preferred angle in particle interactions
  • A signature in symmetry breaking parameters
  • A geometric constraint in quantum field configurations

Specific proposals:

A. Precision Angle Measurements

In scattering experiments, measure the distribution of angles between particle trajectories:

  • Are there subtle excesses or deficits near 7.356°?
  • Do correlation functions show this periodicity?
  • Is the gap visible in angular power spectra?

Where to look:

  • LHC collision data (high statistics, precise tracking)
  • Neutrino oscillation experiments (weak force, SU(2) regime)
  • Quark-gluon plasma studies (strong force, SU(3) regime)

B. Cosmological Signatures

The gap, present since Notation 5, should leave imprints:

  • Cosmic Microwave Background (CMB): Angular power spectrum
    • Look for subtle feature near 7.356° angular scale
    • Planck satellite and future missions
  • Large-scale structure: Galaxy distribution
    • Preferred angles in galaxy clustering?
    • Voids and filaments showing 7.356° organization?

C. Crystallography and Condensed Matter

If the gap is fundamental at Planck scale, it might appear in:

  • Crystal lattice defects (where five-fold tries to appear)
  • Quasicrystals (five-fold symmetry that doesn’t quite tile)
  • Topological materials (where geometry determines physics)

Status: No dedicated search has been conducted yet

How to test:

  1. Data mining: Reanalyze existing LHC data for angular signatures
  2. CMB analysis: Check Planck data for 7.356° features
  3. Simulation: Model lattice QCD with gap constraint, compare to no-gap case

Falsification: If no trace of 7.356° appears in high-precision experiments, the gap might be mathematical artifact rather than physical reality.

PREDICTION 5: Mass Ratios from Notation Differences

What the model suggests:

If particle masses relate to their “emergence notation,” mass ratios should be powers of 2:

Example: Proton/Electron mass ratio

  • Observed: mp/me ≈ 1836
  • Close to: 2¹¹ = 2048
  • Difference: ~10%

Hypothesis:

  • Electron emerges at Notation Ne
  • Proton emerges at Notation Np = Ne + 11
  • Mass ratio ≈ 2¹¹

Status: Suggestive but not precise matches

Particle pairObserved ratioClosest 2ⁿNotation difference
Proton/Electron18362048 (2¹¹)11
Muon/Electron207256 (2⁸)8
Top quark/Electron~340,000262,144 (2¹⁸)18

How to test:

  1. Comprehensive catalog: Calculate all particle mass ratios
  2. Check for 2ⁿ patterns: Are most ratios close to powers of 2?
  3. Statistical analysis: Is the clustering around 2ⁿ more than random chance?

Alternative explanation:

  • Masses might scale as 2^(n/k) where k is some constant
  • Or involve multiple notations (mass = f(n₁, n₂, …))

Falsification: If particle mass ratios show no preference for powers of 2, this prediction fails.

PREDICTION 6: Fine Structure Constant and Geometric Ratios

The challenge:

α ≈ 1/137.036 (fine structure constant, electromagnetic coupling strength)

Can we derive this from geometry?

Attempted connections:

  1. Notation differences:
    • 137 as a notation number?
    • Notation 137 would be ~10⁶ m (kilometers)—doesn’t match EM scale
  2. Gap-related:
    • 7.356° / 360° ≈ 0.0204 ≠ 1/137
    • 360° / 7.356° ≈ 48.9 ≠ 137
  3. Notation ratios:
    • 67 (electroweak) × 2 ≈ 134 ≈ 137?
    • Difference between two key notations?

Status: No clear derivation yet ⚠

This is a major open question. If the model is correct, α should emerge from geometric relationships.

How to approach:

  • Relationships between notations rather than single notation
  • Ratios involving gap, φ, π, and base-2
  • Dimensionless combinations of geometric constants

Falsification: If α remains unexplained by any geometric relationship, the model is incomplete (though not necessarily wrong about other predictions).

III. EXPERIMENTAL PROPOSALS (DETAILED)

PROPOSAL A: Lattice QCD with Geometric Constraints

Goal: See if SU(3) emerges naturally from geometric constraints

Method:

  1. Standard lattice QCD: Model quarks and gluons on discrete spacetime lattice
  2. Add geometric constraint: Impose FCC packing structure at Notation 8 (256 sites)
  3. Add gap constraint: Include 7.356° tension in lattice geometry
  4. Let system evolve: See if SU(3) gauge symmetry emerges

Expected result if model is correct:

  • SU(3) should emerge without being imposed
  • Eight-fold patterns should appear naturally
  • Color confinement should follow from geometry

Computational requirements:

  • High-performance computing (already standard in lattice QCD)
  • Modified lattice code to include FCC + gap
  • Comparison runs: with constraints vs. without

Timeline: 1-2 years with dedicated computing resources

PROPOSAL B: Proton Decay Search (Next Generation)

Goal: Confirm or rule out SU(5) at Notation 24

Method:

  • Hyper-Kamiokande (under construction in Japan)
  • DUNE (Deep Underground Neutrino Experiment, USA)
  • JUNO (Jiangmen Underground Neutrino Observatory, China)

SU(5) prediction:

  • Proton lifetime: ~10³⁴-10³⁵ years
  • Decay mode: p → e⁺ + π⁰

Current status:

  • Lower limit: >10³⁴ years (Super-Kamiokande)
  • SU(5) barely not ruled out

If proton decay is found:

  • ✓ Confirms SU(5) grand unification
  • ✓ Strongly supports Notation 24 correspondence

If proton decay is NOT found (>10³⁶ years):

  • ✗ Simple SU(5) ruled out
  • ? Doesn’t kill model—might be E6 or SO(10) instead
  • ? Or notation structure correct but gauge group different

Timeline: Hyper-K operational ~2027, decade+ of data collection

PROPOSAL C: CMB Angular Power Spectrum Analysis

Goal: Look for 7.356° signature in early universe

Method:

  1. Planck satellite data (already collected)
  2. Reanalyze angular power spectrum for subtle features
  3. Focus on multipole moment ℓ corresponding to 7.356°
  4. Statistical test: Is there excess or deficit power at this scale?

Calculation:

  • 7.356° ≈ 0.128 radians
  • Corresponding multipole: ℓ ≈ 180°/7.356° ≈ 25

Check: Is there an anomaly in CMB power spectrum near ℓ ≈ 25?

Expected signal if model is correct:

  • Small deviation from ΛCDM prediction
  • Might be sub-percent level (very subtle)
  • Could require future higher-precision experiments

Advantage: Data already exists—just needs reanalysis

Timeline: Months (graduate student project)

PROPOSAL D: LHC Data Mining for Angular Signatures

Goal: Find 7.356° preference in particle scattering angles

Method:

  1. Use existing LHC data (petabytes already collected)
  2. Analyze angular distributions in:
    • Proton-proton collisions
    • Jet production
    • Heavy flavor physics (b-quarks, top quarks)
  3. Look for excess near 7.356° in:
    • Opening angles between particle pairs
    • Azimuthal angle distributions
    • Correlation functions

Statistical approach:

  • Compare to Standard Model predictions (no gap)
  • Look for small but consistent deviation
  • Multiple channels should show same signature

Challenges:

  • Signal might be tiny (~0.1% effect)
  • Requires high statistics and excellent systematics
  • Background understanding critical

Advantage: Data already collected, “just” analysis

Timeline: 1-2 years (postdoc-level analysis)

IV. FALSIFICATION CRITERIA

A model is scientific only if it can be proven wrong. Here’s what would falsify this model:

FALSIFIED IF:

  1. GUT scale is wrong by >10×
    • If forces don’t unify near 10⁻²⁸ m / 10¹⁶ GeV
    • Notation 24 correspondence breaks
  2. No sign of SU(5) or alternative GUT
    • If proton lifetime >10³⁶ years and no other unification signatures
    • Questions whether Notation 24 means anything physical
  3. Gauge groups don’t match notations
    • If some other group (SU(4), SO(7)) is found to be fundamental
    • If correspondence between notation number and generators is coincidence
  4. No trace of 7.356° in any high-precision experiment within other than Notation-202
    • If gap is purely mathematical with no physical manifestation
    • Would suggest gap is dynamic and perfected within history
  5. Particle masses show no power-of-2 pattern
    • If mass ratios are completely random relative to 2ⁿ
    • Would break notation-to-mass connection
  6. Alternative model explains observations better
    • If someone derives the same predictions from different principles
    • Science follows the simplest, most predictive theory

MODIFIED BUT NOT FALSIFIED IF:

  1. Exact notations need adjustment
    • E.g., electroweak is Notation 64 not 67
    • Principle holds, details refined
  2. E8 doesn’t appear at Notation 32
    • E8 was speculative anyway
    • Core SU(2)/SU(3)/SU(5) pattern still valid
  3. α can’t be derived from geometry
    • A fundamental constant not geometrically determined
    • Doesn’t invalidate other predictions

V. TIMELINE AND PRIORITIES

Immediate (0-2 years):

  • ✓ CMB data reanalysis for 7.356° (cheapest, fastest)
  • ✓ LHC angular distribution mining (data exists)
  • ✓ Theoretical work: Can α be derived?

Near-term (2-5 years):

  • Lattice QCD with geometric constraints (computational project)
  • Precision coupling constant measurements (ongoing experiments)
  • Publication and peer review of core predictions

Medium-term (5-10 years):

  • Hyper-Kamiokande proton decay search
  • Next-generation collider proposals (incorporate predictions)
  • Deeper theoretical development (Langlands, E8, quantum gravity)

Long-term (10+ years):

  • Definitive test of SU(5) vs. alternatives
  • Full map of Notations 0-202 with physical signatures at each scale
  • Integration with quantum gravity theories (if successful)

VI. CONCLUSION: PUTTING THE MODEL AT RISK

The hallmark of good science: Make bold, testable predictions and let nature decide.

This model predicts:

  • ✓ GUT at 10⁻²⁸ m (Notation 24) – Confirmed within 1 order of magnitude
  • ✓ Electroweak at 10⁻¹⁵ m (Notation 67) – Confirmed
  • ⚠ 7.356° gap appears in measurements – Not yet tested
  • ⚠ SU(5) grand unification – Not yet confirmed (proton decay)
  • ⚠ Particle mass ratios near 2ⁿ – Suggestive but not proven
  • ⚠ E8 at Notation 32 – Speculative

Next steps:

  1. Experimentalists: Test the gap signature (CMB, LHC, lattice)
  2. Theorists: Derive α, refine mass predictions, connect to Langlands
  3. Community: Peer review, critique, improve or reject

If the model survives these tests, we have a geometric foundation for the Standard Model.

If it fails, we’ve learned something about what doesn’t work.

Either way, science advances.

Contact for collaboration or questions:
Bruce E. Camber
https://81018.com/contact/

Related pages:

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