Particles & charges
The representations and charges of one Standard Model family, with a separate geometric construction for three families.
Representation and charge results. Inspect the evidence.
From a common structure to particles and constants.
TFPT connects particle charges, mass relations, mixing angles and cosmological readouts through one specified construction. Start with its numerical predictions and their comparison with data, then follow the shared ingredients.
Predictions, compared with data
Four examples across particles and cosmology. Each has a fixed output and a named measurement.
Electromagnetic couplingα⁻¹ · TFPT 137.035 999 216 8
+1.90σ0.29 parts per billion difference
Cabibbo quark mixingsin θ₁₂ · TFPT 0.224 376 2
−1.17σ0.353% difference
Solar neutrino mixingsin² θ₁₂ · TFPT 0.306 747 4
+0.49σ1.04% difference
Ordinary matter fractionΩb · TFPT 0.048 940 66
+2.21σ1.52% difference
What does the theory determine?
Several parts of physics become outputs of the same specified construction. Some are exact mathematical results; others are conditional physical readouts. A complete physical realization remains an open research goal.
Masses & mixing
Relative charged lepton and quark source masses, a common hierarchy and specified constructions for particle mixing.
Source relations; physical mass transfer has its own conditions. Inspect the evidence.
Electromagnetic coupling
A fixed boundary equation with one positive root close to the measured electromagnetic coupling. The equation, its root and its physical origin are distinct results.
Mathematical closure; physical identification remains a separate task. Inspect the evidence.
Cosmological readouts
Conditional readouts for the rotation of polarized light, the ordinary matter fraction, early cosmic expansion and the vacuum energy hierarchy.
Conditional physical readouts and dated predictions. Inspect the evidence.
Quantum & information structure
Exact connections between the E₈ lattice, coding and finite quantum geometry. Source histories can preserve information that a compressed readout loses.
Scoped mathematical and source reconstruction results. Inspect the evidence.
Clocks & dynamics
Related finite clock actions, exact relaxation in the specified transfer model and constructed state and time bridges.
Operator relations; physical time and a common source remain separate. Inspect the evidence.
“Parameter free” within a specified branch: no separate fitted number for each output. The starting inputs and any physical calibration conditions remain part of the claim.
What does “parameter free” mean here?
Within a specified branch, the inputs fix the stated output. A separate fitted number is not supplied for every observable. The boundary normalization, carrier, marking, transport rules and branch choices still belong to the starting construction. Some physical readouts also require scale calibration, mass scheme transfer or cosmological assumptions. Those conditions remain attached to the result.
Audit the inputs and branch conditionsDistinguish predictions, assigned values and conditional bandsFollow the same structure into a different result.
The two lattice norms that make the E₈ join possible reappear in the specified electromagnetic response. The matter budget enters the same equation. Follow the quantities across that connection.
Carrier and family geometry
Representative squared norms in the two ℤ₄ discriminant groups
D₅ carrier5/4
A₃ family side3/4
5/4 + 3/4 = 2. Matching the full discriminant forms permits an even index four extension. The new cosets complete E₈.
The common invariant data connect the calculations. They do not by themselves derive the full local electromagnetic variation. The guide separates the exact maps, the response contract and the physical readout at the step where each enters.
Work through the complete constructionInspect all ten dated comparisons, inflation bands and the full prediction register
What does TFPT predict, and how close are the numbers?
Compare the fixed outputs with measurements before following their derivations. The same inputs connect electromagnetic strength, particle mixing and cosmological readouts.
TFPT outputMeasurement ±1σZero = measured central value
Values frozen 9 June 2026; primary sources checked 2 November 2026. Distances use the stated measurement or fit uncertainty, with the corresponding side for asymmetric errors. They include no theory error and are not a combined significance. Known measurements retain their comparison status.
Electromagnetic coupling
α⁻¹
Specified equation; physical transfer has its own premises
TFPT137.035 999 216 8
Measured / fitted137.035 999 177 ± 0.000 000 021
+1.90σ0.29 parts per billion relative difference
Meaning, date and source
The strength of the electromagnetic interaction. The difference uses the CODATA standard uncertainty alone. It is a numerical comparison, not a combined theory significance or a derivation of the physical coupling.
CODATA 2022 adjustment. The CODATA adjustment predates the registry freeze.
Physical premise: Ward-origin reading of F_U1 is [P]; the root itself is unconditional given the equation
Solar neutrino mixing
sin² θ₁₂
Conditional solar texture
TFPT0.306 747 4
Measured / fitted0.303 6 ± 0.006 4
+0.49σ1.04% relative difference
Meaning, date and source
How neutrinos mix between the first two states. This comparison uses the normal mass ordering result. The precision does not distinguish the conditional TFPT value from the measured interval.
JUNO 207.2 live days; collaboration preprint, 29 September 2026. The cited collaboration preprint appeared on 29 September 2026. The earlier 59.1 day result, 0.3092 ± 0.0087, was already public on 18 November 2025, before the registry freeze. A prospective test must be assessed against the first public disclosure of the tested value, not its journal date alone.
Physical premise: seam-misalignment lemma (epsilon = (3/4) phi0)
Reactor neutrino mixing
sin² θ₁₃
Specified neutrino readout
TFPT0.023 108 44
Measured / fitted0.022 49 ± 0.000 57
+1.08σ2.75% relative difference
Meaning, date and source
A smaller angle in the neutrino mixing pattern. The selected fit is stated explicitly because the result depends on ordering and the data combination. The older approximate two sigma label is not used for this comparison.
NuFIT 6.1, November 2025 data; normal ordering, IC23 without SK atmospheric data. The global fit predates the registry freeze and shares neutrino data with other comparison rows.
Physical premise: The frozen numerical readout retains the source and physical transfer conditions of its branch.
Cosmic polarization rotation
β
Conditional phase; instrumental systematics remain
TFPT0.242 435°
Measured / fitted0.215° ± 0.074°
+0.37σ12.76% relative difference
Meaning, date and source
A conditional rotation of the polarization of ancient light. The authors retain unresolved instrumental systematics. The published analysis does not establish a cosmological detection or identify a TFPT mechanism.
ACT DR6 analysis, submitted 17 September 2025; revised 14 April 2026. This constant rotation comparison is distinct from later searches for anisotropic or time dependent birefringence.
Physical premise: CMB EB/TB rotation = the same boundary phase as the flavor seed [P]
Cabibbo quark mixing
sin θ₁₂
Standard angle; correlated global fit
TFPT0.224 376 2
Measured / fitted0.225 17 ± 0.000 68
−1.17σ0.353% relative difference
Meaning, date and source
The main angle governing mixing between quark families. The global fit reports the standard mixing angle directly. This is not an approximation using the matrix element |Vus|.
PDG 2026, CKM review, equation 12.28; issued 1 June 2026. The global fit predates the registry freeze. Its CKM parameters have shared fit correlations.
Physical premise: The frozen numerical readout retains the source and physical transfer conditions of its branch.
Second quark mixing angle
sin θ₂₃
Standard angle; asymmetric fit uncertainty
TFPT0.043 427 79
Measured / fitted0.041 89 +0.000 81 / −0.000 69
+1.90σ3.67% relative difference
Meaning, date and source
Mixing between the second and third quark families. The comparison uses the upper fit uncertainty because the frozen value lies above the central value. The error is asymmetric.
PDG 2026, CKM review, equation 12.28; issued 1 June 2026. The global fit predates the registry freeze. Its CKM parameters have shared fit correlations.
Physical premise: The frozen numerical readout retains the source and physical transfer conditions of its branch.
Smallest quark mixing angle
sin θ₁₃
Standard angle; asymmetric fit uncertainty
TFPT0.003 765 384
Measured / fitted0.003 763 +0.000 088 / −0.000 083
+0.03σ0.063% relative difference
Meaning, date and source
The small mixing between the first and third quark families. The comparison uses the upper fit uncertainty because the frozen value lies above the central value. The close central values do not provide an independent fit probability.
PDG 2026, CKM review, equation 12.28; issued 1 June 2026. The global fit predates the registry freeze. Its CKM parameters have shared fit correlations.
Physical premise: The frozen numerical readout retains the source and physical transfer conditions of its branch.
Quark CP violation phase
δCKM (rad)
Leading order; theory correction unquantified
TFPT1.198 232
Measured / fitted1.154 ± 0.025 rad
+1.77σ3.83% relative difference
Meaning, date and source
The phase entering quark CP violation. The frozen TFPT formula is explicitly a leading order holonomy readout. Its subleading theory correction is not quantified here; the displayed distance uses only the fit uncertainty.
PDG 2026, CKM review, equation 12.28; issued 1 June 2026. The global fit predates the registry freeze. Its CKM parameters have shared fit correlations.
Physical premise: leading-order holonomy readout [P]; sub-leading corrections not closed
Ordinary matter fraction
Ωb
Flat ΛCDM; P-ACT-LB2 with DESI DR2
TFPT0.048 940 66
Measured / fitted0.048 21 ± 0.000 33
+2.21σ1.52% relative difference
Meaning, date and source
The cosmic density fraction in ordinary baryonic matter. This uses the directly reported derived Ωb posterior, rather than Ωb h². It is conditional on the named ΛCDM model and P-ACT-LB2 data combination. The frozen value is above its central value by 2.21 stated uncertainties.
ACT DR6 ΛCDM analysis, revised 24 June 2025; Table 5, P-ACT-LB2 (DESI DR2). The data combination predates the registry freeze. Its cosmological parameters are correlated. The alternative DESI DR1 column gives a different comparison and is not substituted here.
Physical premise: seed-budget reading Omega_b + beta_rad = phi0 [P]
Vacuum energy density
ρΛ / M̄⁴
Conditional branch; matched reduced Planck units
TFPT7.125 33 × 10⁻¹²¹
Measured / fitted(7.153 ± 0.191) × 10⁻¹²¹
−0.14σ0.384% relative difference
Meaning, date and source
The small vacuum energy density relative to the reduced Planck scale. Planck gives Λ / m_Pl² = (2.846 ± 0.076) × 10⁻¹²². With M̄ = m_Pl / √(8π) and ρΛ = Λ M̄², multiplying by 8π gives this density in the same reduced Planck convention as the frozen output. The comparison retains flat ΛCDM, the physical branch and dimensional calibration premises.
Planck 2018 VI, §3.2, after Eq. 13; final revision 9 August 2021. The Planck value predates the registry freeze. The TFPT vacuum readout reuses the alpha root, so these are correlated theoretical outputs.
Physical premise: physical Lambda branch selection (8pi)^2 delta_top = 3/(4pi^2) [A]; alpha^-1 <-> Lambda identification [P]
What remains to be tested, and where is there tension?
Primordial gravitational waves
The conditional inflation branch gives r = 0.00333–0.00480 for N★ = 50–60. The cited BK18 analysis gives r₀․₀₅ < 0.036 at 95% confidence.
This limit still permits the whole band. A more sensitive tensor measurement can test it; an upper limit does not measure the predicted value.
The inflation tilt is under tension
The same branch gives nₛ = 0.960–0.96667. ACT P-ACT-LB2 with DESI DR2 reports 0.9752 ± 0.0030.
The upper edge of the frozen band is 2.84 stated measurement uncertainties below that central value. This is a band comparison at the specified reheating range, with no theory error or global significance assigned.
Neutrino CP phase 240° and atmospheric sin² θ₂₃ = 0.5 are assigned textures in the frozen register. They remain visible as testable branches with their own criteria.
The wider prediction programme
The frozen register contains sixteen main values, two assigned textures and two conditional bands. Explore every entry below. Source mass ratios, assigned textures and conditional bands keep their own comparison requirements.
Electromagnetism
A fixed root of the specified boundary equation.
Inverse fine structure constant, α⁻¹
Fixed numerical readout
Quark mixing
Three angles and a leading order CP phase from the shared flavour construction.
Cabibbo mixing, λC
Fixed numerical readout
Quark mixing, s₂₃
Fixed numerical readout
Quark mixing, s₁₃
Fixed numerical readout
Quark CP phase, δ (radians)
Conditional readout
Neutrino mixing
Two numerical readouts, plus the separately assigned atmospheric and CP textures.
Solar neutrino mixing, sin² θ₁₂
Conditional readout
Reactor neutrino mixing, sin² θ₁₃
Fixed numerical readout
Atmospheric neutrino mixing, sin² θ₂₃
Assigned texture
Test the assigned branch; no independent derivation claimedFormula, conditions and test
Neutrino CP phase (degrees)
Assigned texture
Test the assigned branch; no independent derivation claimedFormula, conditions and test
Relative particle masses
These are source scale ratios. A comparison with measured pole or MS̄ masses requires the specified transport and mass scheme.
Muon to tau source mass ratio
Fixed numerical readout
Source to measured mass scheme transfer requiredFormula, conditions and test
Electron to muon source mass ratio
Fixed numerical readout
Source to measured mass scheme transfer requiredFormula, conditions and test
Up to down quark mass ratio
Fixed numerical readout
Source to measured mass scheme transfer requiredFormula, conditions and test
Charm to strange quark mass ratio
Fixed numerical readout
Source to measured mass scheme transfer requiredFormula, conditions and test
Top to bottom quark mass ratio
Fixed numerical readout
Source to measured mass scheme transfer requiredFormula, conditions and test
Cosmic rotation, matter and vacuum
Conditional physical readouts with shared seeds, branch and cosmological assumptions.
Cosmic birefringence, β (degrees)
Conditional readout
Baryon density, Ωb
Conditional readout
Vacuum energy density, ρΛ / M̄⁴
Conditional readout
Inflation and the next tests
The scalaron scale and two conditional bands. The bands use the external reheating range N★ = 50–60.
Scalaron mass ratio, Mscal / M̄
Conditional readout
Physical scalaron identification requiredFormula, conditions and test
Tensor to scalar ratio, r
Conditional band
The cited upper limit still permits this bandFormula, conditions and test
Spectral tilt, ns
Conditional band
Upper band edge 2.84 measurement uncertainties below the cited ACT centerFormula, conditions and test
The source ratios are not automatically measured pole or MS̄ mass ratios. In particular, a broad historical range is not a current precision match for the charm to strange ratio. The required reader must be applied before reporting a physical accuracy.
Follow a construction, rather than a list of correspondences.
The detailed guide works through the operations: an exterior operator changes a carrier state; the family matrices produce mass powers; one common seed feeds four observations; one lattice root becomes a Bell ray in the specified chart.
What has been achieved, and what comes next?
The result library brings the published claim ledger together with later source reviewed research. Each achievement retains its assumptions and its exact scope.
- Established structure
- The E₈ glue, the carrier and charge construction, charged flavour relations, the specified alpha root, finite quantum geometry and explicit source response results.
- Connected recent results
- The common 4/5/20 source, intrinsic event geometry, state and time bridges, source memory, local Higgs responses and the distinction between E₈ events and continuous evolution.
- Common source route
- The original action and partition functional feed full field moments. Under the stated reconstruction hypotheses, OS/CAR supplies the local net, vacuum and positive time together. Physical applications retain the actual measure, limit, geometry and reader conditions.
Follow the common source route and its original theorem
Latest source work: quarter responses, the source vacuum and a joint Higgs constraint
The newest source work distinguishes the two quarter states through their ordered current response and tests the actual eight arc localization. It also separates the five excited inputs from the clustering vacuum under the given source time.
The joint Higgs and two boundary calculation gives a quantitative source constraint using one shared mixture. These tests concern specified source representations. Their physical applications retain the actual source, measure and reader premises.
Snapshot 2026-11-02: 783 active ledger claims and 710 scientific research findings. Includes scoped exclusions and corrections. The 707 registered scripts are a separate inventory, not a new full suite run.
Read the earlier film and presentation in the publication archive