Pentagon Physics is not a theory in the usual sense, with parameters fitted to data. It is a calculational discipline with one alphabet, no numerical parameters, and structural selection rules that produce values for physical constants across every sector of the Standard Model.
Before naming any framework, it is worth asking what a competent geometric foundation of physics would have to deliver. The Standard Model has known limitations, and the question is not rhetorical. If a candidate framework meets these criteria, it is doing what physics has been trying to do.
No existing programme simultaneously addresses all ten. Pentagon Physics claims to address all ten from a single source.
The framework rests on three elements, in a specific order. The order matters because each element flows from the previous one without choice.
A self-referential fixed-point equation. Its positive solution is φ = (1+√5)/2, the golden ratio. This is the simplest non-trivial fixed-point equation on the real line. The framework's claim is that every physical constant is a theorem of this equation.
The axiom forces φ throughout the framework. The unique four-dimensional regular polytope whose symmetry group has φ as a fundamental ratio is the 600-cell: 120 vertices on the unit 3-sphere, with the binary icosahedral group 2I as its symmetry group.
The binary icosahedral group 2I has nine irreducible representations. Their character values lie in the quadratic field ℚ(√5). The character table has 81 entries with 15 distinct values, all expressible as integer combinations of 1 and φ. This is the entire alphabet.
Parameter-free, but not choice-free. There are no tuneable numbers in Pentagon Physics. The axiom is fixed. The geometry is forced. The character table is computed by Burnside's algorithm. What remains are structural choices: which character-table combination maps to which physical quantity. The framework's credibility depends on whether these selections are structurally constrained rather than target-selected — and they are documented with explicit selection rules in every paper.
Many finite groups have character tables. The natural objection is: why 2I rather than another group?
The character table of 2I works because it is the only finite alphabet whose internal arithmetic produces all eight of the non-trivial structural objects that physics demands simultaneously:
The automorphism √5 → −√5 provides a natural two-valuedness: the split between propagating and confined modes.
Exactly two eigenvalues of the 600-cell adjacency matrix produce propagating modes — giving gravity and electromagnetism. The rest are confined.
Three copies of the fundamental representation appear in the character table decomposition, forcing exactly three families of fermions.
The representation dimensions and their tensor products reproduce the gauge group structure of the Standard Model.
No other finite group character table delivers all of these simultaneously. The selection is not aesthetic — it is forced by the requirement that the alphabet be sufficient.
In every quantity where the Standard Model produces a consensus value that differs from the most precise direct measurement, Pentagon Physics aligns with the direct measurement more closely than the SM consensus does.
The Standard Model is not a single calculational method. It is a portfolio of techniques: lattice QCD with multiple discretisation schemes, CKM extraction with inclusive and exclusive routes that disagree, CODATA global least-squares fits combining measurements that pull against each other, nuclear models from liquid-drop to shell-model with five or more fitted terms each.
Each technique has its own adjustable inputs. The methods sometimes disagree. The Standard Model arrives at a consensus value by weighting, averaging, and sometimes discarding outliers.
Pentagon Physics applies one consistent calculational discipline across all quantities. The same 15 character-table values. The same structural selection rules. No sector-specific adjustments, no weighting, no consensus averaging.
The structural observation is that a parameter-free single method, in a fair comparison across many observables, beats a parameter-rich portfolio of methods at the criterion the portfolio is designed to optimise: agreement with the cleanest measurement available.
Most of the 25 quantities are postdictions — derived with knowledge of the experimental targets. The framework's structural ingredients were selected in 2025 and 2026 with knowledge of the target values. Intellectual honesty requires stating this plainly.
However, a genuine subset are forward predictions:
All forward bets have Zenodo timestamps that predate any future adjudication, and all will be resolved within the next decade.
Pentagon Physics is not a competitor to the Standard Model at the level of result. It is a competitor at the level of method.
The framework is falsifiable in three ways, on three timescales. It is not protected by any "future work" deferral.
PP predicts α−1 = 137.035999207 exactly. The most precise direct measurement agrees to the last published digit. If a next-generation measurement of α moves away from this value by more than experimental uncertainty, PP is refuted at the most basic level.
The neutrino sector's four pending bets — atmospheric octant, Dirac phase, mass sum, solar splitting — will be tested by JUNO, DUNE, Hyper-Kamiokande, and CMB-S4. Any single bet failing outside uncertainty kills the neutrino sector derivation.
The claim of parameter-free single-method behaviour depends on the structural selection rules being applied consistently across the corpus. If a structural audit finds that expressions were chosen ad hoc to match targets, the framework collapses to numerology.