Synthesis · dashboard
Results dashboard
One card per result. One door to verification.
This page lists all main results of the PT programme, organised in six families: foundational mathematics, Standard Model physics, relativity-cosmology, chemistry, application domains (biology, geophysics, colour), and meta (predictions, confirmations, audit). Each card states its epistemic status and links to the corresponding monograph chapter and to the website verification page.
Reading : each result carries an explicit status (proved, derived, validated, predicted, conditional). The dashboard does not hide the statuses: it makes them readable at a glance via colour-coded badge.
The hard core
GFT and the T0–T6 / L0 chain form the mathematical backbone. Without it, physical and chemical results lose their PT-derivation status.
The robust showcase
The atomic chemistry + 43 Standard Model observables pair gives the best first contact: measurable numerical MAE, no fitted parameter, direct comparison to PDG.
The open edges
Late cosmology, RH programme, geophysics and applications keep contrasted statuses. The dashboard distinguishes on each card what is proved, derived, validated, or predicted.
Foundational mathematics
The theoretical floor: T0–T6 + L0 + GFT chain, the catalogue of PT_MATH computational tools, and the open leads around the Riemann hypothesis.
T0–T6 + GFT + L0 chain
The demonstrative core. T0 closes uniqueness of the dynamical field, GFT gives the fundamental principle log m = D_KL + H, T5 fixes the attractor μ* = 15.
PT toolbox atlas
32 computational tools (M01–M35) covering algebras, transforms, metrics, CRT error-correcting codes. Each tool is a standalone Python script.
Mechanics of prime gaps
From the sieve to the primes: primorial wheels, square-root window, angular law θ_p ~ √(2/p), renormalised PT-Buchstab equation.
RH programme — leads
6 exploration milestones leading to a candidate reformulation (sub-Lindelöf), three crossings with the Connes programme (Bost-Connes, CCM).
Foundational physics
The Standard Model observables reproduced from s = 1/2, with no fitted continuous parameter, and their validation at collider level.
43 Standard Model observables
α_EM, α_s, sin²θ_W, lepton masses, quark masses, CKM/PMNS mixings, cosmological parameters. All derived from s = 1/2 + T0–T6 cascade.
LEP / SLC / LHC validation
72 precision observables (Z pole, Higgs sector, top, QCD) tested against experimental data, plus a Monte Carlo parton cascade simulation.
Quantum mechanics = amplitude geometry
The six von Neumann axioms (Hilbert space, Born rule, unitary evolution, measurement…) emerge from CRT and the transfer matrix.
Nuclear physics
Cascade s=1/2 → N_c → α_s → M_N → V_NN → E_bind. Magic numbers 2,8,20,28,50,82,126 reconstructed, ab initio HF+MBPT2 for ¹⁶O and ⁴⁰Ca.
Relativity, gravity and cosmology
From the sieve's Fisher metric to Lorentzian signature, Hubble expansion and the dark sector.
Relativity from Fisher
Bianchi I metric, Lorentzian signature g₀₀<0 for μ>μ_c≈6.97, emergent SO(3,1) group, Einstein equations, Newton constant.
Cosmogony: crystallisation of p=2
The Big Bang read as logical order of channel opening. Crystallisation of p=2 into spin/parity boundary, q⁺/q⁻ bifurcation locked at μ*=15.
Hubble and dark energy
H₀ = 67.43 km/s/Mpc (Route D), SH0ES tension treated by superposition of KBC local void + Bianchi I anisotropy. 3 routes for w(z) facing DESI DR2.
Time and emergence of duration
Proper time is not posited. It appears when g₀₀ changes sign, at μ_c ≈ 6.97. Before that, Euclidean signature — no "before".
Chemistry
From the periodic table to molecular bond energies, via ionisations and electron affinities. All derived from the sieve.
Periodic table
Shell-size sequence 2, 8, 8, 18, 18, 32, 32 reconstructed from the sieve. s/p/d/f blocks as consequences of primary channels.
Ionisation energies
Z=1..86 by canonical PTC engine, Z=1..103 by perturbative scheme, Z=104..118 vs FSCC/CCSDT. Peaks, closures, structural residues visible.
Electron affinities
Edge capture, vacancy, halogen/metal cases. All main elements below 10 %.
Molecular chemistry
Dissociation energies D₀ (~849 mol), geometry 0.5 % (12 mol), Marcus-PT kinetics 2.1 % (17 reactions), ω_e frequencies Spearman 1.000.
Benchmark vs experiment (1000 mol)
Atomization energies D_at on 1,644 molecules: 994 ATcT/NIST/JANAF (MAE 0.73 eV, 3.22 % relative, sub-percent on organics) + 650 new from the Burcat Third Millennium DB (MAE 6.55 %, median 4.83 % — covers combustion, explosives, dioxins, terpenes, nucleobases). 0 fails, 0 fitting variables. 546 molecules cross-validated against CCCBDB + Burcat at less than 2 % drift.
Benchmark vs B3LYP/6-31G* (855 mol)
Paired comparison on the 855 mol where B3LYP converges. PTC beats B3LYP with MAE 0.60 eV vs 0.93 eV (−35 % gain), win rate 70.8 %. PTC unbiased, B3LYP biased negative.
3-way benchmark vs def2-TZVP (536 mol)
Test on the "modern" DFT basis. PTC remains best everywhere. def2-TZVP regresses behind 6-31G* on the 9-12 atom bin — structural defect of B3LYP, not curable by better basis.
Application domains
Beyond the Standard Model and chemistry: applications of the PT cascade to biology, seismic geophysics, and colour perception.
Biology: 3 biopolymers
Universal q⁺/q⁻ bifurcation across DNA, RNA, proteins. Ramachandran torus reconstructed (20/20 amino acids), allostery tested by 1000× shuffle, A_m = 1 for RNA [THM].
Colour — Sieve Color Space
Colour space derived from the sieve. 3 opponent channels forced by {3, 5, 7}, γ_p weights computable without fit, Pythagorean metric via CRT.
Meta — falsifiability and audit
How PT is testable, verifiable, and confronted with independent external results.
Falsifiable predictions
Registry of PT predictions with explicit test criteria: neutrinos, Higgs, g−2, αs, superheavies, chemistry, nuclear, emerging signals.
External confirmations
Classical mathematical theorems and recent publications (peer-reviewed and arXiv) compatible with PT — without having been designed to test it.
Transparent audit
Epistemic status by result (THM, DER, VAL, PRED, COND), regression tests, reproducible companion scripts.
Dashboard updated at each new derivation. Primary source: the PT monograph (chapters ch01–ch37). For detailed epistemic statuses, see Result statuses.