Mathematical Evidence — Overview
Where the narrative wiki ends and the working math begins. The /lab toys are interactive simulators that compute, in real time, the predictions of Supreme Polarity Theory and check them against famous experiments. This section walks you through both toys with full step-by-step derivations.
Created 05/14/2026, 15:29 GMT+7Updated 05/14/2026, 15:29 GMT+7
Most of this wiki is narrative — it explains, in plain language, what SPT claims and why it makes physical sense. This section is operational — it shows the actual mathematics, the conditions under which each prediction is computed, and the experimental benchmarks each prediction must match.
Ten interactive toy models + a Derivation Explorer sit at the heart of this section. Drag a slider, watch the equations update live, see PASS / FAIL badges next to every benchmark. The Derivation Explorer is the meta-tool — click any of 18 fundamental constants (c, ℏ, G, α, m_e, m_t, m_H, Λ, H₀, Ω_b, …) to see the step-by-step chain from Toy Action down to the PDG/CODATA value, with one-click LaTeX export.
The toys & meta-tool
★ Derivation Explorer (meta-tool)
Open: /theory/derivation-explorer. Click any of 18 fundamental constants → step-by-step chain from Toy Action → Lagrangian → numerical value. Each entry links back to its source toy + math wiki and exports an arXiv-ready
.tex file. Best place to start if you want the one-page-per-constant view.DANode Master Simulator
Live: /lab/danode · Math: /theory/lab-danode-derivation. Three lenses (duality, phase-lock, membrane twist) all derive from one Toy Action. Recovers Newton's gravity, Coulomb, Schwarzschild metric, Eddington 1919 deflection, Mercury perihelion, GPS dilation, and 5 fundamental constants (spin-½, c, α, G, Λ).
Photon — Electron: Flip & Spin
Live: /lab/photon-flip-spin · Math: /theory/lab-photon-electron-derivation. Same node, two regimes. Pure flip → photon (m=0, v=c, Planck-Einstein E=ℏω). Add spin → electron (m=mₑ, Compton wavelength). One motion-budget rule.
Entanglement — Bell / CHSH
Live: /lab/entanglement · Math: /theory/lab-entanglement-derivation. Two DANodes share one phase. Reaches Tsirelson 2√2; preserves no-signalling.
Black Hole — Phase-Reversal
Live: /lab/black-hole · Math: /theory/lab-black-hole-derivation. Hawking T, Bekenstein S, Page curve from unitary phase-reversal.
Large-N Gravity
Live: /lab/large-n-gravity · Math: /theory/lab-large-n-gravity-derivation. G_eff = G_Pl/N. Solves the 10⁴² hierarchy and reproduces Hubble H₀.
SM Mass Spectrum
Live: /lab/sm-spectrum · Math: /theory/lab-sm-spectrum-derivation. 12 fermion + boson masses + Cabibbo from one calibration parameter d_0 ≈ 0.66.
Higgs / EWSB
Live: /lab/higgs · Math: /theory/lab-higgs-derivation. Mexican hat from V_SPT(φ) = −λ cos(φ/φ₀); recovers v, m_W, m_Z, m_H, sin²θ_W.
CMB Power Spectrum
Live: /lab/cmb · Math: /theory/lab-cmb-derivation. 3 acoustic peaks ℓ = 220, 540, 800 vs Planck-2018 data.
Neutrino Oscillation
Live: /lab/neutrino-oscillation · Math: /theory/lab-neutrino-derivation. PMNS, T2K, NOvA, Daya Bay, KamLAND.
GW Inspiral Chirp
Live: /lab/gw-waveform · Math: /theory/lab-gw-derivation. Chirp mass M_c for 4 LIGO catalog events + ε ≈ 10⁻⁶ phase residual prediction.
Honest Status & 5 Falsifiable Predictions
Read: /theory/spt-honest-status. What's actually derived from geometry, what's calibrated, what's missing — plus 5 specific numerical predictions with experiment timelines (JUNO, DUNE, LIGO O5, HL-LHC).
What passing tests actually proves
Every benchmark in both toys currently passes. This is meaningful — but it is important to be precise about what it proves and what it does not.
✓ What it proves
(1) The Toy Action is internally consistent — no ghosts, tachyons, causality violations, or unitarity loss. (2) It can post-dict — reproduce — well-known constants and experimental results to several significant figures. (3) The same single mechanism (membrane flip + spin + phase-coupling) handles wave-particle duality, force, gravity, photon, and electron in one framework.
✗ What it does NOT prove
(1) That SPT is the unique correct theory of nature — many other frameworks also reproduce these benchmarks. (2) That every paradox of physics is solved — only the specific ones tested in the toys (≈10 benchmarks). (3) That the falsifiable predictions are correct — they are still untested ('open' status). (4) That the constants are derived from first principles — the toy uses CODATA values to calibrate, not strict ab-initio derivation.
Honest summary. The toys demonstrate SPT is consistent with measured physics — a necessary condition for any theory of everything, but not by itself a proof. Real validation requires (a) deriving the constants from a finite set of axioms with no input numbers, (b) one of the falsifiable predictions being confirmed by a future experiment, and (c) peer-reviewed publication. None of these has happened yet. The toys are the strongest evidence so far that SPT is worth taking seriously.
Where this section goes from here
- More toys — phase-lock force in atomic-scale, Bagua-slice tunnelling, dark-matter coupling, FRB phase-burst — each adding a new benchmark dimension.
- Genuine ab-initio — replace CODATA calibration with derivations of α, G, Λ from membrane geometry alone.
- Pre-registered predictions — write down the GW phase-correction and BH-entropy modification with specific numerical predictions, time-stamp them, and let LIGO / future telescopes settle them.
- Independent reproduction — open-source the toy math so other physicists can re-derive everything in their own frameworks.
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