Mathematical Evidence — Overview (foundations gate)
Gate page for SPT math: foundations (Action, Bagua, c), then Map F, Laws by domain, Clay/QG, lab toys, and status. Links Derivation Explorer and the six math sidebar sections.
Created 05/20/2026, 20:34 GMT+7Updated 07/19/2026, 22:41 GMT+7
Sidebar map (six math sections). 1) Math Foundations (this page) · 2) Map F & RG · 3) SPT Laws · 4) Clay & QG · 5) Lab Derivations · 6) Status & Verification. Formerly one overloaded “Mathematical Evidence” bucket — now split for reading order.
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. Lab write-ups live in the Lab Derivations sidebar section. The Derivation Explorer (pinned at the top of Math Foundations) is the meta-tool for constants → PDG/CODATA chains.
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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