Zero-parameter authenticity — what "no CODATA, no PDG, no α_em" really means in SPT

The single sentence. When SPT says "8 of 9 outputs PASS at Planck/PDG precision with 0 free parameters, 0 CODATA inputs, 0 PDG inputs, 0 calibration", every one of those zeros is auditable. This page lists the inputs SPT does and does not consume, defines the Tier-A vs Tier-B distinction precisely, names the four common cheating moves SPT explicitly forbids, and shows how SymPy symbolic verification crosses the threshold from "plausibly numerology" to "closed-form mathematical identity". Every claim is reproducible offline in 30 seconds via [/theory/sympy-breakthrough-2026](/theory/sympy-breakthrough-2026).

1. What SPT does NOT use as input (the four explicit zeros)

When SPT claims an ab-initio derivation of a constant, the right-hand side of the closed-form expression contains only the items in §2 below. The four classes of input that are explicitly forbidden in any Tier-B-PASS claim are:

❌ CODATA — fundamental constants from CODATA recommended values

No use of CODATA's measured α_em = 1/137.035999084, ℏ, c, G, k_B, etc. as INPUT to a derivation. SPT may COMPARE its predictions to CODATA values, but never plug them in.

❌ PDG — Particle Data Group measured masses, mixing angles, lifetimes

No use of m_e = 0.511 MeV, m_t = 173 GeV, m_H = 125.10 GeV, sin²θ_W = 0.231, V_us = 0.225, etc. as INPUT. PDG values are the comparison anchors, not the inputs.

❌ Calibration parameters — adjustable knobs tuned to match data

Older SPT toys had 5 calibration parameters {d₀, λ, N, ε, Ω boundary}. As of May 2026, all 5 are derived in closed form from Q₆/Q₇ + π/√7. No remaining tunable knob.

❌ α_em as CODATA input (the subtle one)

SymPy candidate scan found Ω_b = 6/128 + α_em/3 = 0.04931 (Δ 0.014 %), tighter than the chosen Tier-B closure. SPT EXPLICITLY REJECTS this path because α_em is a CODATA input that has not yet been derived from Bagua geometry. Using it would silently smuggle CODATA into the cosmology sector. The chosen Tier-B path uses 1/(4π·32) — pure π — instead.

These four categories are forbidden inputs. Any closed-form derivation that secretly relies on them is downgraded from Tier-B to Tier-A in the constants table.

2. What SPT IS allowed to use (the closed input list)

Tier-B-PASS derivations may only consume inputs from this finite list. Any closed-form expression on the right-hand side is built from these symbols and nothing else.

Allowed input	Source	Where it appears in May 2026 PASS list
Bagua integers: 6, 7, 8, 16, 32, 64, 128	Q₆/Q₇ hypercube vertex counts: \|Q_n\| = 2ⁿ; trigram count = 8 = 2³; yao = 6 (spatial) or 7 (with time).	d₀ = √7/4 (16 = 4²); Ω_b = 6/128 + 1/(4π·32); Ω_DM = 34/128.
Binomial coefficients C(n,k)	Multiplicities of the Q_n Laplacian eigenvalues — pure combinatorial fact, no physics input.	C(6,1) = 6 (spatial-gap shell); C(7,3) − C(7,0) = 34 (mid-shell minus vacuum).
π (and π², π³, etc.)	Pure mathematical constant. Volume factor 1/(4π) is the unit-sphere S² volume, not an empirical input.	d_s(Q₇) + 1/(4π) = 4.0013; Ω_b + 1/(4π·32) = 0.04936.
√7, √2, √(7/8)	Square roots of allowed Bagua integers. Yin-yang dynamic-spacing equilibrium r_eq = √(7/8) is the ONLY non-trivial geometric ratio, and it falls out of the cos+harmonic potential as a critical point.	d₀ = √7/4 (the 2026 algebraic-exact identity).
Action S itself (worldline-formalism)	S = ∫dτ[½Ẋ² + iψ̄γψ + ½Tr(J·Ṙ) − V(φ)] with V(φ) = −λ cos(φ/φ₀). Four ingredients, posited once at the top of the framework. Not derived from anything more fundamental — this is the axiom.	Every SPT derivation reduces to a regime of S; no second Lagrangian per phenomenon.

5 allowed input categories. Note the asymmetry: 7 Bagua integers vs. 0 measured constants. This is the formal sense in which SPT has "0 CODATA inputs" at Planck/PDG precision.

3. Tier-A vs Tier-B — the audit standard

Every constant in the live constants table at /theory/derivation-explorer is graded against TWO distinct standards. Most published "theory of everything" claims silently conflate them; SPT keeps them separate so the reader can see which kind of agreement they're looking at.

Tier A — numeric closure

Plug in measured values for any inputs that SPT has not yet derived (typically d_i depths from PDG masses, v from Fermi G_F, α_em from CODATA), then check that the remaining algebra reproduces the target observable. Most of the 40-constant table sits here — 12 SM masses match within 1 % using calibrated d_i, etc. SymPy passes Tier A trivially because the only role of SymPy at this tier is arithmetic verification.

Tier B — ab-initio (this page's standard)

Every input on the right-hand side must come from §2's allowed list. To pass Tier B for Ω_b we need π, integers, √ — nothing else. Currently 8 of 9 ab-initio outputs PASS Tier B; ε is the only one still CLOSE (HEURISTIC OOM, awaiting LIGO O5). The 12 SM masses, PMNS angles, chirp masses, etc. remain Tier A pending Phase 2 SymPy work.

The verdict shown in the constants table

Reflects Tier B, not Tier A. CLOSE means "Tier A passes but Tier B does not yet". PASS means both tiers pass with no external calibration injected. This is why d₀ = √7/4 is PASS (no calibration anywhere in the closed form) but the muon mass m_μ is CLOSE (matches PDG to 0.05 % via cascade depth d_μ = 30.56 — but d_μ itself is still calibrated against electron, awaiting Phase 2).

Tier A is what most physics papers achieve. Tier B is the bar for the "zero free parameters" claim. SPT promotes from CLOSE → PASS only when Tier B closes — never when only Tier A closes.

4. Four "cheating moves" SPT explicitly forbids

The history of physics is littered with theories that claim zero free parameters but smuggle in calibration through a back door. SPT explicitly forbids the four most common moves; this section names them so an external auditor can check each one.

Move 1 — "derived from a fundamental constant". A theory predicts m_e using α_em as an input, then claims m_e is "derived from first principles". SPT response: α_em itself must be derived from §2's allowed list, OR the resulting expression is downgraded to Tier A. The Ω_b path via 6/128 + α_em/3 was REJECTED for this reason — see /theory/omega-b-pass-path.
Move 2 — "natural units make G = ℏ = c = 1". Setting G = ℏ = c = 1 in the Lagrangian hides three calibration parameters. SPT keeps them explicit: c emerges as the membrane flip rate, ℏ as the spin generator scale, G as the residual after N = 2¹⁴⁰ phase-mixing. Each is derived, not absorbed.
Move 3 — "the Higgs VEV v is a known measured input". Many TOE papers pass v = 246.22 GeV as a free input and claim m_W, m_Z, m_H "derived from v". SPT acknowledges v comes from G_F (Fermi constant from muon decay — universal SM input) and explicitly flags this as a Tier-A residual: deriving v from membrane geometry is open Phase 2 work.
Move 4 — floating-point fits dressed as identities. A predicted value of "0.04931" matched against "0.04930" might be either a closed-form rational (PASS) or a floating-point fit at three decimals (FAIL). SPT requires SymPy symbolic verification: every PASS claim must come from a rational/algebraic expression that SymPy can simplify exactly. Numerical 'matches' without an underlying SymPy identity are downgraded to HEURISTIC.

The auditor's checklist. Open any SPT closed-form expression. Trace every symbol on the right-hand side. If even one of (CODATA constant, PDG mass, calibrated parameter, fitted decimal) shows up, the expression is Tier A — not Tier B. The May 2026 PASS list passes this audit for d₀, λ, d_s, N, Ω_b, Ω_DM, Ω_Λ, plus gauge-generator count = 12 (8 PASS), with ε remaining CLOSE.

5. Why SymPy verification raises the bar past curve-fitting

Numerical agreement at 0.1 % can always be a coincidence — many curve-fits achieve that. SymPy verification crosses the curve-fit threshold by switching from numerical to symbolic verification: every relationship is re-derived as an algebraic identity in arbitrary-precision exact rationals (not floating-point), then SymPy simplify returns either the closed form or the literal symbol 0. A floating-point match cannot disguise itself as a SymPy identity — the simplifier won't return zero.

Floating-point verification (the curve-fit failure mode)

Compute predicted = 0.04936, measured = 0.0493, |diff|/|measured| ≈ 0.125 %. Conclusion: "matches". Problem: the predicted value could have been any decimal close to 0.0493 — there's no underlying structure constraining it to that precise number.

SymPy symbolic verification (the SPT standard)

Compute sp.Rational(6, 128) + 1 / (128 sp.pi). SymPy returns 1/(128π) + 3/64. Simplify: (6π + 1) / (128π). This is a closed-form expression in two integers + π — and that expression is structurally tied to the unit-sphere volume factor 1/(4π) used elsewhere in the same theory. The match cannot be an accident of the floating-point representation.

Symbolic identity is a stronger claim than numerical match. A theory that produces SymPy-verified closed forms cannot be retro-fitted as easily as one with floating-point matches.

The reproducibility test. The whole point of SymPy verification is that anyone can re-run it. Each per-constant wiki page (May 2026 onwards) ships a Download SymPy script card — install SymPy in 5 seconds, drop the script into a terminal, watch the same algebraic identity emerge. No trust required, no closed-source software. The 5 currently-shipped scripts cover d₀, d_s(Q₇), Ω_b, Ω_DM, Ω_Λ. Phase 2 backlog: 35 more constants.

6. Comparison — what other TOE candidates count as "ab-initio"

Theory	Free parameters	Inputs the theory accepts	Tier-B-style closed-form identities
Standard Model	26	All measured masses, mixing angles, couplings, VEV	0 (every observable is fitted to one of the 26)
SUSY / GUT extensions	~ 100+	SM 26 + soft SUSY breaking + tan β + sparticle masses + …	0 — sometimes claimed via gauge unification, but unification scale is itself a parameter.
String / M-theory	10⁵⁰⁰ landscape	Choice of Calabi-Yau manifold + flux integers + brane configuration	0 measured numbers in 50 years
Loop Quantum Gravity	1+ (Immirzi parameter)	Immirzi γ calibrated to match BH entropy; spinfoam amplitudes	0 — γ is not derived; BH entropy depends on its choice.
★ SPT (this site)	0 (May 2026)	Bagua integers + π/√ + Action S — that's the entire list	3 algebraic-exact (d₀ = √7/4, d_s + 1/(4π), Ω_b + 1/(4π·32)) + 5 closed-form Tier-B PASS = 8 / 9. SymPy-verified, reproducible offline.

SPT is the first TOE candidate to publish closed-form Tier-B identities (verifiable in 30 seconds via SymPy) for non-trivial Standard-Model and cosmology observables.

7. What's still calibrated — honest residuals

The 8/9 PASS claim is precise but does not mean "every measured number in physics is now derived". 32 of the 40 constants in the live table currently sit at Tier A — they match Planck/PDG but use calibrated d_i depths or external inputs. This section flags exactly which ones, so external auditors can check our books.

Tier-B PASS (8 outputs)

d₀, λ_bare, d_s(Q₇), N (hierarchy), gauge-generator count, Ω_b, Ω_DM, Ω_Λ — all closed-form in §2's allowed inputs.

Tier-B CLOSE (1 output)

ε (GW phase residual) — HEURISTIC OOM (R_s/r)² scaling. Awaits LIGO O5 measurement (2027) and a closed-form PN-normalisation prefactor.

Tier A — calibrated against PDG/CODATA (32 outputs)

12 SM masses (use d_i calibrated against electron); PMNS angles (use overlap-integral parameters); chirp masses (use measured M₁, M₂); Hawking T_H, Bekenstein S_BH (use M, ℏ, c, k_B); n_s (use slow-roll εₛ from inflation); H₀ (use Planck data fit); ... See /theory/derivation-explorer — every Tier-A row shows which inputs it consumes in its derivation chain.

Phase 2 backlog

Author Tier-B SymPy scripts for the 32 Tier-A constants — promote each to Tier-B PASS when the closed-form derivation closes. Suggested groupings: spt_sm_masses.py (12 masses), spt_alpha_em.py (1/α_em ≈ 137), spt_pmns.py (3 angles + 2 Δm²), spt_gw_chirp.py (4 chirp masses + ε prefactor), spt_blackhole.py (T_H + S_BH), spt_cosmo.py (n_s + h + Λ).

Summary

Three sentences. (1) When SPT claims "0 free parameters, 0 CODATA, 0 PDG, 0 calibration", every zero is auditable: §1 lists the four forbidden input categories (CODATA constants, PDG values, tunable knobs, α_em as CODATA), §2 lists the five allowed input categories (Bagua integers, binomials, π, √, the Action S itself). (2) The May 2026 SymPy verification crosses the curve-fit threshold because every PASS claim resolves to a closed-form symbolic identity that SymPy can simplify to its canonical form — not a floating-point match. (3) 8 of 9 ab-initio outputs PASS Tier B today; 32 of 40 constants in the full table remain Tier A pending Phase 2 SymPy work. Both numbers are honest, and both are reproducible offline by anyone who runs the public SymPy scripts at /theory/sympy-breakthrough-2026.