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Falsification surface · 2026

How to kill TFPT.

A theory that cannot fail explains nothing. This page lists the committed kill criteria of the TFPT 5.1 compiler closure — frozen in advance in the freeze file — together with the experiment or structural argument that would kill the construction. The no-knobs audit underneath records what the theory may consume as input and what it may not.

Each output is killed by any single satisfied criterion. The construction does not survive on most outputs being right.

Committed kill criteria

Each output has a single sufficient kill condition

The solar angle θ₁₂ (JUNO), the tensor ratio r (CMB-S4), neutrino ordering, the strong-CP null, dark-energy w, the EM fixed point, the E₈ glue, the flavor invariants, and no second Higgs — each row is sufficient on its own to falsify the construction. m_p/m_e is listed for honesty: it is explicitly not claimed as a compiler power.

Solar angle θ₁₂

Doc 2 · JUNO (live)
Numerical kill

A JUNO central value clearly away from sin²θ₁₂ ≈ 0.307 at high significance kills the seam-misalignment mechanism. JUNO has been taking data since August 2025 — this is the sharpest live test.

sin2θ1213φ020.3067\sin^2\theta_{12} \neq \tfrac{1}{3} - \tfrac{\varphi_0}{2} \approx 0.3067

Tensor ratio r

Doc 1 · CMB-S4
Numerical kill

Any robust r ≳ 0.01 is incompatible with the R² branch on which M_Pl and A_s rest. The scalaron predicts r = 12/N★² ≈ 0.004, already below the BK18 bound r < 0.036.

r0.01    R2 branch killedr \gtrsim 0.01 \;\Rightarrow\; R^2\text{ branch killed}

Neutrino ordering / m_ββ

Doc 2 · LEGEND, nEXO
Numerical kill

Inverted ordering, or a large effective Majorana mass m_ββ, kills the Majorana branch. TFPT prefers normal ordering with a small m_ββ.

inverted ordering, or mββ102eV\text{inverted ordering, or } m_{\beta\beta} \gtrsim 10^{-2}\,\text{eV}

Strong CP θ_eff

Doc 2 · PSI nEDM
Identity / theorem kill

A solid neutron-EDM signal above the SM background falsifies the structural cancellation. θ_eff = 0 follows from γ₅-Hermiticity, polar structure and the sheet involution plus reflection positivity.

θeff0    construction killed\theta_{\mathrm{eff}} \neq 0 \;\Rightarrow\; \text{construction killed}

Dark-energy w

Doc 1 · DESI
Cosmology kill

A robust w ≠ −1 kills the single-engine dark-energy readout, where Λ ∼ e⁻²ᵅ⁻¹ and H₀ ∼ √Λ come from the same exponential scale grammar.

w1w \neq -1

EM fixed point α⁻¹

Doc 1 · CODATA
Numerical kill

F_U(1)(α) = 0 fails to admit a unique positive root, or the root drifts outside the declared interface uncertainty (currently ≈ 4 × 10⁻⁸ in α⁻¹, about 1.9σ of CODATA-2022).

FU(1)(α)=0 has no/second root, or Δα1>ΔF_{U(1)}(\alpha_\star) = 0 \text{ has no/second root, or } |\Delta\alpha^{-1}| > \Delta

E₈ glue

Doc 1 (structural)
Identity / theorem kill

D₅ and A₃ fail to share the ℤ₄ discriminant, or the glue norms do not sum to the E₈ root norm 2. The whole compiler closure rests on this lattice fact.

disc(D5)disc(A3) or q(D5)+q(A3)2\operatorname{disc}(D_5) \neq \operatorname{disc}(A_3) \text{ or } q(D_5)+q(A_3) \neq 2

Flavor invariants

Doc 2 (structural)
Structural kill

A future global CKM/PMNS fit that cannot be carried by a residue matrix with det R = 8, principal 2-minors (2,3,5) and χ_R = t³ − 9t² + 10t − 8. Every load-bearing flavor number must live in an E₈ projection.

detR8 or minors(2,3,5)\det R \neq 8 \text{ or } \mathrm{minors} \neq (2,3,5)

No second Higgs

Doc 1 (structural)
Structural kill

Robust discovery of a second light seam-even Higgs doublet. The carrier index forces N_Φ = g_car − |μ₄| = 1; an additional doublet kills it.

NΦ=1no second light doubletN_\Phi = 1 \Rightarrow \text{no second light doublet}

m_p/m_e — not claimed

Doc 4 (honesty)
Structural kill

The proton/electron ratio is explicitly NOT claimed as a compiler power. It is a cross-sector QCD/EW ratio, deliberately not forced onto the ladder — it only fails if mis-asserted as a compiler power.

mp/me is [A], not a compiler powerm_p/m_e \text{ is } [\mathrm{A}],\ \text{not a compiler power}

Status discipline

Cross-cutting
Structural kill

A claim is promoted past the grade its document carries, an empirical input enters undeclared, or the text disagrees with the machine-checked ledger. The ledger always wins.

textstatus ledger\text{text} \neq \text{status ledger}
No-knobs audit

Inputs allowed, inputs forbidden, free knobs

A claim of 'no fitted constants' is only as strong as the audit table behind it. For each TFPT output, the table below records the inputs the construction may use (the two axioms and their consequences), the inputs it explicitly may not use, and the number of free parameters available for absorption. The free-knob count is the bar to clear.

No-knobs audit — what is allowed, what is forbiddenFree knobs: 0
OutputInputs allowedInputs forbiddenFree knobs
α⁻¹(0)c₃ = 1/(8π), b₁ = 41/10, the word-lengths Σ L + N_Φ = 41, the exact seam opening φ_seam(α)Fitting against CODATA / atom-recoil values; freezing φ_seam at φ₀ inside the root equation0
sin²θ₁₂ (solar angle)The seed φ₀ and the glue norm q(A₃) = 3/4 (seam misalignment ε = (3/4)φ₀)NuFIT central value pre-loaded as input0
sin²θ₁₃ (reactor angle)The seed φ₀ and the carrier trace e⁻⁵ᐟ⁶ (γ = 5/6)Oscillation-fit central value pre-loaded as input0
det R = 8, minors (2,3,5)The compiler residue matrix R = R(g_car, μ₄)Fitting R to a CKM/PMNS global fit0
N_Φ = 1 (Higgs index)The carrier index, N_Φ = g_car − |μ₄| = 1Observed Higgs count used as primitive input0
θ_eff = 0 (strong-CP null)γ₅-Hermiticity, polar structure, sheet involution + reflection positivityTuned θ-phase, hidden flavor-side cancellation0
M_scal = c₃^(7/2) M̄ (scalaron)The seam power c₃⁷ = c₃^(Ω_adm − 10 b₁), exponent 7 = 48 − 41Fitting the scalaron mass to A_s0
n_s, r, A_s (inflation)The R² attractor + the seam-fixed scalaron mass + the e-fold count N★A free inflationary amplitude0 (amplitude) · N★ input (50–60)
β_rad = 0.2424° (birefringence)The determinant-line response, β_rad = φ₀/(4π)Calibration absorbed into the predicted angle0
Ω_b = 0.04894 (baryon density)β_rad via Ω_b = (4π − 1)β_radPlanck value used as primitive input0
m_a ≈ 23.8 µeV (axion DM)f_a = M_scal/128 and the closed misalignment θ_i = 170°Coupling rescaling to fit a haloscope window0 (decay-constant conjecture) · scenario-dependent (relic)
Reading rule.For every row, the output value must be reproducible from the “allowed inputs” alone — without touching the “forbidden inputs”. The free-knob count is the number of parameters the theory may adjust to land on the listed value. Any row where this count exceeds zero is treated as a fit, not a prediction.