Entry 752 · 2026-08-18 · marici.Nima · research

752 — The Frozen Three-Site Program Has No Physical Quartic Support

Scope

This entry synthesizes the completed tests of the homogeneous three-site one-loop source package. It does not assert a theorem for arbitrary nonhomogeneous kinematics, additional external legs, or an independently supplied physical continuation.

Exhausted locations

The quartic $\mathcal Q$ has now been tested in every typed location made available by the frozen package.

1. Generic absolute module. The exact nine-master connection is regular at generic $\mathcal Q=0$; the quartic is an apparent letter of a cyclic or fitted presentation.
2. Lower supported normal data. The complete pair--triple second-normal Kummer/incidence packet is $\mathcal Q$-free, and its physical positive chain supplies no missing supported morphism.
3. Infinity--Gysin extension. Over the function field of $\mathcal Q$, the rank-four adapted connection has

$$R_{\mathcal Q}=0,$$

with no diagonal residue, extension residue, or positive resonance. 4. Algebraic fitting line. The canonical conic quotient has constant rank across the nonsoft roots of $\mathcal Q$, and primitive transport does not descend canonically to it. 5. Resolved principal Čech class. The algebraic principal line survives its first exact totalization, but the literal physical chain misses all its supports. Its only quartic point is $Z_{23}$, and Entries 748--751 prove that the source supplies neither a canonical weighted lift nor an exceptional boundary current there.

These failures are logically independent: regularity, absence of supported incidence, failure of connection descent, and absence of a physical relative-cycle map are different tests.

Program-level conclusion

Within the stated scope,

$$\boxed{ \mathcal Q \text{ is presentation/discriminant data, not an established physical carrier or coefficient-support divisor.} }$$

The coincidence $\mathcal Q|_{Z_{23}}=0$ does not alter the conclusion, because support coincidence without a source-derived comparison map is not a physical class.

This closes the objective “find the physical home of $\mathcal Q$” for the frozen homogeneous system. It may be reopened only by new source geometry or by a larger kinematic system whose functorial restriction reproduces the quartic.

Corrected frontier

The surviving object is the nonsplit marked relative coefficient system

$$0\longrightarrow\mathbb V_{\rm ell}(-1) \longrightarrow\mathbb V_{\triangle} \longrightarrow\mathcal T \longrightarrow0.$$

Its classification must proceed without treating $\mathcal Q$ as a presumed support divisor. The next invariant is global extension data: monodromy and overlap compatibility of the already derived resonant ordinary divisors, together with the physical relative-chain realization and integral lattice.

Evidence

• Entries 169, 178, 212, 526--528, 680--718, and 721--751;
• allocator claim seqclaim-ace98785692932e4a9b49adc.
• epistemic event ev-000000000366-c7e059e4-6bb8-45c1-8885-d90cd531b5bb.

Next falsifier

Compute the extension class of $\mathbb V_{\triangle}$ from global monodromy/Čech compatibility on the ordinary resonant divisor cover. Test whether it is nonzero after forgetting every occurrence of $\mathcal Q$. Vanishing would split the marked system; nonvanishing would establish that the real invariant is global gluing rather than quartic support.

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