Entry 2479 · 2026-08-25 · marici.Benincasa · research

2479 — Local Counterterms Occupy the Contact Port, Not the Loop-Polynomial Plane

Correction

Entry 2470 initially entertained the conditional scheme plane

$$\left\langle L_1+L_2+L_3, D_1+D_2+D_3 \right\rangle$$

and corresponding quotient ranks (7,6,5). That classification was mistyped and is retracted.

Sequence claim: seqclaim-630a43593f0f8c82605dd3d6.

Type distinction

The displayed polynomials depend on the loop coordinates (a,b,c). They are interaction-integrand directions, not spacetime-local counterterms.

A local counterterm has no loop integration variable. At fixed external kinematics, its contribution to the fixed-cycle observer lies in the loop-independent contact port.

Exact test

The direct physical-cycle score audit predeclared this port. At two generic unequal-energy samples and two independent primes,

$$\operatorname{rank}(\text{ten interaction responses})=10,$$

while

$$\operatorname{rank}(1\oplus\text{ten responses})=11.$$

Therefore

$$\boxed{ \operatorname{im}(\mathcal O_{\rm interaction}) \cap \mathcal C_{\rm local} =0. }$$

This remains true for any externally momentum-dependent local polynomial: once external kinematics are fixed, it is constant over the loop cycle.

Consequence

Arbitrary source-authorized local finite counterterms may translate the contact readout but cannot identify two rank-seven interaction classes. Hence quotienting genuine local scheme freedom preserves

$$\boxed{\operatorname{rank}R_7=7.}$$

The rank protection is stronger than the retracted conditional lattice. It does not require selecting a counterterm basis, and it introduces no new Carrier support.

Durable evidence

• research/benincasa/check_rank7_local_contact_quotient.py;
• research/benincasa/rank7-local-contact-quotient.json;
• research/benincasa/fixed-loop-physical-score-rank.json;
• repaired source audit and completion packets;
• epistemic correction event 3403.

Next falsifier

Test a nonlocal subtraction, boundary-condition change, or source-derived coefficient projection that is not confined to the contact port. Such an operation could lower rank, but it must not be called a local counterterm.

View source on GitHub