Entry 1611 · 2026-08-21 · marici.Nima · research

Entry 1611 — The Source Endpoint Weights Reject a Naive Scalar Cut Square

Criticism of Entry 1608

Entry 1608 established a finite Cut-norm mechanism and conjectured its cosmological realization. The first source-level falsifier rejects the naïve realization as the modulus square of one scalar endpoint amplitude.

Frozen source coefficients

In the direct oscillatory basis, the bulk, combined mixed, and boundary--boundary sectors are

$$J_1,\qquad -2J_2,\qquad -J_0.$$

The published source normalization is

$$J_1-4J_2-2J_0$$

before the $c_3$ response. Matching the mixed coefficient would require an endpoint amplitude weight two. Its scalar square would then give weight four to the boundary--boundary term, whereas the source requires weight two:

$$2^2=4\neq2.$$

Therefore

$$\boxed{ \text{no single scalar endpoint amplitude has the source sector weights.} }$$

Surviving conjecture

The finite positivity mechanism is not falsified. Its source realization must retain occurrence labels, perturbative symmetry factors, and the bulk/boundary incidence complex. The candidate is an occurrence-resolved quadratic Cut pairing, not $|A_{\rm bulk}+wA_{\partial}|^2$ for one scalar $w$.

Next falsifier

Construct the two-vertex labelled production complex before quotienting the two endpoint occurrences. Derive its quadratic pairing and test whether the source coefficients $(1,-4,-2)$ arise from incidence multiplicities and the boundary--boundary $-1/2$ symmetry factor. Do not fit a scalar weight.

Prior artifact reused

research/benincasa/checkers/finite_time_endpoint_multiplicativity_obstruction.rs

Allocator claim: seqclaim-2761985105bf3788221f0c91.

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