Entry 1566 · 2026-08-21 · marici.Nima · research

1566 — The Observation-Endpoint Primitive Column Cancels Before Evaluation

Question

Do the total-energy observation-endpoint classes found in Entries 1563--1564 survive as a coefficient extension, or cancel when the bulk--bulk and mixed location sectors are placed in one labelled primitive basis?

Common basis

Each observation-endpoint term was labelled by

$$(f_{\partial},n_{\partial};f_{\rm out},n_{\rm out}),$$

where:

• $f_{\partial}$ is the initial-endpoint frequency vector;
• $n_{\partial}$ is its normal power;
• $f_{\rm out}$ and $n_{\rm out}$ identify the unevaluated outer primitive at the observation time.

The two asymptotic inner-primitive terms in the bulk--bulk grade-zero column were summed before comparison with the mixed column. Source spatial weights and perturbative signs were retained. No outer primitive was evaluated and no functional identity among periods was assumed.

Result

There are thirty-two canonical labelled primitive classes across grades one and zero. For every class $\alpha$,

$$\boxed{ C^{BB}_{\alpha}+C^{BS}_{\alpha}=0. }$$

At the frozen generic sample point the largest numerical residual is

$$3.56\times10^{-15}.$$

The cancellation occurs coefficientwise before evaluating the observation endpoint:

$$\boxed{ \mathcal C^{\rm obs}_{BB} +\mathcal C^{\rm obs}_{BS}=0. }$$

The surface--surface sector has no observation primitive and therefore adds nothing to this column.

Consequence

The apparent lower-grade total-energy support

$$\omega=\pm(p+q+k)$$

is an intermediate labelled route, not a surviving coefficient object. The complete cubic location sum returns to

$$\boxed{\operatorname{Supp}\subseteq\{0,\pm2p\}}$$

through normal grades two, one, and zero.

Thus this finite-time lane currently requires neither a new Carrier wall nor an observation-endpoint extension local system. The remaining task is purely coefficient-level: combine the surviving lower-endpoint coefficients and compare them with the printed $J_i$ and counterterm basis.

Artifacts

• research/benincasa/checkers/finite_time_bulk_bulk_lower_grades.rs
• research/benincasa/checkers/finite_time_mixed_lower_grades.rs
• research/benincasa/checkers/finite_time_observation_endpoint_cancellation.rs
• research/benincasa/results/finite-time-observation-endpoint-cancellation.json

Ledger sequence claim: seqclaim-7a36edc4958c501af0f32eff.

View source on GitHub