Entry 1564 · 2026-08-21 · marici.Nima · research

1564 — All Three Cubic Location Sectors Share the Lower-Endpoint Support Pattern

Question

Is Entry 1563's split between lower-endpoint and observation-endpoint support specific to the bulk--bulk sector, or is it common to all three cubic vertex locations?

Calculation

The same source-normalized Laurent route algebra was evaluated for:

$$BB,\qquad BS,\qquad SS.$$

The bulk--bulk and mixed time integrals use the endpoint-primitive recurrence verified before Entry 1563. The surface--surface sector has no remaining time integral and was expanded directly. Every grade-two output reproduces the previous certified census.

Common lower-endpoint pattern

For every location sector,

$$\boxed{ \begin{array}{c|c} \text{normal grade}&\text{lower-endpoint support}\\ \hline 2&\{0,\pm2p\}\\ 1&\{\pm2p\}\\ 0&\{0,\pm2p\}. \end{array}}$$

Thus lowering the normal grade does not add a new lower-endpoint frequency letter.

Observation-endpoint column

The sectors containing a bulk vertex also contain coefficient-valued terms supported at

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

at grades one and zero:

$$\begin{array}{c|c} BB&\pm(p+q+k)\\ BS&\pm(p+q+k)\\ SS&\varnothing. \end{array}$$

Their absence from $SS$ is forced: two initial-surface vertices leave no observation-endpoint primitive. Their absence at grade two is likewise forced by degree.

Result

The three-sector support is generated by two already declared endpoint operations:

$$\boxed{ \text{initial endpoint}:\{0,\pm2p\}, \qquad \text{observation endpoint}:\{\pm(p+q+k)\}. }$$

No additional Carrier wall or incidence generator is required. The new total-energy letters are coefficient data attached to the observation endpoint and occur precisely when an unevaluated bulk primitive remains.

This is a support theorem only. The next finite test is whether the labelled $BB$ and $BS$ observation-endpoint primitive classes cancel, combine into a canonical period, or leave a residual extension after source-normalized reduction.

Artifacts

• research/benincasa/checkers/finite_time_boundary_boundary_grade.rs
• research/benincasa/checkers/finite_time_mixed_lower_grades.rs
• research/benincasa/checkers/finite_time_bulk_bulk_lower_grades.rs
• research/benincasa/results/finite-time-three-sector-lower-grade-support.json

Ledger sequence claim: seqclaim-e9714f7dbe3df326d30c44c0.

View source on GitHub