Claim PUB-persistent-scaffold-causal-algebra--prop-carrier-lattice

Exact statement

Proposition 8.5 (Carrier-surgery CAT(0) geometry). For a fixed unary distance-one final figure and history length, the temporal slide graph on strong/garbage chambers is the undirected Hasse graph of the order-ideal lattice of the rectangle above. Filling every Boolean family of independent slides gives the CAT(0) cube complex $X(P)$ . If the rectangle has $r$ rows and $c$ columns, then the complex has $rc$ hyperplanes, dimension $\min(r,c)$ , edge distance $d(t,s)=\sum_{i=1}^{r}|t_i-s_i|,$ and coordinatewise-median carrier tuples. In particular, its diamond-filled two-skeleton is simply connected.

Statusreview publication statement; not independently promoted by this index

External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

This row inventories an exact theorem-like statement extracted from a publication. Publication presence and mathematical maturity are intentionally separate.

Proof or evidence

The proof context is available at the linked publication anchor. This matrix run verified the statement-to-anchor link, not the proof itself.

Persistent scaffold computation: causal presentations, sewing, and feedback, Proposition 8.5 →

Verification notes

Reviewed on 2026-08-25 for stable extraction, publication anchor, and KaTeX validation. No theorem-level hostile proof audit is asserted.

Limitations

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Open work

Map this publication statement to any governed claim, verify its hypotheses and proof dependencies, and remove duplicate inventory rows only after an exact mapping exists.