← SRBRD: The Symmetric Root-Bounded Relation Domain and the Sieve–Parity Boundary / SRBRD-01 · Structural compression and the first-order no-go

SRBRD: The Symmetric Root-Bounded Relation Domain and the Sieve–Parity Boundary SRBRD-01 · Structural compression and the first-order no-go Author line in the source: Neo.K; Aletheia (GPT-5.6 Sol)

Structural Compression Audit: Exact Cell Cardinalities, Center-Divisor Collapse, CRT Overlap, Tree-Overlap Upper Bound and a First-Order No-Go

Closed-form left/right cell cardinalities, same-prime left/right collapse iff r divides m, CRT pairwise intersections, and a spanning-tree union bound that gives a finite non-cover certificate; also shows first-order capacity and pairwise-tree bounds are not universal (they fail by m = 1000 and 5000).

Finds a non-trivial exact compression, but the verdict is 'GLOBAL NONCOVER GATE NOT PASSED': there is no non-cover theorem uniform in m. The tree bound is a classical Hunter–Worsley-type inequality that the paper lists as a 'new exact structure' without citation. The 8-row audit table of Appendix B (m = 34, 50, 100, 199, 210, 211, 1000, 5000) was reproduced in all six columns in the pre-publication read-through.

Connections · Connections

PreviousSRBRD-00 · The exact representation kernel · The Exact Representation Kernel: Finiteness, Two-Way Equivalence and a Count-Level Bijection for the Symmetric Root-Bounded Relation Domain

NextSRBRD-03 · Center–frontier occupancy · Center–Frontier Occupancy: The Exact Bonferroni Remainder and a Cap-Corrected Non-Cover Certificate

This is a full-text translation of the Chinese source, which remains authoritative for its research claims. Translation is not independent mathematical verification and does not upgrade the original evidence level.

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