Exact realization of nonflat Boolean parity costs on Sun trees: Intrinsic recognition and exact construction at treewidth two
Abstract
For rational nonnegative Boolean cost tables with a strict parity gap, intrinsic cut tests and four-point node costs characterize exact minimum-scope realization over all trivalent Sun-tree shapes at ordinary treewidth two. A rooted subset recurrence minimizes the scalar capacity budget without enumerating complete labelled trees. Recognition is polynomial in the explicit table length and entry bit length, rather than in the number of boundary variables. A successful test gives an exact nonnegative network with 4n-9 hidden variables and 9(n-2) genuine pair scopes. Input-grid preservation keeps every primitive cell on the target's original common rational grid and between zero and the maximum target value. A target-bound Bellman certificate, checked by a separately written verifier, rejects every minimum-scope presentation conditional on the equality-graph premise. The supplied-tree scalar criterion, input-grid construction and all-tree recognition retain their explicit imported equality-graph and ternary-synthesis premises. These are proof-supported conditional candidate results. No succinct-input, unrestricted-treewidth or all-optima classification claim is made.
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BibTeX
@misc{barritz2026exact,
title = {{Exact realization of nonflat Boolean parity costs on Sun trees: Intrinsic recognition and exact construction at treewidth two}},
author = {Robert Barritz},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23620355},
url = {https://zenodo.org/records/23620355},
note = {CC0},
}
RIS
TY - UNPB
TI - Exact realization of nonflat Boolean parity costs on Sun trees: Intrinsic recognition and exact construction at treewidth two
AU - Robert Barritz
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23620355
UR - https://zenodo.org/records/23620355
AB - For rational nonnegative Boolean cost tables with a strict parity gap, intrinsic cut tests and four-point node costs characterize exact minimum-scope realization over all trivalent Sun-tree shapes at ordinary treewidth two. A rooted subset recurrence minimizes the scalar capacity budget without enumerating complete labelled trees. Recognition is polynomial in the explicit table length and entry bit length, rather than in the number of boundary variables. A successful test gives an exact nonnegative network with 4n-9 hidden variables and 9(n-2) genuine pair scopes. Input-grid preservation keeps every primitive cell on the target's original common rational grid and between zero and the maximum target value. A target-bound Bellman certificate, checked by a separately written verifier, rejects every minimum-scope presentation conditional on the equality-graph premise. The supplied-tree scalar criterion, input-grid construction and all-tree recognition retain their explicit imported equality-graph and ternary-synthesis premises. These are proof-supported conditional candidate results. No succinct-input, unrestricted-treewidth or all-optima classification claim is made.
ER -