Balanced Support Calibrations for Moser's Worm Problem: Exact Certificate and Bound of Triangular Cover
Abstract
Moser's worm problem asks for a planar region of minimum area containing a congruent copy of every rectifiable planar arc of length one. We study the Bellman's lost-in-a-forest problem escape path for the isosceles triangle T=conv{(−c,0),(c,0),(0,s)}, s=766/√(625565), c=197/√(625565). The paper gives an exact positive four-source support calibration, a continuum to standard-polygonal reduction, a selected Λ-gap estimate, a corrected high-angle side-meeting argument, and exact finite ledgers. The original inner-anchor ledger covers 25 temporal orders: its 275 nonzero suffix states reduce to 13 exact squared norms and satisfy |R|<27131/25000. If either near anchor fails, a new delimiter-gap lemma produces one or two omitted hull edges whose normals range over an exact compact fan interval. A dependency-free rational replay checks 512 one-delimiter orders over 1540 signed half-angle intervals and 4096 two-delimiter orders over a finite signed rectangle cover. These three exhaustive branches give unconditionally E(T)≥ D:=82074390584/84861020075 =0.9671624323094728… Hence, the convex universal cover of Moser's worm area(T)/D2 =11511821678274125/44639604443512928 =0.257883595112076188….
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BibTeX
@misc{deng2026balanced,
title = {{Balanced Support Calibrations for Moser's Worm Problem: Exact Certificate and Bound of Triangular Cover}},
author = {Zhipeng Deng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04591},
eprint = {2609.04591},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04591},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Balanced Support Calibrations for Moser's Worm Problem: Exact Certificate and Bound of Triangular Cover
AU - Zhipeng Deng
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04591
UR - https://arxiv.org/abs/2609.04591
AB - Moser's worm problem asks for a planar region of minimum area containing a congruent copy of every rectifiable planar arc of length one. We study the Bellman's lost-in-a-forest problem escape path for the isosceles triangle T=conv{(−c,0),(c,0),(0,s)}, s=766/√(625565), c=197/√(625565). The paper gives an exact positive four-source support calibration, a continuum to standard-polygonal reduction, a selected Λ-gap estimate, a corrected high-angle side-meeting argument, and exact finite ledgers. The original inner-anchor ledger covers 25 temporal orders: its 275 nonzero suffix states reduce to 13 exact squared norms and satisfy |R|<27131/25000. If either near anchor fails, a new delimiter-gap lemma produces one or two omitted hull edges whose normals range over an exact compact fan interval. A dependency-free rational replay checks 512 one-delimiter orders over 1540 signed half-angle intervals and 4096 two-delimiter orders over a finite signed rectangle cover. These three exhaustive branches give unconditionally E(T)≥ D:=82074390584/84861020075 =0.9671624323094728… Hence, the convex universal cover of Moser's worm area(T)/D^2 =11511821678274125/44639604443512928 =0.257883595112076188….
ER -