Position-colour-preserving isomorphisms of binary rewrite graphs with unbordered difference words
Abstract
For any two binary keywords of the same length L ≥ 2 whose adjacent-difference words are unbordered, the paper proves that their rewrite graphs admit a position-colour-preserving isomorphism for every word length n ≥ 0. Applying the result to 10000 and 01000 gives a negative answer to Open Problem 18 in the JIS version of Bates et al. (2025). Version 0.3.0 recasts the earlier Chinese working paper in formal English and AMS-style LaTeX while retaining the theorem and recorded computational ranges. The complete proof, appendix, references and reproducibility materials support scrutiny and further research. Finite computation is distinguished from the general proof; completed independent human line-by-line verification and journal peer review are not recorded.
對任意兩個等長且長度 L ≥ 2 的二元關鍵字,若其相鄰差分字均為 unbordered(沒有相同的非空真前綴與真後綴),本文證明其替換圖對每個字長 n ≥ 0 都存在保位置顏色同構。套用於10000與01000,得到Bates等人(2025)JIS版Open Problem 18的負答。v0.3.0將較早中文工作論文重整為正式英文與AMS風格LaTeX,保留同一定理與計算範圍,提供完整證明、附錄、參考文獻及重現材料,供論證檢查與延伸研究。有限計算與一般證明分開,尚未完成獨立人類逐行核驗或期刊同儕審查。
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BibTeX
@misc{chu2026positioncolourpreserving,
title = {{Position-colour-preserving isomorphisms of binary rewrite graphs with unbordered difference words}},
author = {Chen-Yu Chu},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23615596},
url = {https://zenodo.org/records/23615596},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Position-colour-preserving isomorphisms of binary rewrite graphs with unbordered difference words
AU - Chen-Yu Chu
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23615596
UR - https://zenodo.org/records/23615596
AB - For any two binary keywords of the same length L ≥ 2 whose adjacent-difference words are unbordered, the paper proves that their rewrite graphs admit a position-colour-preserving isomorphism for every word length n ≥ 0. Applying the result to 10000 and 01000 gives a negative answer to Open Problem 18 in the JIS version of Bates et al. (2025). Version 0.3.0 recasts the earlier Chinese working paper in formal English and AMS-style LaTeX while retaining the theorem and recorded computational ranges. The complete proof, appendix, references and reproducibility materials support scrutiny and further research. Finite computation is distinguished from the general proof; completed independent human line-by-line verification and journal peer review are not recorded. 對任意兩個等長且長度 L ≥ 2 的二元關鍵字,若其相鄰差分字均為 unbordered(沒有相同的非空真前綴與真後綴),本文證明其替換圖對每個字長 n ≥ 0 都存在保位置顏色同構。套用於10000與01000,得到Bates等人(2025)JIS版Open Problem 18的負答。v0.3.0將較早中文工作論文重整為正式英文與AMS風格LaTeX,保留同一定理與計算範圍,提供完整證明、附錄、參考文獻及重現材料,供論證檢查與延伸研究。有限計算與一般證明分開,尚未完成獨立人類逐行核驗或期刊同儕審查。
ER -