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2 | 2 |
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3 | 3 | ## 署名与版本 / Attribution and versions |
4 | 4 |
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5 | | -作者使用公开署名 **OccamGC**。[CITATION.cff](CITATION.cff)描述整个仓库;引用某项数学结论时,请使用下方对应研究笔记的条目,并注明实际使用的版本。四邻接的三次方界与补树障碍引用研究提交 `640ae4ac52a1ce5a3082022162611839f97591fe`;仅对角邻接拓展引用自己的提交 `3fe652bb9f3458ed41071e5f2377141272848dbc`。这些研究版本均发布于 2026-10-12,链接分别固定到包含该成果的证明版本。 |
| 5 | +作者使用公开署名 **OccamGC**。[CITATION.cff](CITATION.cff)描述整个仓库;引用某项数学结论时,请使用下方对应研究笔记的条目,并注明实际使用的版本。四邻接的三次方界与补树障碍引用研究提交 `640ae4ac52a1ce5a3082022162611839f97591fe`;仅对角邻接拓展引用自己的提交 `3fe652bb9f3458ed41071e5f2377141272848dbc`;八邻接拓展引用 `4d73b14e9b307412dd037bfa2f7bbe72543f36bc`。这些研究版本均发布于 2026-10-12,链接分别固定到包含该成果的证明版本。 |
6 | 6 |
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7 | | -The public author name is **OccamGC**. [CITATION.cff](CITATION.cff) describes the whole repository. For a particular mathematical result, use its separate research-note entry below and identify the version actually used. The orthogonal cubic bound and tree obstructions cite research commit `640ae4ac52a1ce5a3082022162611839f97591fe`; the diagonal-only extension cites its own commit `3fe652bb9f3458ed41071e5f2377141272848dbc`. These research versions were published on 2026-10-12, with immutable links to versions that contain the respective results. |
| 7 | +The public author name is **OccamGC**. [CITATION.cff](CITATION.cff) describes the whole repository. For a particular mathematical result, use its separate research-note entry below and identify the version actually used. The orthogonal cubic bound and tree obstructions cite research commit `640ae4ac52a1ce5a3082022162611839f97591fe`; the diagonal-only extension cites `3fe652bb9f3458ed41071e5f2377141272848dbc`; the eight-neighbor extension cites `4d73b14e9b307412dd037bfa2f7bbe72543f36bc`. These research versions were published on 2026-10-12, with immutable links to versions that contain the respective results. |
8 | 8 |
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9 | 9 | 入口页及默认分支会继续维护;以下固定链接不会随默认分支变化。条目类型为公开研究笔记,不表示期刊或会议发表。程序复核记录是辅助证据,不替代文字证明。 |
10 | 10 |
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@@ -67,3 +67,25 @@ This result transfers the orthogonal cubic bound, algorithm-specific worst-case |
67 | 67 | url = {https://github.com/OccamGC/MyAlgorithmProblems/blob/3fe652bb9f3458ed41071e5f2377141272848dbc/topics/simulation/grid-forest-matching/research/results/diagonal-only.en.md} |
68 | 68 | } |
69 | 69 | ``` |
| 70 | + |
| 71 | +## 八邻接拓展 / Eight-neighbor extension |
| 72 | + |
| 73 | +OccamGC. (2026). *Eight-neighbor induced forests retain the cubic bound*. MyAlgorithmProblems, research note, commit `4d73b14`. |
| 74 | + |
| 75 | +本项沿用原完整历史收费证明,将方向词从两对扩为四对互逆符号,保留有限第二轴引理、相同检查次数上界和条带最坏下界。其固定版本包含中英文证明、八邻接验证器及 881 个完整收费实例的报告;它不建立八邻接的补树障碍。 |
| 76 | + |
| 77 | +This result extends the original complete-history charge from two to four inverse direction pairs, preserving the finite second-axis lemma, exact check bound, and stripe worst-case lower bound. Its snapshot includes bilingual proofs, the eight-neighbor verifier, and a report with 881 complete-charge cases. It does not establish eight-neighbor tree-extension obstructions. |
| 78 | + |
| 79 | +[当前中文证明](topics/simulation/grid-forest-matching/research/results/eight-neighbor.zh.md) · [Current English proof](topics/simulation/grid-forest-matching/research/results/eight-neighbor.en.md) · [固定中文证明](https://github.com/OccamGC/MyAlgorithmProblems/blob/4d73b14e9b307412dd037bfa2f7bbe72543f36bc/topics/simulation/grid-forest-matching/research/results/eight-neighbor.zh.md) · [Versioned English proof](https://github.com/OccamGC/MyAlgorithmProblems/blob/4d73b14e9b307412dd037bfa2f7bbe72543f36bc/topics/simulation/grid-forest-matching/research/results/eight-neighbor.en.md) |
| 80 | + |
| 81 | +```bibtex |
| 82 | +@misc{OccamGC2026EightNeighborGridForest, |
| 83 | + author = {{OccamGC}}, |
| 84 | + title = {Eight-neighbor induced forests retain the cubic bound}, |
| 85 | + year = {2026}, |
| 86 | + month = oct, |
| 87 | + howpublished = {MyAlgorithmProblems research note}, |
| 88 | + note = {Published 2026-10-12. Git commit 4d73b14e9b307412dd037bfa2f7bbe72543f36bc. Extension of the complete-history cubic charging proof}, |
| 89 | + url = {https://github.com/OccamGC/MyAlgorithmProblems/blob/4d73b14e9b307412dd037bfa2f7bbe72543f36bc/topics/simulation/grid-forest-matching/research/results/eight-neighbor.en.md} |
| 90 | +} |
| 91 | +``` |
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