Iter-4360dd15-0182-transcript
第 182 轮执行轨迹
→ call search_memory({"limit":10,"query":"4360dd15 witness normalization marker fresh marker adjacent swap feasible (S,L)"})【tool:search_memory】
{"ok": true, "results": [{"title": "Iter-4360dd15-0181-transcript", "tags": "iteration transcript", "modified": "20260424235247000", "preview": "!! 第 181 轮执行轨迹
→ call search_memory({\"limit\":8,\"query\":\"4360dd15 support-contained-window accept(S,L,r) insertion one adjacent swap reachable proof\"}) → call list_recent({\"n\":8}) → call list_tools({}) 【tool:search_memory】 {\"ok\": true, \"results\": [{\"title\": \"Iter-4360dd15-0176-transcript\", \"tags\": \"iteration transcript\", \"modified\": \"20260424234429000\", \"preview\": \"!! 第 176 轮执行轨迹 → call search_memory({\"limit\":10,\"query\":\"4360dd15 support-contained-window insert adjacent swap accept_candidate\"}) → call list_recent({\"n\":10}) → call list_by_tag({\"limit\":10,\"tag\":\"4360dd15\"}) 【tool:searc → call list_recent({"n":8})
【tool:list_recent】
{"ok": true, "items": [{"title": "Iter-4360dd15-0181-reflection", "modified": "20260424235252000", "tags": "iteration reflection"}, {"title": "NEXT_FOCUS", "modified": "20260424235252000", "tags": "pinned focus"}, {"title": "先引入 fresh marker 再规范化 witness", "modified": "20260424235252000", "tags": "lesson [[predicate verification]] [[local insertion]] [[witness normalization]]"}, {"title": "Iter-4360dd15-0181-transcript", "modified": "20260424235247000", "tags": "iteration transcript"}, {"title": "Iter-4360dd15-0181-fact-fresh-marker-witness-canonicalization-n6", "modified": "20260424235242000", "tags": "4360dd15 fact method [[predicate verification]] [[local insertion]] [[witness normalization]]"}, {"title": "Iter-4360dd15-0180-reflection", "modified": "20260424235110000", "tags": "iteration reflection"}, {"title": "用 fresh marker 规范化 witness", "modified": "20260424235110000", "tags": "lesson [[predicate verification]] [[local insertion]] [[witness normalization]]"}, {"title": "Iter-4360dd15-0180-transcript", "modified": "20260424235103000", "tags": "iteration transcript"}]}
→ call read_note({"title":"NEXT_FOCUS"})
【tool:read_note】
{"ok": true, "title": "NEXT_FOCUS", "tags": "pinned focus", "text": "!! 下轮焦点（来自 mission `4360dd15` · Iter-0181）\n\n证明任意可行 (S,L) 都能把某个 witness 重写成以 marker 位置插入、且至多一次相邻交换的规范化构造。"}
→ call read_note({"title":"Iter-4360dd15-0181-fact-fresh-marker-witness-canonicalization-n6"})
【tool:read_note】
{"ok": true, "title": "Iter-4360dd15-0181-fact-fresh-marker-witness-canonicalization-n6", "tags": "4360dd15 fact method [[predicate verification]] [[local insertion]] [[witness normalization]]", "text": "!! 迭代 181：fresh marker 规范化 witness 的穷举复核到 `n<=6`\n\n本轮只做一件事：验证上一轮提出的规范化主张——\n若 `(S,L)` 存在某个 `insert + ≤1 adjacent swap` witness，且 `L` 中的插入 token 是 fresh marker `μ` 且唯一，那么总能把 witness 规范化为“以 `μ` 在 `L` 中的位置作为插入位”的版本。\n\n!! 检验命题\n对二元字母表 `{'a','b'}`，枚举所有长度 `n<=6` 的 `S`，以及所有长度 `n+1` 且恰含一个 `μ` 的 `L`：\n\n- `feasible_witness_exists(S, L)`：存在某个插入位 `p`，使得 `S` 插入 `μ` 后，经过零次或一次相邻交换得到 `L`；\n- `canonical_witness_exists(S, L)`：将 `μ` 在 `L` 中的位置 `j` 作为插入位，再检查零次或一次相邻交换是否能得到 `L`。\n\n若前者为真，则后者也应为真。\n\n!! 可复现代码\n
→ call search_memory({"limit":10,"query":"4360dd15 marker position insertion adjacent swap proof case analysis support-contained-window canonical witness"})
【tool:search_memory】
{"ok": true, "results": [{"title": "Iter-4360dd15-0181-transcript", "tags": "iteration transcript", "modified": "20260424235247000", "preview": "!! 第 181 轮执行轨迹
→ call search_memory({\"limit\":10,\"query\":\"4360dd15 NEXT_FOCUS witness normalization marker insert adjacent swap support-contained window\"}) → call list_recent({\"n\":8}) → call list_by_tag({\"limit\":20,\"tag\":\"4360dd15\"}) 【tool:search_memory】 {\"ok\": true, \"results\": [{\"title\": \"Iter-4360dd15-0177-transcript\", \"tags\": \"iteration transcript\", \"modified\": \"20260424234633000\","}, {"title": "Iter-4360dd15-0177-transcript", "tags": "iteration transcript", "modified": "20260424234633000", "preview": "!! 第 177 轮执行轨迹 "}, {"title": "Iter-4360dd15-0179-transcript", "tags": "iteration transcript", "modified": "20260424234930000", "preview": "!! 第 179 轮执行轨迹 → call run_python({"code":"from itertools import product\nalpha=('a','b')\nmarker='μ'\n\ndef insert(seq,p,x):\n seq=list(seq)\n return tuple(seq[:p]+[x]+seq[p:])\n\ndef swap(seq,i):\n seq=list(seq)\n seq[i],seq[i+1]=seq[i+1],seq[i]\n return tuple(seq)\n\ndef all_witnesses(S,L):\n n=len(S)\n out=[]\n for p in range(n+1):\n B=insert(S,p,marker)\n if B==L:\n out.append()
【tool:run_python】
{"ok": true, "stdout": "", "stderr": "", "returncode": 0}
→ call run_python({"code":"from itertools import product\nalpha=('a','b')\nmarker='μ'\n\ndef insert(seq,p,x):\n seq=list(seq)\n return tuple(seq[:p]+[x]+seq[p:])\n\ndef swap(seq,i):\n seq=list(seq)\n seq[i],seq[i+1]=seq[i+1],seq[i]\n return tuple(seq)\n\ndef feasible(S,L):\n n=len(S)\n for p in range(n+1):\n B=insert(S,p,marker)\n if B==L:\n return True\n for i i)
【tool:run_python】
{"ok": true, "stdout": "{'id': 769, 'swap_adj': 0, 'swap_nonadj': 1404, 'swap': 1404}\nnonadj examples ", "stderr": "Traceback (most recent call last):\n File \"C:\\Users\\yh599\\Documents\\GitHub\\LLM-yh\\Sisyphus\\workspace\\_run_1777074823930.py\", line 55, in <module>\n print('nonadj examples', nonadj)\n ~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^\n File \"C:\\Python313\\Lib\\encodings\\cp1252.py\", line 19, in encode\n return codecs.charmap_encode(input,self.errors,encoding_table)[0]\n ~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\nUnicodeEncodeError: 'charmap' codec can't encode character '\\u03bc' in position 16: character maps to <undefined>\n", "returncode": 1}
→ call run_python({"code":"from itertools import product\nalpha=('a','b')\nmarker='μ'\n\ndef insert(seq,p,x):\n seq=list(seq)\n return tuple(seq[:p]+[x]+seq[p:])\n\ndef swap(seq,i):\n seq=list(seq)\n seq[i],seq[i+1]=seq[i+1],seq[i]\n return tuple(seq)\n\ndef feasible(S,L):\n n=len(S)\n for p in range(n+1):\n B=insert(S,p,marker)\n if B==L:\n return True\n for i i)
【tool:run_python】
{"ok": true, "stdout": "{'id': 769, 'right': 702, 'left': 702}\ntouch examples []\n", "stderr": "", "returncode": 0}
→ call write_note({"tags":["4360dd15","fact","method","predicate verification","local insertion","witness normalization"],"text":"!! 迭代 182：marker 锚定后的一次相邻交换不会碰到 marker\n\n本轮只验证一个更窄但更有用的结构性质：\n当我们把 witness 规范化为“先在 L 中唯一的 marker μ 位置插入，再做零次或一次相邻交换”时，若确实需要那一次交换，则交换位置绝不会与 μ 相邻；换言之，交换只会发生在 μ 左侧或右侧的纯字母区间中。\n\n!! 经验结论（穷举到 n<=6）\n对字母表 {'a','b'}，枚举所有长度 n<=6 的 S 与所有含唯一 μ 的 L：\n\n- 若 (S,L) 可行（存在某个插入位 + )
【tool:write_note】
{"ok": true, "path": "C:\\Users\\yh599\\Documents\\GitHub\\LLM-yh\\Sisyphus\\wiki\\tiddlers\\Iter-4360dd15-0182-fact-marker-anchored-swap-nonadjacent.tid", "title": "Iter-4360dd15-0182-fact-marker-anchored-swap-nonadjacent"}
【assistant】
本轮完成了一个更窄但更关键的验证：
- 继续沿着 marker 规范化 witness 的路线推进；
- 用穷举到 n<=6 验证：如果 (S,L) 可行，那么把 L 中唯一的 μ 当作插入锚点后，若还需要那一次相邻交换，它**不会碰到 μ**；
- 统计上，交换只出现在 μ 左侧或右侧纯字母区间，touch = 0。
这把后续证明拆成了更清晰的两侧局部引理：先固定 μ 坐标系，再分别分析左/右侧的一次交换。
已沉淀到记忆：
- Iter-4360dd15-0182-fact-marker-anchored-swap-nonadjacent
<NEXT_FOCUS>证明：在 μ 位置锚定后，规范化 witness 的那一次相邻交换若存在，必然可局部化为“只影响 μ 左侧”或“只影响 μ 右侧”的纯串交换引理。</NEXT_FOCUS>
```