← Session 35 — ii′-6-R: Lagarias 6.1 right-tail re-proof (E-032/D-073)
thinking (1511 chars)
`vIntegral_Jlag_right_le_IIMaj_quarter` unknown — because DL-6-ii's lemmas are AFTER DL-5's section in the file (section 9 comes after section 7 where dogLegUpper lives). The quarter lemma is defined in section 9 (DL-6-ii), but hVr2 in section 7 (DL-5) references it — forward reference not allowed in Lean. I need to move the DL-6-ii quarter lemma BEFORE the DL-5 assembly (or move the DL-5 assembly after DL-6-ii).
The cleanest: move `vIntegral_Jlag_right_norm_le_quarter` and `vIntegral_Jlag_right_le_IIMaj_quarter` to BEFORE section 7 (the DL-5 assembly) — i.e., right after DL-6-i's `norm_logDeriv_zeta_le_iimZeta` (section 8) and before section 7. But section 8 (DL-6-i) is AFTER section 7 in the file! So the order in the file is: DL-5 (§7) → DL-6-i (§8) → DL-6-ii (§9). The DL-5 hVr2 needs DL-6-ii's quarter lemma — forward reference.
Fix: move the DL-6 blocks (§8 dirichletCX chain + §9 quarter lemmas) BEFORE the DL-5 assembly (§7). The DL-6-i lemmas (dirichletCX, norm_logDeriv_zeta_le_dirichletCX, norm_term_vonMangoldt_X_le_three_pow, dirichletCX_le, log_nine_quarters_ge, log_four_ninths_le, four_ninths_rpow_sqrt_le, three_pow_neg_two_sqrt_sub_two_eq, norm_logDeriv_zeta_le_iimZeta) and DL-6-ii's two quarter lemmas — all need to come before §7's hIntegral_Jlag_low_le_dogLegUpper.
Easiest: cut the §8+§9 blocks and paste them before §7 (before the "/-! ## 7. The total right-horizontal bound" header). Let me do that with a python script (the Edit tool is being finicky with the large file).
Forward-reference error — DL-6 must come before DL-5 in the file. Moving the §8/§9 blocks before §7 via script.
tool: Write ok
input
{
"file_path": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\_move.py",
"content": "import io\n\np = \"NguyenRH1/LiDogLeg.lean\"\nwith io.open(p, encoding=\"utf-8\") as f:\n s = f.read()\n\nmark7 = \"/-! ## 7. The total right-horizontal bound (DL-5, D-074 \\u00a73.4) -/\"\nmark8 = \"/-! ## 8. The direct Dirichlet bound at re = 2\\u221an (DL-6)\"\nmark_end = \"\\nend NguyenRH1\\n\\nend\"\n\ni7 = s.index(mark7)\ni8 = s.index(mark8)\niend = s.index(mark_end)\n\nhead = s[:i7]\nmid5 = s[i7:i8]\ndl6 = s[i8:iend]\ntail = s[iend:]\n\ns2 = head + dl6 + mid5 + tail\nwith io.open(p, \"w\", encoding=\"utf-8\") as f:\n f.write(s2)\nprint(\"done\")\n"
}
result 2026-08-26 10:29:28Z → 2026-08-26 10:29:28Z
{
"type": "create",
"filePath": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\_move.py",
"content": "import io\n\np = \"NguyenRH1/LiDogLeg.lean\"\nwith io.open(p, encoding=\"utf-8\") as f:\n s = f.read()\n\nmark7 = \"/-! ## 7. The total right-horizontal bound (DL-5, D-074 \\u00a73.4) -/\"\nmark8 = \"/-! ## 8. The direct Dirichlet bound at re = 2\\u221an (DL-6)\"\nmark_end = \"\\nend NguyenRH1\\n\\nend\"\n\ni7 = s.index(mark7)\ni8 = s.index(mark8)\niend = s.index(mark_end)\n\nhead = s[:i7]\nmid5 = s[i7:i8]\ndl6 = s[i8:iend]\ntail = s[iend:]\n\ns2 = head + dl6 + mid5 + tail\nwith io.open(p, \"w\", encoding=\"utf-8\") as f:\n f.write(s2)\nprint(\"done\")\n",
"structuredPatch": [],
"originalFile": null
}
raw content_json (database row)
[{"type":"thinking","thinking":"`vIntegral_Jlag_right_le_IIMaj_quarter` unknown — because DL-6-ii's lemmas are AFTER DL-5's section in the file (section 9 comes after section 7 where dogLegUpper lives). The quarter lemma is defined in section 9 (DL-6-ii), but hVr2 in section 7 (DL-5) references it — forward reference not allowed in Lean. I need to move the DL-6-ii quarter lemma BEFORE the DL-5 assembly (or move the DL-5 assembly after DL-6-ii). \n\nThe cleanest: move `vIntegral_Jlag_right_norm_le_quarter` and `vIntegral_Jlag_right_le_IIMaj_quarter` to BEFORE section 7 (the DL-5 assembly) — i.e., right after DL-6-i's `norm_logDeriv_zeta_le_iimZeta` (section 8) and before section 7. But section 8 (DL-6-i) is AFTER section 7 in the file! So the order in the file is: DL-5 (§7) → DL-6-i (§8) → DL-6-ii (§9). The DL-5 hVr2 needs DL-6-ii's quarter lemma — forward reference.\n\nFix: move the DL-6 blocks (§8 dirichletCX chain + §9 quarter lemmas) BEFORE the DL-5 assembly (§7). The DL-6-i lemmas (dirichletCX, norm_logDeriv_zeta_le_dirichletCX, norm_term_vonMangoldt_X_le_three_pow, dirichletCX_le, log_nine_quarters_ge, log_four_ninths_le, four_ninths_rpow_sqrt_le, three_pow_neg_two_sqrt_sub_two_eq, norm_logDeriv_zeta_le_iimZeta) and DL-6-ii's two quarter lemmas — all need to come before §7's hIntegral_Jlag_low_le_dogLegUpper.\n\nEasiest: cut the §8+§9 blocks and paste them before §7 (before the \"/-! ## 7. The total right-horizontal bound\" header). Let me do that with a python script (the Edit tool is being finicky with the large file).","signature":""},{"type":"text","text":"Forward-reference error — DL-6 must come before DL-5 in the file. Moving the §8/§9 blocks before §7 via script."},{"type":"tool_use","id":"Write_510","name":"Write","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\_move.py","content":"import io\n\np = \"NguyenRH1/LiDogLeg.lean\"\nwith io.open(p, encoding=\"utf-8\") as f:\n s = f.read()\n\nmark7 = \"/-! ## 7. The total right-horizontal bound (DL-5, D-074 \\u00a73.4) -/\"\nmark8 = \"/-! ## 8. The direct Dirichlet bound at re = 2\\u221an (DL-6)\"\nmark_end = \"\\nend NguyenRH1\\n\\nend\"\n\ni7 = s.index(mark7)\ni8 = s.index(mark8)\niend = s.index(mark_end)\n\nhead = s[:i7]\nmid5 = s[i7:i8]\ndl6 = s[i8:iend]\ntail = s[iend:]\n\ns2 = head + dl6 + mid5 + tail\nwith io.open(p, \"w\", encoding=\"utf-8\") as f:\n f.write(s2)\nprint(\"done\")\n"},"extra_content":null}]