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3602 bytes, as of the version from 2026-10-30 22:06 (current). Recorded here, not run.
{
"table": "T633",
"skill_manifest": "../20261030T215605Z-build-skills/manifest.json",
"sources": [
{
"url": "https://arxiv.org/pdf/0904.0744",
"locator": "Section 3, equations (4), (6)-(9), and total/coexact zeta relation preceding (3)",
"checked": "Unit sphere spectra, SU(2) projector, complex versus real dimensions, Hodge decomposition."
},
{
"url": "https://arxiv.org/pdf/hep-th/9212022",
"locator": "Sections 2-4; equation (1.1), PDF page 2",
"checked": "Scalar and coexact determinant controls; their sum is the full nontrivial projective-line logarithm."
},
{
"url": "https://sigma-journal.com/2022/091/sigma22-091.pdf",
"locator": "Equation (4.3), PDF page 14; Proposition 5.1, PDF page 15",
"checked": "Unit-radius trivial torsion and nontrivial-character torsion with inverse quotient exponents."
},
{
"url": "https://www.uni-muenster.de/FB10/mjm/vol_15/mjm_vol_15_12.pdf",
"locator": "Theorem 1.3, page 392",
"checked": "Unoriented classification by negation and inversion."
}
],
"database_documents_read": [
"T631",
"T632",
"T599",
"T595",
"T600",
"T622",
"T623",
"T14",
"T94"
],
"companion_slugs": {
"T631": "Coexact_one-form_Laplacian_determinants_on_lens_spaces",
"T632": "Scalar_Laplacian_determinants_on_lens_spaces",
"T599": "Ray_Singer_torsion_of_lens_spaces"
},
"attachment_provenance": {
"T631/generate.py": {
"url": "https://numberdb.org/files/T631/generate.py?raw=1",
"sha256": "fb65d748f6ec248cc8e8551ea7a9fdb6e8b5aa3a7df8fe69d533e4fe56e4062a"
},
"T631/checks.py": {
"url": "https://numberdb.org/files/T631/checks.py?raw=1",
"sha256": "3f2f175e7ec4b18625c634e8546d5fa0eea9b4284274dceacbde6eb53d358a07"
},
"T631/continuation.md": {
"url": "https://numberdb.org/files/T631/continuation.md?raw=1",
"sha256": "f6963983c78a8e188d3443742af555b0c8f2cc326ce9247851bd11a9840d7321"
},
"T631/argument-selection.md": {
"url": "https://numberdb.org/files/T631/argument-selection.md?raw=1",
"sha256": "ab921fca645864f48a8666fa76cf82bd93dee4a5361b851617bcc4b64f49893c"
},
"T632/generate.py": {
"url": "https://numberdb.org/files/T632/generate.py?raw=1",
"sha256": "d39d7691bd55396f57b24009fdde3f532b5f087e4e2d21d0682aedc294d44c8c"
},
"T632/checks.py": {
"url": "https://numberdb.org/files/T632/checks.py?raw=1",
"sha256": "39b6e189ef749f1367d0c2673fc9231c600bb6b78077534a81d076db277cd790"
},
"T632/continuation.md": {
"url": "https://numberdb.org/files/T632/continuation.md?raw=1",
"sha256": "037783f591550023d585fae1e51337f946fac9fdb5ea20047749aeafeb777fb3"
},
"T632/argument-selection.md": {
"url": "https://numberdb.org/files/T632/argument-selection.md?raw=1",
"sha256": "2d53bb6c7e369c1e8865c571fc3fb0a7380a8967ca6d76cee92ac639b06a98d4"
}
},
"screening": "screening.json and preclaim.json record already_here, already_asked, value lookup and existing tags; no full one-form table found.",
"convention_decisions": "Retained family radius one, complex multiplicities once, full exact-plus-coexact spectrum, all types and characters in p<=20. Used direct spectra for generation and torsion only for checks.",
"companion_visibility": "T631 and T632 were accessible with the bot account and their attached files were read; public page requests returned 404 in this run. Their concrete slugs were read from authenticated pages. No companion was edited."
}