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5358 bytes, as of the version from 2026-11-09 12:01 (current). Recorded here, not run.
# Sources and corpus evidence for T689
The family issue #306 was read first and archived as `family-306.md` in the
build work directory. The live companion is T688, with the same target and
hyperplane-degree conventions. Its full document was fetched through the
NumberDB client; its metadata at discovery named revision 5055, digest
15f8380b619a49dde036d86b03ecfc975952912aa18fe46ca2b64e2a3530776c,
and status offered_for_review. It is still a draft, and this build edits no
companion. Its eventual publication and reciprocal links remain with the
controller and family review.
The authenticated catalogue, text searches using `already_here`, issue search
using `already_asked`, and numeric lookups were rerun. No competing GV/instanton
table was found. `already_asked` identified closed historical issue #184, which
is not reopened or treated as an answered request of this run. Valid structured
lookups for 609250, 317206375 and 92288 returned no results. The initial three
lookup attempts sent an invalid bare number and returned an error; they were
replaced with the client API's structured integer records. Those errors were
not interpreted as absence. The source snapshot's client lacks `list_tables`,
so the documented paginated `/api/tables?include_drafts=1` fallback was used.
Full live documents read: T688, T332, T333, T398, T674, T679, T680.
Addresses for published companions came from live text-search results or the
existing companion document; T688 uses the verified identifier link returned
by its metadata API. The links concern distinct enumerative, topological,
analytic and arithmetic quantities, with the relations stated individually.
No `repeats` is appropriate: the degree-one equalities with T688 follow from
the multiple-cover identity, rather than duplicating a stored computation.
## Mathematical sources checked
* [Chou–Lee, Quantum K-invariants and Gopakumar–Vafa invariants II](https://arxiv.org/html/2305.08480v4),
Section 1.1, equation (1.1): defines the cohomological unmarked GW invariant,
the genus-zero GV multiple-cover relation and its Möbius inversion. It also
explains the BPS terminology. This is the table's defining convention.
* [Givental, Equivariant Gromov-Witten invariants](https://arxiv.org/html/alg-geom/9603021),
introductory theorem and Section 11: the nilpotent-parameter Frobenius series,
mirror coordinate, geometric quintic constant 5 and Lambert expansion;
the theorem states the analogous projective-complete-intersection result.
Its introductory values independently confirm the quintic controls through
degree 4. No literal embedded-curve-count assertion in all degrees is adopted.
* [Givental, A mirror theorem for toric complete intersections](https://arxiv.org/html/alg-geom/9701016),
Theorem 0.1 and Calabi–Yau specialization: supplies the identification between
the hypergeometric construction and the geometric stable-map theory.
* [EnumerationCurves rationalCurve documentation](https://macaulay2.com/doc/Macaulay2/share/doc/Macaulay2/EnumerationCurves/html/_rational__Curve.html),
Description and outputs o3, o7, o11, o14, o15, o16: the five targets and 18
corrected instanton controls. Outputs o3, o5, o9, o12, o13 give 17 rational
stable-map controls. The controls are transcribed in `localization-controls.json`
and `checks.py`. The package's [index](https://macaulay2.com/doc/Macaulay2/share/doc/Macaulay2/EnumerationCurves/html/index.html)
states that the implementation uses Kontsevich's torus-localization formulas.
These source pages were read successfully using the web tool. A separate
direct urllib archive request returned HTTP 403; no claim is made that this
response archived the page. The programs snippet is the documented conic
calculation. Macaulay2 itself was unavailable and was not executed.
* [Ionel–Parker, The Gopakumar-Vafa formula for symplectic manifolds](https://annals.math.princeton.edu/2018/187-1/p01),
abstract and bibliographic record: the integrality result applies to
symplectic Calabi–Yau six-manifolds and hence projective Calabi–Yau threefolds.
DOI 10.4007/annals.2018.187.1.1 is stored in its reference field.
* [CY differential-operator database](https://cydb.mathematik.uni-mainz.de/about.php),
Frobenius basis and Instanton numbers: distinguishes the normalized constant
term 1 from the intersection-scaled convention used here. Its coordinate
description is not used to replace the precisely specified G/F mirror map.
## Tags
The live T688 uses `algebra` and `sequence`; T689 keeps both and adds `physics`
because the BPS interpretation is stated. `curves` currently points only to
T107's split-Jacobian equations and is not used as the primary subject grouping.
The tag endpoint for `enumerative geometry` has zero tables; `Calabi-Yau` was
unavailable. Propose a populated enumerative-geometry grouping for T398, T688
and T689, and a Calabi–Yau grouping for T674, T679, T680, T688 and T689. No new
tag or changes to companions are made in this build.
## Policy archive
The governing archive is
`agents/runs/20261109T113247Z-build-skills/manifest.json`.
Both skill versions, and the canonical source-snapshot file, have SHA-256
886390324dd1971e381a43cf3b46b822ab0bc67d62f31d8481e29ec79556746b.
See the attached `skill-manifest.json` for the authoritative exact digests.