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3776 bytes, as of the version from 2026-11-09 12:11 (current). Recorded here, not run.
# Sources and convention evidence for T688
The family issue #306 was read before discovery, and a copy is retained with
the run artifacts. It supplies shared conventions, not a mathematical source.
The following primary mathematical and software sources were inspected in
this run on 2026-11-09.
* https://arxiv.org/html/alg-geom/9603021, introductory theorem and Section 11:
Frobenius-period construction, normalized mirror coordinate and geometric
Yukawa coefficient. The quintic intersection factor is 5.
* https://arxiv.org/html/alg-geom/9701016, Theorem 0.1: mirror identification for
nonnegative toric complete intersections, including the projective targets.
* https://arxiv.org/html/2305.08480v4, Section 1.1, equation (1.1): unmarked
genus-zero GW invariants and the divisor-sum/Möbius conversion to GV.
* https://macaulay2.com/doc/Macaulay2/share/doc/Macaulay2/EnumerationCurves/html/_rational__Curve.html,
description and outputs o3, o5, o9, o12, o13: all five targets and 17 raw GW
values in localization-controls.json. The conic subtractions in o6/o7 and
cubic subtractions in o10/o11 distinguish GW from integer instanton counts.
* https://macaulay2.com/doc/Macaulay2/share/doc/Macaulay2/EnumerationCurves/html/index.html:
the package uses Kontsevich's torus-localization formulas, independent of
the mirror-period computation. Version 0.1, Hiep Dang.
* https://cydb.mathematik.uni-mainz.de/about.php, “Frobenius basis” and
“Instanton numbers”: logarithmic-period normalization and the operator
convention whose Yukawa constant is 1. T688 retains geometric kappa.
The web reader returned both Macaulay2 pages and their documented outputs.
Direct urllib archival requests returned HTTP 403 for those two pages;
source-manifest.json records that limitation. The values and exact source
locators are preserved in localization-controls.json. Other downloaded source
bytes and SHA-256 hashes are retained in the run artifact directory.
The live documents of T332, T333, T398, T674, T679 and T680 were read, including
parameters, completeness and formulas. Their actual slugs were obtained from
search results. T679/T680 template keys and coefficients agree with the five
factorial periods, including 2.2.4 for multidegree (2,4). T398 has point
insertions on a surface; it does not supply these threefold invariants.
The sibling GV table did not exist during this build, so no link to an
invented or draft sibling is included. A later family review can add it.
Authenticated catalogue pagination and already_here/already_asked were run.
The latter reported no title match; it does not erase historical #184 or the
umbrella requests documented in #306. Additional searches for Gromov,
Gopakumar, instanton and Yukawa found no duplicate family. api/lookup text
queries for 4876875/8, 8564575000/27 and 423549/8 returned no hits. The 2875
text search returned unrelated digit matches, not a family duplicate.
Tags were checked through api/tag. “algebra” and “curves” exist. The audit rejected the sparse “curves” tag,
which had only one published table, T107. The final tags are “algebra” and
“sequence”, consistent with indexing by curve degree and with the T398 neighbour.
“enumerative geometry” exists as an empty tag (0 tables), so it was not added
as a single-table tag. A coordinated tag assignment would serve T688, the
proposed GV sibling and T398. “Calabi-Yau” is absent; it would serve these two
proposals plus T674/T679/T680 (and T675). No existing table was edited.
Instruction evidence: agents/runs/20261109T110159Z-build-skills/manifest.json,
local and live SHA-256 both
886390324dd1971e381a43cf3b46b822ab0bc67d62f31d8481e29ec79556746b.
The same manifest is attached as skill-manifest.json.