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4153 bytes, as of the version from 2026-10-25 09:43 (current). Recorded here, not run.
# T481 build evidence, 2026-10-25
Family #203 read first. Exact title and family searches, already_here and already_asked, and api/lookup samples found no existing coverage. Lookup samples: 27.226877, 26.18486 (the initial literature approximation), 9.0733 (a neighbouring graph class). The final 2-connected constant was calculated from the defining equation, not copied from a decimal approximation.
Conventions are in convention.md. The five selected classes are the basic connectivity subclasses and maximal planar graphs. Other planar subclasses and unlabelled counting are outside this initial table. There is no arbitrary parameter grid.
The asymptotic enumeration tag exists but is attached to zero tables, according to api/tag with the literal tag name. The family proposal names six possible users. This draft uses the existing combinatorics and generating function tags. T448 and T447 are the already built neighbouring family tables that could join a coordinated tag update. No published table was edited.
Sources read:
- Giménez and Noy, JAMS 22 (2009), 309–329. Theorem 1, Lemmas 3 and 4, section 4, and Appendix. PDF: https://web.mat.upc.edu/marc.noy/uploads/2013/05/Graphs-Planar1.pdf
- Giménez and Noy, Counting planar graphs and related families of graphs, section 5: https://web.mat.upc.edu/marc.noy/uploads/2013/05/survey.pdf
- Tutte triangulation formula also checked against the primary-author mathematical lecture at https://semflajolet.math.cnrs.fr/wp-content/uploads/2022/03/Albenque-slides-IHP.pdf and the linked OEIS A007816 record.
The source PDF formula pages were visually inspected to check signs and denominators against the extracted text. The standalone checks use the original planar-map/network characteristic system and the separate B2 formula; they do not call the generator's Y or radius formula to obtain their comparison values. They also check a known sqrt(2) root-finding control, six initial exact triangulation counts, 50 exact consecutive-count ratios, the exact ratio limit, algebraic sign brackets, equality and class-inclusion ordering.
The numerical tests do not prove the enumeration theorems; the cited papers do. The 100-digit enclosures are certified by the existence/uniqueness theorem, rational root brackets with Arb-certified signs, and Arb evaluation of the published expressions. Independent mpmath computations at 160 and 200 digits agree within 1e-150. Every nonrational output ball has radius less than 1e-108.
Local dry_run.py completed successfully: five entries, longest native ball spelling 146 characters, entry block about 1.3 KB. Every serialized nonrational number has exactly 100 significant digits; maximal is the exact rational 256/27.
All initial calculations and proof checks completed before sending numbers. The draft is to remain unpublished and unoffered until the controller's separate critique and repair stages complete.
## Local checks output
```text
Arb root bracket, finite balls, and radii below 1e-108: PASS
{
"all": "27.22687776858857646707945805149445828748980158778683601072408694361933497626231372197177075979856106",
"connected": "27.22687776858857646707945805149445828748980158778683601072408694361933497626231372197177075979856106",
"2-connected": "26.18411255565814849687701423391145071624340896693389384842102062412262621583107003393138467686433097",
"3-connected": "21.04904247552719059763633201509619139553885290760127482226864664557480400747376912256162975130181053",
"maximal": "256/27"
}
Every written interval contains the independent value; equality, ordering, and algebraic bracket pass.
Tutte counts, 50 exact ratios, and ratio limit 256/27: PASS
Independent network/map computations agree at 160 and 200 digits: PASS
Measurement: {'entries': 5, 'longest': 146, 'longest_at': '3-connected', 'block_kb': 1.1044921875}
```
## Source checksums
gimenez-noy.pdf: SHA-256 a95e50ec1878383034a379932734f018fc8d714bf6a2f5314f0c95d497da6a29
survey.pdf: SHA-256 bd36ee257bd035faef66b627f1e45867b600f09844ac9b899aa25f75370033e2
## Dependency versions
SageMath 10.9; numberdb 0.1.10; mpmath 1.4.1; PyMuPDF 2.0 for PDF inspection.