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7680 bytes, as of the version from 2026-10-25 11:31 (current). Recorded here, not run.
# Build evidence for T484
Built 2026-10-25 for family numberdb-data#203. The four rows cover site and bond animals on the square and simple cubic lattices. Parameter order: class, lattice, d, size, labelling. Site animals count occupied cells; bond animals count chosen edges. All animals are unlabelled and fixed up to translation. The stored quantity is gamma, not log(gamma).
## Numerical provenance
- Square site animals: Jensen, *Enumerations of lattice animals and trees*, J. Stat. Phys. 102 (2001), 865–881, abstract and series analysis, arXiv:cond-mat/0007239v2. Source value 4.062570(8), transcribed as `4.062570 +/- 0.000008`.
- Simple cubic site animals: Hsu, Nadler and Grassberger, *Simulations of lattice animals and trees*, J. Phys. A 38 (2005), 775–806, Table 1 p.788. Source partially constrained fit log(gamma)=2.1218588(25). The stored `8.346638 +/- 0.000022` encloses exp([2.1218563,2.1218613]). This also encloses the fully constrained fit exp(2.1218592 +/- 0.0000020).
- Square bond animals: the same Hsu paper, Section 5.2 p.801, 5.20789 +/- 0.00004, by number of edges.
- Simple cubic bond animals: the same section, 10.61539 +/- 0.00006, by number of edges.
The generator reproduces the transcriptions and interval conversion. It does not reproduce the original simulations. Every row has heuristic rigour. None supports 100 significant digits.
## Checks actually run before filling
1. The repository's `dry_run.py` and `check.py` accepted all four values: no floats, no disguised exact numbers, named Sage imports, no problematic entry prose. Longest value 21 characters; entries block about 1.2 KB.
2. Arb exponentiation at 192 and 384 bits produced the same rounded cubic-site interval. Independent Python Decimal exponentiation at 70 digits gave endpoints 8.346616941015704128864008111158... and 8.346658674204742093035419030670..., both strictly inside the stored interval. Its width is less than 1.1 times the transformed source width. Control exp(log(2)) agreed with 2 to within 10^-65 before the comparison.
3. All four stored intervals lie inside independent, broader published estimates: square-site Monte Carlo log(gamma)=1.4018155(30); cubic-site earlier series log(gamma)=2.120(2); square-bond series 5.208(4); cubic-bond series 10.62(8). The earlier cubic and bond series values were read as quoted in Hsu's paper; their original papers were not independently read. This is a source comparison, not an independent high-precision simulation.
4. Site values satisfy the quoted rigorous bounds: square 4.00253 < gamma <= 4.5238, and cubic gamma <= 9.3835. The primary sources for the upper bounds were read. The numerical lower bound is read in Barequet and Ben-Shachar's paper, attributed there to Barequet, Rote and Shalah; the original lower-bound paper could not be downloaded directly.
5. Exact finite enumeration gave square site counts 1,2,6,19,63,216,760,2725 through eight cells, and cubic counts 1,3,15,86,534,3481 through six cells. These match the published count lists. Enumerating bond sets by adding edges and, independently, by choosing connected spanning edge subsets of induced site graphs gave square counts 2,6,22,88 and cubic counts 3,15,95,681 through four edges. The square values also match Janse van Rensburg's textbook, p.40. One-dimensional site and bond controls both gave one object at every size tested.
6. Polynomial extrapolation in 1/n of n*a_n/((n-1)*a_(n-1)), using two windows of seven corrected published square-site counts, gave 4.06256550736454024 and 4.06256687331609736, both inside the retained Jensen interval. The same method gives exactly 7 on the control a_n=7^n/n. This is only a coarse heuristic consistency check; it does not validate a narrower uncertainty.
`checks.py` accepts `--stored` to repeat these checks using database values. `generate.py` verifies every stored entry. Both need the key for an unpublished draft. All relevant Python source and the transcribed check data accompany the draft.
## Decisions and unresolved source issues
- No higher-dimensional rows were guessed. Hsu's arXiv Table I and journal Table 1 both print 2.5878583(30) and 2.5878483(30) for different d=4 fits while the text describes the fits as mutually consistent. Their quoted intervals are disjoint. No erratum was located, so the range is the complete two-class by two-lattice rectangle in dimensions 2 and 3.
- Barequet and Ben-Shachar report two newer square-site estimates, 4.06256912(2) and 4.06256903(5), from two methods communicated by Jensen. Their intervals are disjoint, and the methods are not described sufficiently to diagnose the difference. Neither is selected. Both are contained in Jensen's older wider interval used here, which independently agrees with Hsu's Monte Carlo estimate and the finite-series checks. The table explicitly identifies the old estimate and does not claim a best-current precision.
- The count at n=67 in the 2026 paper and OEIS b-file is 288146737936083547752609866746184117546. The authors' October 2026 correction subtracts 2. The corrected integer is used in the check data. The authors identify a sum/transcription error rather than a counting-code error.
- Janse van Rensburg's 2015 textbook Table 2.1 p.44 prints 5.201789(4), attributed to Hsu, for the square bond-animal estimate. Hsu's actual paper states 5.20789 +/- 0.00004. The generator follows the original paper. The textbook is used for its independently enumerated small counts, not for this transcribed estimate.
- The family-proposed tag `asymptotic enumeration` has no published-table coverage. Existing family tables T448, T481 and T483 carry `combinatorics` and `generating function`; these and `statistical mechanics` are used. An eventual `asymptotic enumeration` tag could group T448, T481, T482, T483 and T484, but this draft does not create a singleton tag.
## Sources and reproducibility
Primary numerical PDFs: https://arxiv.org/pdf/cond-mat/0007239 and https://www.staff.uni-mainz.de/hsu/mypaper/JPA05-animal.pdf . The arXiv Hsu version https://arxiv.org/pdf/cond-mat/0408061 was compared with the journal version on all selected inputs. Recent square counts/correction: https://arxiv.org/pdf/2610.10632 . Bound sources: https://arxiv.org/pdf/1906.11447 and https://arxiv.org/pdf/2511.00461 . Cubic counts: https://oeis.org/A001931/b001931.txt . Bond count control: Janse van Rensburg, second edition (2015), section 2.1 p.40, publisher's preview. Source PDF SHA-256 digests are in source-data.json.
Raw PDFs, screenshots of the source tables, extracted text, screening results, and numerical logs are retained as build artifacts. The website database and its attachments are the authoritative draft.
## Audit interpretation
The initial audit asked about three symbolic parameters: class, lattice and size. These are indices of the objects and their size statistic, not names of different quantities: every row stores the same exponential growth constant gamma. This follows family #203's explicit class/size/labelling/lattice convention. The document now makes that distinction explicit. The structural audit deliberately cannot read this explanation, so those three questions remain for the separate critique. They have not been suppressed by changing the data shape. The audit's definition-length suggestion was addressed by moving the displayed limit into Formulas.
The API returned the Numbers block as a nested mapping even though the submission used flat records. The readback checker now uses the client's own stored-entry parser, checks the exact set of four identities, and applies every check to the actual stored strings. No numbers changed as a result.