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# T483 build handoff
Draft: https://numberdb.org/T483
Title: Growth constants of the classes of planar maps
Family: numberdb-data#203
Run: 20261025T102046Z-build
The draft is filled and remains unpublished and unoffered. This build did
not review the table or invoke an offer/publication endpoint. The controller
owns the separate critique, repair and offer stages. The proposal queue has
not been marked built by this build session.
## Scope and conventions
Eleven rooted unlabelled classes, with parameter order `class, size,
labelling`. All maps are embeddings in the oriented sphere modulo
orientation-preserving homeomorphisms, rooted at a directed edge.
* By edges: arbitrary (12), 2-connected (27/4), 3-connected (4), bipartite
(8), Eulerian (8), loopless (256/27).
* By all vertices: type I triangulations (12 sqrt(3)), type II (27/2),
type III (256/27).
* By all faces: quadrangulations (12), simple quadrangulations (27/4).
The ten rational entries are stored exactly. The radical is a certified
100-significant-digit decimal from 397-bit Arb arithmetic, with computed
radius 7.4353765e-119 before serialization. The exact decimal endpoints
bracket the positive root of x^2-432.
The proposal supplied the common growth-constant convention and parameter
keys, but not a finite list of map classes. The selection covers the basic
connectivity, parity and angulation classes. It is explicitly incomplete.
The size choice for each class follows the standard enumeration sources;
using vertices for triangulations and faces for quadrangulations avoids
periodic gaps in their counting sequences. All three triangulation types
are defined explicitly. No arbitrary parameter grid was used.
## Screening and neighbours
Read issue #203 before building. Ran `already_here`, `already_asked`,
text searches for maps/triangulations/quadrangulations, and numerical
lookups of 12, 27/4, 256/27 and 27/2. There was no existing table for this
family. All responses are preserved in screening.json. Created the empty
draft as the claim, then computed privately before filling it once.
Read T448, T481 and T482 from the API. T448's slug was read from a search
result; T481 is linked through its verified permanent T-number because it
is a private companion draft. No slugs were inferred from titles. Equal
values across different constructions were not declared as `repeats`.
The proposed `asymptotic enumeration` tag is absent. Used existing
`combinatorics` and `generating function`, matching the companion tables.
The proposed tag would apply to at least T448, T447, T481, T482 and T483;
a human can consider it for the whole family.
## Evidence
* dry-run.txt: all eleven entries pass exactness and prose checks; the
longest computed ball representation is 137 characters. The measured
entries block including comments is about 2.4 KB.
* checks-before-fill.json: nine factorial-ratio sequences checked at
n=2..81 and their limiting ratios derived exactly. Type I has eighty
exact two-step ratio checks with limit 432.
* checks-stored.json: every stored value checked against independently
derived constants, including exact endpoint-sign tests for the radical;
`verify(sample=None)` reports 11/11 matched, no missing or extra values.
* Exact formal series through degree 44 verify the simple-quadrangulation
parametrisation, the 2-core parametrisation and corner substitution,
and the 3-core inverse relation. The 3-connected series starts with one
tetrahedron at six edges, zero at seven edges, and four rooted square
pyramids at eight edges.
* Independent enumeration of connected genus-zero rotation systems with
one through four edges yields arbitrary-map counts 2, 9, 54, 378;
loopless 1, 3, 13, 68; bipartite/Eulerian 1, 3, 12, 56. It checks
triangulations at three edges and quadrangulations through four edges.
Controls are the loop/bridge at one edge and Catalan tree counts
1, 2, 5, 14. This enumeration uses no counting formula.
* The generator, checks, shared checking helper and source notes are
attached to the website. Evidence and dependency versions are retained
in this run's work directory; source PDFs are also retained.
## Source discrepancy
Corollary 3.3 of arXiv:1103.3657v2 prints a simple-quadrangulation factorial
formula with a one-face index shift relative to its own displayed series
and parametrisation. Coefficient extraction and actual enumeration resolve
it: q_2=1, and q_n=2(3n-3)!/(n!(2n-1)!). The constant remains 27/4.
The draft uses the consistent parametrisation and total-face index, and
explains the discrepancy in rigour details and attached source-notes.md.
A summary table in arXiv:2202.13929v3 also disagrees with its preceding
asymptotic for 2-connected bipartite maps. That class is outside this draft;
no included value was taken from the erroneous summary row.
## Remaining audit finding
The API audit returns `clean: false` with exactly one finding, concerning
`size` having the three symbolic values edges/faces/vertices. This is the
structural multi-quantity heuristic. It does not inspect the explanation
or whether class/size pairs repeat: no class here is listed at multiple
sizes, and every entry is the same quantity gamma. Family #203 expressly
requires the size parameter and permits these different counting statistics.
The definition now explicitly says that size is the counting convention
for the common quantity gamma. Splitting or dropping this parameter would
conflict with the family convention. Retained it and report the finding
for the independent critique. No other audit findings remain.
No data was published, no published table edited, and no review requested.