Simple Hurwitz numbers H_{g,mu} — T463

The table stores exact rational numbers for every partition mu of degrees
1 through 10 and genera 0 through 5 satisfying 2*g-2+len(mu)>0: 793 entries.
Preimages of infinity are labelled; the finite simple branch points are fixed.
Covers are connected and weighted by the reciprocal of the automorphism group
preserving their labels. The unlabelled convention is smaller by the product
of the factorials of the multiplicities of equal parts. No factor r! divides
the stored values. The largest entry is 40 characters.

Reproduce with SageMath and the numberdb Python package:

    sage -pip install numberdb
    sage -python checks.py
    sage -python generate.py
    sage -python checks.py --stored
    sage -python companion_checks.py

The generator's default action is verification. Offline checks need generate.py,
independent.py, check.py and published-examples.json beside checks.py. The
companion check also uses T458.json and T462.json, frozen API reads for the
family's geometric normalization; with T463-stored.json beside it, it compares
the stored Hurwitz numbers. Otherwise it computes them from the generator.

For a private draft, the last two online verification commands need its owner's
NUMBERDB_API_KEY. Alternatively set NUMBERDB_KEY_FROM_STDIN=1 and pipe the key
on standard input. Do not put a key in any downloaded source file.

Independent expected answers use characters of S_d, calculated from rim strips,
and component subtraction to impose transitivity. No generator recurrence is
used in that calculation. Every character table through degree 10 passes full
column orthogonality and hook-dimension checks. Known-answer controls and
incorrect normalization controls run before the data comparisons.

Additional numerical evidence:
- 793 of 793 independent character comparisons, before and after storage.
- 111 of 111 author-manuscript examples after converting the unlabelled convention.
- 103 genus-zero closed-form checks and 138 genus-one geometric ELSV checks.
- 50 one-part character-formula checks and 58 direct monodromy counts through degree 4.
- 112 genus-one ELSV evaluations using companion table snapshots, checked both
  before and after storage, with 18 cotangent and 12 lambda_1 integral rows.
- Generator.verify(): 793 matched, 0 differing, 0 missing, 0 extra.

The document contains no full higher-genus ELSV formula; higher-genus values
were checked by characters and the available published numerical examples,
not by an independent calculation of all linear Hodge integrals.

This is a build artifact. It is not a critique, a human review, or an offer for
review. T463 remains a draft. A separate controller handles the later stages.