T497 build evidence, 2026-10-25.
Convention: exact reciprocal orders of full integral isometry groups.
Range: odd dimensions 1..32; even dimensions 0,8,16,24,32.
Source PDFs: Conway-Sloane (1982), King (2003); Finch (2005) consulted for the rank-one exception.
The primary printed rank-one value 1 disagrees with its own full-group definition.
Resolved from O(Z)={+1,-1}: mass 1/2; King Table 6 and Finch page 3 agree.
Range measurements (entries, longest written value):
32: 37, 116; 48: 55, 298; 64: 73, 602; 96: 109, 1604.
The chosen endpoint follows the standard published reference range rather than the size cap.

DRY RUN
== the generator itself ==
   names its rings, initialises Sage

== computing every entry ==
   37 entries computed

== exactness ==
   every value is exact, or carries its own error bound

== exact in disguise ==
  none
== prose ==
   no comment carries a backslash before a quote, or says below or above

== size ==
   37 entries, longest 116 characters at n=32,parity=I, block 3.4 KB

Nothing was sent. Create the table only when the above is clean and
the identities have been checked; then fill it once.

INDEPENDENT CHECKS
Checking locally generated values and the dated T496 snapshot.
Sage 10.9 ; entries 37
/home/sage/sage/local/var/lib/sage/venv-python3.12/lib/python3.12/site-packages/sage/categories/category_types.py:102: UserWarning: Resolving lazy import Objects during startup
  return [Objects()]
/home/sage/sage/local/var/lib/sage/venv-python3.12/lib/python3.12/site-packages/sage/quadratic_forms/genera/genus.py:3242: UserWarning: Resolving lazy import maxima during startup
  return QQ(mass.canonicalize_radical())
General genus-mass controls: ranks 1, 2 and E8 passed.
General local-density mass computation: 37/37 exact agreements.
Published rational values: 36/36 agreements; rank 1 separately equals 1/2.
Class-sum controls: odd ranks 1..11; even ranks 0,8,16,24 passed.
Odd/even mass relation: 4/4 exact agreements.
Negative controls: doubling the E8 mass and omitting Leech both fail.
Measurement: {'entries': 37, 'longest': 116, 'longest_at': ('I', 32), 'block_kb': 2.9248046875}

SOURCE SHA256
conway-sloane.pdf aa027c0f78c5dce8ae9b2d5d13cbd23a35c0a960a817c899c2c5c38d0b0c20f4
king.pdf 64d4d18706e91432c12ee229bedee7ea864a6da38add3f2a4f3a4bcc7d19db89
finch.pdf 3d8122fb8c7fcd5e410412b1354e4409f9dc884660ba76dc067825cd93d790f2