# Sources and corpus evidence for T610

Governing policy: ../20261029T134044Z-build-skills/manifest.json, with matching
local/live SHA-256 28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199.
The archive was read in this run; skill-evidence.json preserves both digests.

Checked primary sources:

- https://arxiv.org/html/1209.6621v2 : Section 2.1, Theorem 1 defines global
  dimension as the sum of squared quantum dimensions. Section 2.2 gives
  G=1/S00^2 and the type-A quantum factorial product. Substituting rank N-1,
  dual Coxeter number N and inverse Cartan determinant 1/N gives
  G=N*(N+k)^(N-1)/product((2*sin(pi*j/(N+k)))^(2*(N-j)),j=1,...,N-1).
  Section 2.3 gives k*G(N,k)=N*G(k,N). Its notation for rank/Coxeter number
  is translated to the family’s N=matrix size.
- https://arxiv.org/pdf/1003.2589 : Sections 2.2–2.4 specify the quantum
  character and vacuum S normalisations. Section 3.4, printed page 17,
  gives SU(2) examples G(2,4)=12 and G(2,10)=24*(2+sqrt(3)); these are
  separate printed controls, not values inferred from output digits.
- https://arxiv.org/html/hep-th/0510092v2 : equations (3)–(4) define the
  positive total quantum dimension and give the inverse total dimension
  of SU(2) at integral level k.

The exact algebraic computation uses zeta=q^2 and
(2*sin(pi*j/m))^2=2-zeta^j-zeta^(-j). Testing membership in Q is exact.
The positive total can be rational only if G is a rational square, so this
also detects every rational total without guessing from decimal digits.

The family map and live tables T609, T607, T60, T61, T99, T122, T256 and T397
were read. T609 contains individual dimensions for 37 complete alcoves and
is a companion, not a duplicate. T607 holds infinite sums of inverse powers
of ordinary dimensions; it is related, not a specialization of this table.
T609's long URL was read from its live page; T607's URL from search results.
Both actual documents are preserved as artifacts.

already_here and already_asked were rerun. Searches for quantum, fusion,
topological, Witten and global dimension found no existing aggregate table.
The decimal lookups for G(2,3) and G(3,2) returned no hits. Integer lookups
for 2 and 4 returned many unrelated hits, which are not family duplicates.
The complete responses are in screening.json. The title claim then created
T610 as an unpublished, unoffered draft. No title collision was bypassed.

All 73 tags across both live tag pages were inspected. algebraic, groups and
physics exist and are used. Representation theory remains a proposed tag,
applicable to T609, T610, T122, T256 and T607; no published table was retagged.