# Sources and conventions for T605

- Olaf Mordhorst, The optimal constants in Khintchine's inequality for the
  case 2 < p < 3, Colloquium Mathematicum 147 (2017), 203–216.
  DOI: 10.4064/cm6861-7-2016.
  https://www.impan.pl/shop/en/publication/transaction/download/product/91999
  Theorem 1.1 on page 203 states the sharp lower minimum formula for every
  p > 0 with finite real coefficient vectors and equiprobable random signs.
  The text following the theorem states A_p = 1 for p >= 2. This is the
  full-text source actually checked for the sharp-constant formula.
- F. Bayart, D. Pellegrino and J. B. Seoane-Sepulveda, The Bohr radius of the
  n-dimensional polydisk is equivalent to sqrt((log n)/n), Advances in
  Mathematics 264 (2014), 726–746. DOI: 10.1016/j.aim.2014.07.029.
  https://arxiv.org/abs/1310.2834 (v2, 15 October 2013).
  Section 3 defines A_{R,p} on the other side of the norm comparison, so
  A_{R,p} = 1/A_p in this table's notation. Proposition 3.1 uses exponents
  2k/(k+1); Corollary 3.3 concerns the real case. This directly supports the
  documented application selection, not the exploratory rational group.
- Uffe Haagerup, The best constants in the Khintchine inequality, Studia
  Mathematica 70 (1981), 231–283, DOI: 10.4064/sm-70-3-231-283.
  The publisher's bibliographic record was accessible. Its download returned
  HTTP 403 to the browser tool; the generator relies on the checked theorem
  in Mordhorst's paper, which explicitly attributes the complete proof to
  Haagerup. No claim is made to have read the unavailable original full text.

The downloaded PDFs, source URLs and SHA-256 digests are retained in
source-manifest.json in the run artifacts. Arithmetic checks of all table
values use explicit four-sign sums and Gaussian quadrature without Gamma.
The quadrature is an independent diagnostic; certified enclosures come from
Arb evaluation of the published theorem, not from numerical experiments.

Existing corpus: Values_of_the_Gamma_function_at_rational_numbers was resolved
through search_text and then read using numberdb.table. The formula links it
at the first mention of Gamma. Searches for Khintchine, Rademacher and
Haagerup returned no matching table before draft creation. Khinchin hits
concerned continued fractions or other families. Three lookup probes found
only different mathematical contexts or no hits. All three requested tags
exist. The upper-constant sibling had no identifier when this table was built.

Instructions read: agents/runs/20261029T085909Z-build-skills/manifest.json.
Both the runner-archived local canonical skill and live /skill version were
read and match SHA-256
28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199.
The source-snapshot canonical file has the same digest. The attached
skill-manifest.json preserves both records. The builder supplies no independent
argument-review acceptance; that is the separate critique actor's task.