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bibkey: kotesovec2016a277829a278770 authors: Vaclav Kotesovec year: 2016 title: “OEIS A277829 and A278770: squared-Catalan Hankel determinants” doi: null url: https://oeis.org/A277829 claim: “A277829 and A278770 conjecture that the logarithms of their squared-Catalan Hankel determinants, divided by n^2, tend to 2*log(2).” strata_touched:

  • D5/S3/Constants/Moments/CatalanSquareHankelGrowth
  • D5/S3/Constants/Moments/CatalanSquareHankelLimits license: citation-only triage: anchor

Kotesovec’s squared-Catalan Hankel limits

Verified locator

The supplied primary-source audit read the live OEIS entries at https://oeis.org/A277829 and https://oeis.org/A278770 and their exact definitions. It reports these two conjecture lines:

  • A277829, Vaclav Kotesovec, November 29, 2016: “Conjecture: lim n->infinity log(a(n))/n^2 = 2*log(2).”
  • A278770, Vaclav Kotesovec, November 28, 2016: “Conjecture: lim n->infinity log(a(n))/n^2 = 2*log(2).”

For C_m=binomial(2m,m)/(m+1), the one-based program for A277829 uses the matrix entry C_(i+j-1)^2, while A278770 uses C_(i+j)^2. Reindexing rows and columns from zero identifies these with D_1(n)=det[(C_(i+j+1))^2] and D_2(n)=det[(C_(i+j+2))^2], respectively, over 0<=i,j<n. The formal determinant convention gives D_r(0)=1.

The second primary locator is https://oeis.org/A278770. This note groups the two entries because the formal endpoint proves their two literal limit assertions as one conjunction; it does not identify the sequences with one another.

Status and scope

Issue https://github.com/the-omega-institute/trureturing/issues/9530 preregistered both exact source assertions before the proof probes. The supplied bounded audit checked the live OEIS entries, the Lin and Simon sources recorded in adjacent Library notes, arXiv/OpenAlex/Crossref identifier and square-Catalan/Hankel searches, five directly titled related papers, and five accessible works citing Lin. It found no explicit settlement of either named OEIS assertion in that inspected scope. One citing text returned HTTP 403 and Semantic Scholar returned HTTP 429; those are access limits, not evidence of absence.

This is bounded prior clearance only. It does not certify worldwide unresolved status, publication priority, or global novelty. The formal delivery settles the two named assertions; it does not claim a new general theory of regular measures or Hankel determinants.