v2.1.0: R(B_57, B_58) = 231, journal version

R(B_57, B_58) = 231, the case n = 58 of Wesley's conjecture R(B_{n−1}, B_n) = 4n − 1, as the
journal manuscript submitted to Discrete Mathematics.

This release adds the one-column journal version of the paper (Elsevier elsarticle, 10 pages):
paper/paper1/book-ramsey-58.pdf and its LaTeX source paper/paper2/book-ramsey-58-tex.zip, both
attached here. Table 1 now stands on the page after Theorem 3.1, which it proves, instead of after
the references. The mathematics, the data, the C and Python checks and the Lean 4 proofs are those
of v2.0.0.

The lower bound is a graph on 230 vertices, a two-block circulant graph over Z_115, with no B_57
whose complement has no B_58; the upper bound is Rousseau–Sheehan. The paper reduces both book
conditions to one inequality, checked at the 57 values d = 1, …, 57 in its Table 1, and the
equality is proved in Lean 4 with the standard axioms only. The hand-checkable proof of
R(B_66, B_67) = 267 (Chung, Du and Wesley, Station data, 24 August 2026; not new here) is kept.

The conjecture stays open in general; for n ≤ 100 the open values are 59, 60, 64, 65, 68, 72, 73,
76, 78, 80, 81, 84, 88, 89, 92, 93, 94, 96 and 100.

Author: Deep Bhattacharjee (ORCID 0000-0003-0466-750X).

v2.0.0: R(B_57, B_58) = 231, and a hand-checkable proof of R(B_66, B_67) = 267

A new exact value of a book Ramsey number: R(B_57, B_58) = 231, the case n = 58 of Wesley's
conjecture R(B_{n−1}, B_n) = 4n − 1 (Discrete Math. 349 (2026), 114913), which was its smallest open
case. The lower bound is a graph on 230 vertices, a two-block circulant graph over Z_115 of the shape
Turturean uses for even n (|A| = 58, |B| = 57), with no B_57 whose complement has no B_58; the upper
bound is Rousseau–Sheehan. The paper reduces both book conditions to one inequality, checked at the
57 values d = 1, …, 57 in its Table 1. The graph was found by a two-phase local search (Turturean's
scheme, with a breakout-weighted search for B) and checked on all 26,335 pairs of vertices in C and
in Python. The equality itself is proved in Lean 4 (core Lean, standard axioms only): the kernel
checks the graph, and Goodman's count, formalised for every graph, gives the upper bound. The
priority check of 15 October 2026 found no earlier source.

This release also keeps the hand-checkable proof of R(B_66, B_67) = 267, a value first shown by
Chung, Du and Wesley in the Station data of 24 August 2026 (not new here; see v1.0.1), now also
proved in full in Lean 4.

Attached: both papers (PDF), their LaTeX sources with the figures as PNG, and the arXiv tarballs.
The conjecture stays open in general; for n ≤ 100 the open values are now 59, 60, 64, 65, 68, 72,
73, 76, 78, 80, 81, 84, 88, 89, 92, 93, 94, 96 and 100.

Author: Deep Bhattacharjee (ORCID 0000-0003-0466-750X).

v1.0.1: A hand-checkable proof that R(B_66, B_67) = 267

A hand-checkable proof that R(B_66, B_67) = 267, the case n = 67 of Wesley's conjecture
R(B_{n−1}, B_n) = 4n − 1 (Discrete Math. 349 (2026), 114913). The value was first shown by Chung, Du
and Wesley in the Station data of 24 August 2026 (github.com/dualverse-ai/station_data_v2, notebook
Section 5.1), by a 266-vertex certificate. This release describes that graph, up to isomorphism, as
a two-block circulant graph on Z_133 × {0, 1} whose connection sets are unions of orbits of the cube
roots of unity modulo 133; the proof reduces both book conditions to one inequality, checked by hand
on ten orbits. Version 1.0.0 presented the value as new; that was wrong, and this version corrects it.

Attached: the paper (PDF), its LaTeX source with the figures as PNG, and the arXiv tarball. The
repository contains the Lean 4 kernel check of all 35,245 pairs of vertices (core Lean, standard
axioms only), independent checks in C and Python, the isomorphism with the Station certificate, the
CP-SAT search, and the dated priority check. No new value of n is settled; the conjecture stays open.

Author: Deep Bhattacharjee (ORCID 0000-0003-0466-750X).

v1.0.0: The book Ramsey number R(B_66, B_67)

R(B_66, B_67) = 267: the case n = 67 of Wesley's conjecture R(B_{n−1}, B_n) = 4n − 1 (Discrete
Math. 349 (2026), 114913), which no earlier construction covered. The upper bound is Rousseau and
Sheehan's (J. Graph Theory 2 (1978)); the lower bound is a two-block circulant graph on
Z_133 × {0, 1} with no B_66 whose complement has no B_67, its connection sets being unions of orbits
of the cube roots of unity modulo 133. The proof reduces both book conditions to one inequality,
checked by hand on ten orbits.

Attached: the paper (PDF), its LaTeX source with the figures as PNG, and the arXiv tarball. The
repository contains the Lean 4 kernel check of all 35,245 pairs of vertices (core Lean, standard
axioms only), independent checks in C and Python, the CP-SAT search, and the dated priority check.
Only n = 67 is settled; the conjecture stays open in general.

Author: Deep Bhattacharjee (ORCID 0000-0003-0466-750X).