Erdős #962 / OEIS A327909: exact finite cells through n=2003, recorded 2026-11-06.

Claim: A327909(2001) = A327909(2002) = 1550254764943 = s0, and
A327909(2003) = 1575356265925.
Next cell: A327909(2004) >= 1575356265925 by monotonicity; no upper bound is claimed.

Method: the frozen a(2000) receipt has a maximal 2002-integer run at s0. The
same smoothness class applies at n=2000, 2001, and 2002, so that run and
monotonicity determine both plateau cells. For prime n=2003, the original
ordered W=10^11 probe began at s0 and reported 1575356265925 as the first
start in (s0,s0+W]. Its witness contains 2203 consecutive integers, bounded
by 2003-smooth integers 1575356265924 and 1575356268128.

Independent checks: the original checker uses sympy full factorization for
all 2003 needed witness integers; its planted damaged witness is rejected.
The separate stdlib verifier repeats the entire 2203-integer run and both
smooth endpoints by gcd, recomputes the plateau, tests evidence hashes, and
rejects shifted and deliberately damaged inputs. The isolated source replay
was repeated for publication and passed; no search was rerun.

Source receipt sha256 384af3ee37b9aee04a3780a0398da06d5bed353ea753020a7013bd0b9427c245.
The unchanged original falsifier, source-text archives, and controls accompany
this summary. The sanitized source-receipt copy keeps the original numbers and
source hashes; the unchanged original is in the atlas PR. The public atlas has hash pins and replay
instructions at PR #214 (open, not merged), exact head
13bc9b409a276c639f3c70b96144de3815474f7e.
The canonical receipt sha256 applies to the atlas original; the sanitized public
copy and exact source bodies in this folder have their own serving SHA256SUMS.

Boundary: this is an ordered finite-search receipt, rated about 7/10. It is
not a full [1,X] table or a formal/Lean proof. The fast verifier does not
replay minimality; its optional multi-hour search replay was not run. No
probe was relaunched during publication. The asymptotic Erdős #962 question
is unchanged, and no new OEIS submission is represented.

Full atlas PR head: https://github.com/techno-optimist/erdos-frontier-atlas/pull/214/commits/13bc9b409a276c639f3c70b96144de3815474f7e