Ford receipt — Erdős #357 / OEIS A364153: a(17) = 26 lands in the Erdős Frontier Atlas
Recorded 2026-10-29 (America/Denver), Ford rotation (sprintBL search, sprintBM atlas, sprintBO board).

Claim: A364153(17) = 26, i.e. 26 is the least N such that some sequence of 17 distinct values from {1..N}, in any order,
has all 153 segment sums (sums of consecutive terms) distinct. An exhaustive computer search by two independent engines,
not a proof.
New: OEIS A364153 lists a(1..13) = 1, 2, 3, 5, 6, 7, 9, 10, 12, 13, 14, 17, 18; re-checked 2026-10-29 03:50 MDT.
The atlas certificate had already decided a(14..16) = 20, 22, 24 (contract erdos-357-a364132-a364153-new).

Method: Ford's separately written engine ss_cleanroom.c (sha256 cc5d0992e8856f440c1fb851b3498eb09bcf23e84fdd9e20df6a6c28ff77d514),
any order, the search at N split into 19 parts that together cover it. Answers: NONE on 19 of 19 parts at N = 24 and at
N = 25; FOUND at N = 26 with 1, 2, 12, 16, 18, 23, 17, 20, 22, 25, 26, 10, 19, 24, 11, 21, 6 (17 distinct terms, max 26,
153 of 153 segment sums distinct by brute force). Control a16@23 part 0/14 NONE, node count exact. About 7.8e10 nodes.
Second engine: the atlas's unchanged segsum.c (sha256 b0228c31c7ac9ea83a9ba7793f614a1c7450b75592cb66bc7d831672f068d145)
answers none at 24 and at 25; its a16@23 node count 7,920,625,479 equals the one pinned in RESULT.json.

Atlas PR https://github.com/techno-optimist/erdos-frontier-atlas/pull/186, merged as 6bff3752aaba9f0550c631d6048cb1b143de4b34.
  New files in certificates/erdos-357 (RESULT.json, verify.py, segsum.c unchanged):
    ford_searches_a364153_17.txt  sha256 700780bdd3491d2c2edd30df4714a766800e70000978c93b86fa6173da118415
    g4_crosscheck_a364153_17.txt  sha256 ee70683575a2d863b60467e97b848b05bafd7ff4c953611f11f326647503ee69
    verify_ford_a17.py            sha256 693fb87f19b910e2332331723990e22e965db35d6587997b6d7766e96e9e5201
  New promoted contract erdos-357-a364153-17. Fast profile PASS; atlas gates PASS locally; GitHub fast-claim-gate SUCCESS.

Disclosed: the two engines are independent code using the same segment-sum bitset method, not independent mathematics.
PR #186 merged before the certifying --full replay finished, per Kevin's direction to publish verified results promptly.
That replay was interrupted by a box restart at about 03:00 MDT on 2026-10-29 and restarted at 03:21 MDT on the merged
main; it is still pending and its result will be posted on PR #186. The restored copy of the atlas-step falsifier file
(sprintBM/FALSIFIER_atlas_a17.txt) hashes to 44a8de00…f401, not the fafff66c… prefix cited in the PR #186 body, so that
hash is not relied on here. Says nothing about the asymptotic question of Erdős #357. Not submitted to OEIS; Kevin
submits OEIS extensions himself.