{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KGTQEHSCH5T6BROQ7WBGAXWE34","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f986694fb19a4f05b2c1e1ab6f4eb67f72b23f4d49dd84415f74fc69b308d89a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-02T14:28:22Z","title_canon_sha256":"acccb2dfde67860a8ea5cc3a9a110ab28fb2566f68191e13045257589b326ba1"},"schema_version":"1.0","source":{"id":"2607.02226","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02226","created_at":"2026-07-03T01:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02226v1","created_at":"2026-07-03T01:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02226","created_at":"2026-07-03T01:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"KGTQEHSCH5T6","created_at":"2026-07-03T01:17:45Z"},{"alias_kind":"pith_short_16","alias_value":"KGTQEHSCH5T6BROQ","created_at":"2026-07-03T01:17:45Z"},{"alias_kind":"pith_short_8","alias_value":"KGTQEHSC","created_at":"2026-07-03T01:17:45Z"}],"graph_snapshots":[{"event_id":"sha256:1b452d24d587812831dd0f9a03a0fe37e9f5081e41007bd21b63c00266aa4933","target":"graph","created_at":"2026-07-03T01:17:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.02226/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A coloring of the Hales--Jewett cube $[t]^n$ is symmetric if it is invariant under all coordinate permutations, and one-weight if it reads only an integer-weighted count of the letters. We prove that the two classes coincide -- a radix weight realizes every symmetric coloring -- so the symmetric lower-bound problem for the Hales--Jewett numbers is exactly a one-dimensional coloring problem about homothetic copies of a $t$-point set, the case $d=1$ of Gallai's theorem. Optimizing the weight yields $\\mathrm{HJ}(3,3)\\ge22$ and $\\mathrm{HJ}(4,2)\\ge14$, the latter in closed form from the new Gallai","authors_text":"Younes Mouhib","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-02T14:28:22Z","title":"One-Weight Colorings, the Symmetric Class, and Lower Bounds for Hales--Jewett Numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02226","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6075a1eb5138879b53e3f5849027e0b08e716922cf7707a50edb69679ed9da46","target":"record","created_at":"2026-07-03T01:17:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f986694fb19a4f05b2c1e1ab6f4eb67f72b23f4d49dd84415f74fc69b308d89a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-02T14:28:22Z","title_canon_sha256":"acccb2dfde67860a8ea5cc3a9a110ab28fb2566f68191e13045257589b326ba1"},"schema_version":"1.0","source":{"id":"2607.02226","kind":"arxiv","version":1}},"canonical_sha256":"51a7021e423f67e0c5d0fd82605ec4df218a24f005ed71ca757e8049878ac420","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51a7021e423f67e0c5d0fd82605ec4df218a24f005ed71ca757e8049878ac420","first_computed_at":"2026-07-03T01:17:45.785156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:45.785156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SBB4CzyjENHRgzjhiI57SbW3fu4yHSNL0SqPpsqpRk1MgGCUcYfckt25L92rcOFw6n8vg0UCLivPSt55KXQKAg==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:45.785604Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.02226","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6075a1eb5138879b53e3f5849027e0b08e716922cf7707a50edb69679ed9da46","sha256:1b452d24d587812831dd0f9a03a0fe37e9f5081e41007bd21b63c00266aa4933"],"state_sha256":"60e711ac94b98a5ddeb61614ba756c26a01242cf451a1308adbc5aa4dd5987a0"}