{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7AHH5R3HRVTFOFICF7QYGWOZAK","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":"28ab6fbf8f9ca86742950111dcd7d645012fe8f46f1f6669be3d3dc7db407998","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-06-09T16:30:26Z","title_canon_sha256":"70e5cec688da24a7ed73c867fedaf7c254f32d1afef49dda4a0a0f07f07a961d"},"schema_version":"1.0","source":{"id":"2606.11067","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.11067","created_at":"2026-06-10T01:11:08Z"},{"alias_kind":"arxiv_version","alias_value":"2606.11067v1","created_at":"2026-06-10T01:11:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.11067","created_at":"2026-06-10T01:11:08Z"},{"alias_kind":"pith_short_12","alias_value":"7AHH5R3HRVTF","created_at":"2026-06-10T01:11:08Z"},{"alias_kind":"pith_short_16","alias_value":"7AHH5R3HRVTFOFIC","created_at":"2026-06-10T01:11:08Z"},{"alias_kind":"pith_short_8","alias_value":"7AHH5R3H","created_at":"2026-06-10T01:11:08Z"}],"graph_snapshots":[{"event_id":"sha256:7f19c57af0a2a758226f339dd071f1579d92c49c91118b067c09cf301988a7e8","target":"graph","created_at":"2026-06-10T01:11:08Z","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/2606.11067/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a simple $\\mathcal{O}\\left( n^2 \\frac{ \\log N }{ \\log \\log N } + N \\right)$ enumeration algorithm for solving a problem from mathematical and computational music analysis where, given a strictly increasing integer sequence, $S$, with $n$ entries and maximum value $N$, the task is to enumerate all $m$ $\\textit{inclusion-maximal arithmetic progressions (IMAPs)}$ in this sequence. An IMAP is a subsequence, $S' \\subseteq S$ with $k>2$ integers, in which (i) the difference between any two consecutive integers is the same number, $d$ (i.e., $S'$ is an $\\textit{arithmetic progression}$), (","authors_text":"Brian Bemman, George B. Mertzios, Maximilien Gadouleau, Oliver W. Gnilke","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-06-09T16:30:26Z","title":"Enumerating Inclusion-Maximal Arithmetic Progressions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11067","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":"sha256:922d41f9f37a60b873f2e30563a2cc088d6e3336cd92b49770f0e338481eb55b","target":"record","created_at":"2026-06-10T01:11:08Z","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":"28ab6fbf8f9ca86742950111dcd7d645012fe8f46f1f6669be3d3dc7db407998","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-06-09T16:30:26Z","title_canon_sha256":"70e5cec688da24a7ed73c867fedaf7c254f32d1afef49dda4a0a0f07f07a961d"},"schema_version":"1.0","source":{"id":"2606.11067","kind":"arxiv","version":1}},"canonical_sha256":"f80e7ec7678d665715022fe18359d9028af083e43974ba9fc3d761f368f47e2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f80e7ec7678d665715022fe18359d9028af083e43974ba9fc3d761f368f47e2a","first_computed_at":"2026-06-10T01:11:08.008090Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:11:08.008090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LYyDooAzO3kux3TZ5h9zJck6RB7Cnj8k4lbpGZwSHtUl3TxXKK03cH0wr3kIhrYUzikRwH78gws5QcGjut0NCQ==","signature_status":"signed_v1","signed_at":"2026-06-10T01:11:08.009102Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.11067","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:922d41f9f37a60b873f2e30563a2cc088d6e3336cd92b49770f0e338481eb55b","sha256:7f19c57af0a2a758226f339dd071f1579d92c49c91118b067c09cf301988a7e8"],"state_sha256":"c1b2bf26373b0dfc8f06ec29efee345f70957e4377df8aa93923cb522fe13e76"}