{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:CWOZ74TUYLLXMDRRKJZ74OL4GV","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":"c4d919e8eea75356128e393537b46231910b1226237675bf8a1e5e2f5fe5d83e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-01-08T10:03:56Z","title_canon_sha256":"9637cbd496f99d1a0c0adef662c983c13b8070ee0d76947002579dd155939ae5"},"schema_version":"1.0","source":{"id":"2401.03781","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.03781","created_at":"2026-07-05T07:31:13Z"},{"alias_kind":"arxiv_version","alias_value":"2401.03781v1","created_at":"2026-07-05T07:31:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.03781","created_at":"2026-07-05T07:31:13Z"},{"alias_kind":"pith_short_12","alias_value":"CWOZ74TUYLLX","created_at":"2026-07-05T07:31:13Z"},{"alias_kind":"pith_short_16","alias_value":"CWOZ74TUYLLXMDRR","created_at":"2026-07-05T07:31:13Z"},{"alias_kind":"pith_short_8","alias_value":"CWOZ74TU","created_at":"2026-07-05T07:31:13Z"}],"graph_snapshots":[{"event_id":"sha256:78a13619f2435ccb90feab7a6f58f72d3d37e99cb92ea3f58728b96fb9c92d50","target":"graph","created_at":"2026-07-05T07:31:13Z","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/2401.03781/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we give some new consequences that follow from our formula for increments of the Hardy-Littlewood integral. The main of these ones are $\\mathcal{T}_1$ and $\\mathcal{T}_2$ equivalents of the Fermat-Wiles theorem.","authors_text":"Jan Moser","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-01-08T10:03:56Z","title":"Jacob's ladders, almost linear increments of the Hardy-Littlewood integral (1918) and their relation to the Titchmarsh's sums (1943) and the Fermat-Wiles theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.03781","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:f43b603daea87e8889077027e0c6af8a9e921a1d8e7c82c5e752bd6f1837d15c","target":"record","created_at":"2026-07-05T07:31:13Z","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":"c4d919e8eea75356128e393537b46231910b1226237675bf8a1e5e2f5fe5d83e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-01-08T10:03:56Z","title_canon_sha256":"9637cbd496f99d1a0c0adef662c983c13b8070ee0d76947002579dd155939ae5"},"schema_version":"1.0","source":{"id":"2401.03781","kind":"arxiv","version":1}},"canonical_sha256":"159d9ff274c2d7760e315273fe397c357d127d98a52d3274eab894d06c185544","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"159d9ff274c2d7760e315273fe397c357d127d98a52d3274eab894d06c185544","first_computed_at":"2026-07-05T07:31:13.747668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:31:13.747668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OkLB8s7PUCinjneZ7GWyyLOqtsFbwU4YMNKI+DmmkxgHynqbNRVeXpQSJn6+Jk06IXOHIPXXSnjViUGfZi5jDw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:31:13.748147Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.03781","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f43b603daea87e8889077027e0c6af8a9e921a1d8e7c82c5e752bd6f1837d15c","sha256:78a13619f2435ccb90feab7a6f58f72d3d37e99cb92ea3f58728b96fb9c92d50"],"state_sha256":"fed556d1cb649caf3b5d8b0d60c2c7ca36f07d42db69a99b9ca1b70369eb4560"}