{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:OBMNSGZNB22TXI5U2ILOC5MRAV","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":"db8c1332683ddeb0052ae18cd3e334aeeadc88817b6bcfe351ad2beb00d19996","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GM","submitted_at":"2025-01-21T18:40:16Z","title_canon_sha256":"1c5eb8c3c985bd2928082a5cd520ddd8983d7f8e796d514778514e9a9c4b5598"},"schema_version":"1.0","source":{"id":"2502.03474","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.03474","created_at":"2026-07-05T10:10:10Z"},{"alias_kind":"arxiv_version","alias_value":"2502.03474v1","created_at":"2026-07-05T10:10:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.03474","created_at":"2026-07-05T10:10:10Z"},{"alias_kind":"pith_short_12","alias_value":"OBMNSGZNB22T","created_at":"2026-07-05T10:10:10Z"},{"alias_kind":"pith_short_16","alias_value":"OBMNSGZNB22TXI5U","created_at":"2026-07-05T10:10:10Z"},{"alias_kind":"pith_short_8","alias_value":"OBMNSGZN","created_at":"2026-07-05T10:10:10Z"}],"graph_snapshots":[{"event_id":"sha256:5649e8e4fe4d7d18f24b3e0e067012fd505dbbdaecd8cb9d9aa8ce11664b758e","target":"graph","created_at":"2026-07-05T10:10:10Z","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/2502.03474/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove the convergence of the FLINT-HILLS series and establish new criteria for a similar type of diophantine or lacunary series, which faces issues due to spaced long terms coming from the trigonometric nature of functions, e.g., cosecant in the FLINT-HILLS series. We connect the FLINT-HILLS series to the Fermi-Dirac integral via the Riemann-Stieltjes integral and YOUNG'S inequality criteria but also proved that the upper bound of the irrationality measure of pi is equal or lower than 2.5 expected if the FLINT-HILLS series converged.","authors_text":"Carlos L\\'opez Zapata, Nikos Mantzakouras","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GM","submitted_at":"2025-01-21T18:40:16Z","title":"Diophantine FLINT-HILLS series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.03474","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":"sha256:3bd5f1405bf69b8a895effcec3909a87b3d3bdf8391905e8f608ef1fde6ab7a1","target":"record","created_at":"2026-07-05T10:10:10Z","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":"db8c1332683ddeb0052ae18cd3e334aeeadc88817b6bcfe351ad2beb00d19996","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.GM","submitted_at":"2025-01-21T18:40:16Z","title_canon_sha256":"1c5eb8c3c985bd2928082a5cd520ddd8983d7f8e796d514778514e9a9c4b5598"},"schema_version":"1.0","source":{"id":"2502.03474","kind":"arxiv","version":1}},"canonical_sha256":"7058d91b2d0eb53ba3b4d216e17591057b582ace67696948020d82a3f9aac150","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7058d91b2d0eb53ba3b4d216e17591057b582ace67696948020d82a3f9aac150","first_computed_at":"2026-07-05T10:10:10.945705Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:10:10.945705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"91J9KFDHin0bId7iUYab+kJqrDwVo3vgoXKio40gL/phzwEh0wHyg2eD2Rlxl/IjJ0euY5y9jJf0wV1/USeGDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:10:10.946132Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.03474","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3bd5f1405bf69b8a895effcec3909a87b3d3bdf8391905e8f608ef1fde6ab7a1","sha256:5649e8e4fe4d7d18f24b3e0e067012fd505dbbdaecd8cb9d9aa8ce11664b758e"],"state_sha256":"519b4bd5637ebec3a70907c4d8dbe63370f263c4a9277412c232b1d532d2efd0"}