{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:T6M7ZHXXO4FZL7KXOPD4SHH5KS","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":"9e453665f0a9473dcb137595e4a185528e368678790ec85acc3dc9d09afca72e","cross_cats_sorted":["physics.gen-ph"],"license":"","primary_cat":"physics.class-ph","submitted_at":"2001-03-20T13:12:39Z","title_canon_sha256":"331bd96a59d2c340e67a5050b5d4f1a11fbd55a0514fe203e218b61600ec0e06"},"schema_version":"1.0","source":{"id":"physics/0103058","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"physics/0103058","created_at":"2026-05-18T01:38:11Z"},{"alias_kind":"arxiv_version","alias_value":"physics/0103058v1","created_at":"2026-05-18T01:38:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.physics/0103058","created_at":"2026-05-18T01:38:11Z"},{"alias_kind":"pith_short_12","alias_value":"T6M7ZHXXO4FZ","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"T6M7ZHXXO4FZL7KX","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"T6M7ZHXX","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:1b192c625bccd70e46752a61da289f7c9fb779fd17d7f0ecc76d9d55dce17927","target":"graph","created_at":"2026-05-18T01:38:11Z","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"},"paper":{"abstract_excerpt":"The question: \"How many different trajectories are there on a single invariant torus within the phase space of an integrable Hamiltonian system?\" is posed. A rigorous answer to the question is found both for the rational and the irrational tori. The relevant notion of non-measurable sets is discussed.","authors_text":"Krzysztof W. Wojciechowski, Piotr Pieranski","cross_cats":["physics.gen-ph"],"headline":"","license":"","primary_cat":"physics.class-ph","submitted_at":"2001-03-20T13:12:39Z","title":"On non-measurable sets and invariant tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0103058","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":"sha256:3a923f6ea08b055f4670770541b130a3577aeaabe0282076a1f51575a8915225","target":"record","created_at":"2026-05-18T01:38:11Z","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":"9e453665f0a9473dcb137595e4a185528e368678790ec85acc3dc9d09afca72e","cross_cats_sorted":["physics.gen-ph"],"license":"","primary_cat":"physics.class-ph","submitted_at":"2001-03-20T13:12:39Z","title_canon_sha256":"331bd96a59d2c340e67a5050b5d4f1a11fbd55a0514fe203e218b61600ec0e06"},"schema_version":"1.0","source":{"id":"physics/0103058","kind":"arxiv","version":1}},"canonical_sha256":"9f99fc9ef7770b95fd5773c7c91cfd548bd4c38834a5d2d6bddfea4df7c61fbd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f99fc9ef7770b95fd5773c7c91cfd548bd4c38834a5d2d6bddfea4df7c61fbd","first_computed_at":"2026-05-18T01:38:11.236721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:11.236721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KtZE9f6oEqqS45wnasaFEJeApZW0fo6WPQMdgQnI9vHobJwF0AgkArJO7qcfsKx2FtKuC3DwlCnkrvQ2TQowCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:11.237299Z","signed_message":"canonical_sha256_bytes"},"source_id":"physics/0103058","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a923f6ea08b055f4670770541b130a3577aeaabe0282076a1f51575a8915225","sha256:1b192c625bccd70e46752a61da289f7c9fb779fd17d7f0ecc76d9d55dce17927"],"state_sha256":"fbca42c81448277f517c89a46e75bce1b3d9aaa556185a0fde2dbf851d34dc39"}