{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:T6M7ZHXXO4FZL7KXOPD4SHH5KS","short_pith_number":"pith:T6M7ZHXX","schema_version":"1.0","canonical_sha256":"9f99fc9ef7770b95fd5773c7c91cfd548bd4c38834a5d2d6bddfea4df7c61fbd","source":{"kind":"arxiv","id":"physics/0103058","version":1},"attestation_state":"computed","paper":{"title":"On non-measurable sets and invariant tori","license":"","headline":"","cross_cats":["physics.gen-ph"],"primary_cat":"physics.class-ph","authors_text":"Krzysztof W. Wojciechowski, Piotr Pieranski","submitted_at":"2001-03-20T13:12:39Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"physics/0103058","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"physics.class-ph","submitted_at":"2001-03-20T13:12:39Z","cross_cats_sorted":["physics.gen-ph"],"title_canon_sha256":"331bd96a59d2c340e67a5050b5d4f1a11fbd55a0514fe203e218b61600ec0e06","abstract_canon_sha256":"9e453665f0a9473dcb137595e4a185528e368678790ec85acc3dc9d09afca72e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:11.237299Z","signature_b64":"KtZE9f6oEqqS45wnasaFEJeApZW0fo6WPQMdgQnI9vHobJwF0AgkArJO7qcfsKx2FtKuC3DwlCnkrvQ2TQowCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f99fc9ef7770b95fd5773c7c91cfd548bd4c38834a5d2d6bddfea4df7c61fbd","last_reissued_at":"2026-05-18T01:38:11.236721Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:11.236721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On non-measurable sets and invariant tori","license":"","headline":"","cross_cats":["physics.gen-ph"],"primary_cat":"physics.class-ph","authors_text":"Krzysztof W. Wojciechowski, Piotr Pieranski","submitted_at":"2001-03-20T13:12:39Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0103058","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"physics/0103058","created_at":"2026-05-18T01:38:11.236808+00:00"},{"alias_kind":"arxiv_version","alias_value":"physics/0103058v1","created_at":"2026-05-18T01:38:11.236808+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.physics/0103058","created_at":"2026-05-18T01:38:11.236808+00:00"},{"alias_kind":"pith_short_12","alias_value":"T6M7ZHXXO4FZ","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_16","alias_value":"T6M7ZHXXO4FZL7KX","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_8","alias_value":"T6M7ZHXX","created_at":"2026-05-18T12:25:50.845339+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/T6M7ZHXXO4FZL7KXOPD4SHH5KS","json":"https://pith.science/pith/T6M7ZHXXO4FZL7KXOPD4SHH5KS.json","graph_json":"https://pith.science/api/pith-number/T6M7ZHXXO4FZL7KXOPD4SHH5KS/graph.json","events_json":"https://pith.science/api/pith-number/T6M7ZHXXO4FZL7KXOPD4SHH5KS/events.json","paper":"https://pith.science/paper/T6M7ZHXX"},"agent_actions":{"view_html":"https://pith.science/pith/T6M7ZHXXO4FZL7KXOPD4SHH5KS","download_json":"https://pith.science/pith/T6M7ZHXXO4FZL7KXOPD4SHH5KS.json","view_paper":"https://pith.science/paper/T6M7ZHXX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=physics/0103058&json=true","fetch_graph":"https://pith.science/api/pith-number/T6M7ZHXXO4FZL7KXOPD4SHH5KS/graph.json","fetch_events":"https://pith.science/api/pith-number/T6M7ZHXXO4FZL7KXOPD4SHH5KS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T6M7ZHXXO4FZL7KXOPD4SHH5KS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T6M7ZHXXO4FZL7KXOPD4SHH5KS/action/storage_attestation","attest_author":"https://pith.science/pith/T6M7ZHXXO4FZL7KXOPD4SHH5KS/action/author_attestation","sign_citation":"https://pith.science/pith/T6M7ZHXXO4FZL7KXOPD4SHH5KS/action/citation_signature","submit_replication":"https://pith.science/pith/T6M7ZHXXO4FZL7KXOPD4SHH5KS/action/replication_record"}},"created_at":"2026-05-18T01:38:11.236808+00:00","updated_at":"2026-05-18T01:38:11.236808+00:00"}