{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3QV5RXLMPRTQL4HPCGQN3C4GAD","short_pith_number":"pith:3QV5RXLM","canonical_record":{"source":{"id":"1404.7641","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-30T09:11:06Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"8c13ef6191e21eb1b11468aeab05e897bc9f7a0a9ff8f5effd050f9c56dd4a20","abstract_canon_sha256":"58ed30bc2438729f42b11be957d245a925fb3b82d6088177e9c2d89defe0de86"},"schema_version":"1.0"},"canonical_sha256":"dc2bd8dd6c7c6705f0ef11a0dd8b8600c513dbad9f8fc4a2c56b5a2a7fc82918","source":{"kind":"arxiv","id":"1404.7641","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.7641","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"arxiv_version","alias_value":"1404.7641v3","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7641","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"pith_short_12","alias_value":"3QV5RXLMPRTQ","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3QV5RXLMPRTQL4HP","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3QV5RXLM","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3QV5RXLMPRTQL4HPCGQN3C4GAD","target":"record","payload":{"canonical_record":{"source":{"id":"1404.7641","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-30T09:11:06Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"8c13ef6191e21eb1b11468aeab05e897bc9f7a0a9ff8f5effd050f9c56dd4a20","abstract_canon_sha256":"58ed30bc2438729f42b11be957d245a925fb3b82d6088177e9c2d89defe0de86"},"schema_version":"1.0"},"canonical_sha256":"dc2bd8dd6c7c6705f0ef11a0dd8b8600c513dbad9f8fc4a2c56b5a2a7fc82918","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:02.390679Z","signature_b64":"yo+bRXFpDjvT0L6mfq+Mi3y4vrhQo5fCEGhH6OC9NIEJkn6twgNw1sBRaByh6r8pvBtUniy+Ggij1Osqtj3kCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc2bd8dd6c7c6705f0ef11a0dd8b8600c513dbad9f8fc4a2c56b5a2a7fc82918","last_reissued_at":"2026-05-18T00:52:02.390106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:02.390106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.7641","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BA69YsbMbLshjOjcgnG/Vq9E6pKigNFxRMfwUx5fR96Hjp+D1/xjlsAnlnOs16XDF9d5yiyxvS0W0nN7U5jGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:02:42.642472Z"},"content_sha256":"0cd3652c91513eee5109d67ed2e588e1c059df70569f68c24586b326e740771f","schema_version":"1.0","event_id":"sha256:0cd3652c91513eee5109d67ed2e588e1c059df70569f68c24586b326e740771f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3QV5RXLMPRTQL4HPCGQN3C4GAD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DS","authors_text":"Alberto Abbondandolo, Gabriel P. Paternain, Leonardo Macarini, Marco Mazzucchelli","submitted_at":"2014-04-30T09:11:06Z","abstract_excerpt":"We consider an exact magnetic flow on the tangent bundle of a closed surface. We prove that for almost every energy level $\\kappa$ below the Ma\\~n\\'e critical value of the universal cover there are infinitely many periodic orbits with energy $\\kappa$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7641","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B44jdhQ/clBn7yfDBL45pu+WG8xMDWRE5zeaKfit68KH6OM05FSXZ9GZJ5LfOJBKZXo4ci+2qicQ0477/mBqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:02:42.642821Z"},"content_sha256":"ec2ccfba805b371f9d2797fc4cf92f467ea5b46a8cb5c4505a532812d06f9048","schema_version":"1.0","event_id":"sha256:ec2ccfba805b371f9d2797fc4cf92f467ea5b46a8cb5c4505a532812d06f9048"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3QV5RXLMPRTQL4HPCGQN3C4GAD/bundle.json","state_url":"https://pith.science/pith/3QV5RXLMPRTQL4HPCGQN3C4GAD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3QV5RXLMPRTQL4HPCGQN3C4GAD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T05:02:42Z","links":{"resolver":"https://pith.science/pith/3QV5RXLMPRTQL4HPCGQN3C4GAD","bundle":"https://pith.science/pith/3QV5RXLMPRTQL4HPCGQN3C4GAD/bundle.json","state":"https://pith.science/pith/3QV5RXLMPRTQL4HPCGQN3C4GAD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3QV5RXLMPRTQL4HPCGQN3C4GAD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3QV5RXLMPRTQL4HPCGQN3C4GAD","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":"58ed30bc2438729f42b11be957d245a925fb3b82d6088177e9c2d89defe0de86","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-30T09:11:06Z","title_canon_sha256":"8c13ef6191e21eb1b11468aeab05e897bc9f7a0a9ff8f5effd050f9c56dd4a20"},"schema_version":"1.0","source":{"id":"1404.7641","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.7641","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"arxiv_version","alias_value":"1404.7641v3","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7641","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"pith_short_12","alias_value":"3QV5RXLMPRTQ","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3QV5RXLMPRTQL4HP","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3QV5RXLM","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:ec2ccfba805b371f9d2797fc4cf92f467ea5b46a8cb5c4505a532812d06f9048","target":"graph","created_at":"2026-05-18T00:52:02Z","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":"We consider an exact magnetic flow on the tangent bundle of a closed surface. We prove that for almost every energy level $\\kappa$ below the Ma\\~n\\'e critical value of the universal cover there are infinitely many periodic orbits with energy $\\kappa$.","authors_text":"Alberto Abbondandolo, Gabriel P. Paternain, Leonardo Macarini, Marco Mazzucchelli","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-30T09:11:06Z","title":"Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7641","kind":"arxiv","version":3},"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":"sha256:0cd3652c91513eee5109d67ed2e588e1c059df70569f68c24586b326e740771f","target":"record","created_at":"2026-05-18T00:52:02Z","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":"58ed30bc2438729f42b11be957d245a925fb3b82d6088177e9c2d89defe0de86","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-30T09:11:06Z","title_canon_sha256":"8c13ef6191e21eb1b11468aeab05e897bc9f7a0a9ff8f5effd050f9c56dd4a20"},"schema_version":"1.0","source":{"id":"1404.7641","kind":"arxiv","version":3}},"canonical_sha256":"dc2bd8dd6c7c6705f0ef11a0dd8b8600c513dbad9f8fc4a2c56b5a2a7fc82918","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc2bd8dd6c7c6705f0ef11a0dd8b8600c513dbad9f8fc4a2c56b5a2a7fc82918","first_computed_at":"2026-05-18T00:52:02.390106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:02.390106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yo+bRXFpDjvT0L6mfq+Mi3y4vrhQo5fCEGhH6OC9NIEJkn6twgNw1sBRaByh6r8pvBtUniy+Ggij1Osqtj3kCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:02.390679Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.7641","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0cd3652c91513eee5109d67ed2e588e1c059df70569f68c24586b326e740771f","sha256:ec2ccfba805b371f9d2797fc4cf92f467ea5b46a8cb5c4505a532812d06f9048"],"state_sha256":"9e248e181ea84795f86b51c6299729f505a44db79207fc0df16e5fa48ab9ef25"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CMG8tpMFKWUY2wX/IDfyIV8yvSHwW9KV7eX9R4ixyMBL67shQS2MPgbLOOLrub7TULyixIMEUA8gxoXaTnIFAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T05:02:42.644915Z","bundle_sha256":"da113a383ed69f12f28d954fee97d86c83bd9ffa4ceca3de4fb39ed290a21b03"}}