{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5CY65MRCDHJIHDEFSUMSXSZ2B2","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":"0c9d8912559ff5b84b66553d1ba7a91a1c7aa1c57e4a133440b9f29e76eba890","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-05-08T16:24:43Z","title_canon_sha256":"4d660bb4cc195fe1b650dbd8b2363193a8c8ee96eedfc91f9e5034251aa7a493"},"schema_version":"1.0","source":{"id":"1305.1871","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1871","created_at":"2026-05-18T01:46:14Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1871v1","created_at":"2026-05-18T01:46:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1871","created_at":"2026-05-18T01:46:14Z"},{"alias_kind":"pith_short_12","alias_value":"5CY65MRCDHJI","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5CY65MRCDHJIHDEF","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5CY65MRC","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:d7851aa6bfc92e5b15b5672d3fdc4279855d173a99033fb44b250fa79c196e42","target":"graph","created_at":"2026-05-18T01:46:14Z","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 exact magnetic flows on closed orientable surfaces. We show that for almost every energy $\\kappa$ below Ma\\~n\\'e's critical value of the universal covering there are always at least three distinct closed magnetic geodesics with energy $\\kappa$. If in addition the energy level is assumed to be non-degenerate we prove existence of infinitely many closed magnetic geodesics.","authors_text":"Alberto Abbondandolo, Gabriel P. Paternain, Leonardo Macarini","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-05-08T16:24:43Z","title":"On the existence of three closed magnetic geodesics for subcritical energies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1871","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":"sha256:0b62fc8fa83b9a004ff0b75028f4c45555d2dcfe19020769efc3505228c1f088","target":"record","created_at":"2026-05-18T01:46:14Z","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":"0c9d8912559ff5b84b66553d1ba7a91a1c7aa1c57e4a133440b9f29e76eba890","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-05-08T16:24:43Z","title_canon_sha256":"4d660bb4cc195fe1b650dbd8b2363193a8c8ee96eedfc91f9e5034251aa7a493"},"schema_version":"1.0","source":{"id":"1305.1871","kind":"arxiv","version":1}},"canonical_sha256":"e8b1eeb22219d2838c8595192bcb3a0e954a74e32543b2167c8f629af6ad198b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8b1eeb22219d2838c8595192bcb3a0e954a74e32543b2167c8f629af6ad198b","first_computed_at":"2026-05-18T01:46:14.373120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:46:14.373120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZrfopzREKqFs9wxcIMRT+24+ucSAhPvMiTUbrWIVB8Fo2hYmpalWB2067f9aeBMuLvAO2vakb2ip3vksH/ZNCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:46:14.373830Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1871","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b62fc8fa83b9a004ff0b75028f4c45555d2dcfe19020769efc3505228c1f088","sha256:d7851aa6bfc92e5b15b5672d3fdc4279855d173a99033fb44b250fa79c196e42"],"state_sha256":"0907bd9bc5c1fef5632a07aeacf11abc51cde7d9ac271ed080d73fbd19365a29"}