{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:P3SNXAYRZALP3PCJL7BDFHAH5K","short_pith_number":"pith:P3SNXAYR","schema_version":"1.0","canonical_sha256":"7ee4db8311c816fdbc495fc2329c07ea866cdd95658535091e55d6ddbab12036","source":{"kind":"arxiv","id":"1305.2799","version":2},"attestation_state":"computed","paper":{"title":"Linking and closed orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP","math.SG"],"primary_cat":"math.DS","authors_text":"Kai Zehmisch, Stefan Suhr","submitted_at":"2013-05-13T14:58:07Z","abstract_excerpt":"We show that the Lagrangian of classical mechanics on a Riemannian manifold of bounded geometry carries a periodic solution of motion with rescribed energy, provided the potential satisfies an asymptotic growth condition, changes sign, and the negative set of the potential is non-trivial in the relative homology."},"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":"1305.2799","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-05-13T14:58:07Z","cross_cats_sorted":["math-ph","math.DG","math.MP","math.SG"],"title_canon_sha256":"88a35f499829db232532c7164bd281b838256dae31367f5d1c627ae7c7a64fe1","abstract_canon_sha256":"a3eec3d86491e2a119918316496cfa0e12653daaf347e90d234191f9ff8f9e6c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:00.676272Z","signature_b64":"GbVLM9s858wUDHsGYTxIxRznaG8hWrg6BUmX4F2/v82wB5AipxBH+mwkqmh1cydNwp7ckT5f44EhmToCi2vQBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ee4db8311c816fdbc495fc2329c07ea866cdd95658535091e55d6ddbab12036","last_reissued_at":"2026-05-18T01:19:00.675519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:00.675519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linking and closed orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP","math.SG"],"primary_cat":"math.DS","authors_text":"Kai Zehmisch, Stefan Suhr","submitted_at":"2013-05-13T14:58:07Z","abstract_excerpt":"We show that the Lagrangian of classical mechanics on a Riemannian manifold of bounded geometry carries a periodic solution of motion with rescribed energy, provided the potential satisfies an asymptotic growth condition, changes sign, and the negative set of the potential is non-trivial in the relative homology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2799","kind":"arxiv","version":2},"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":"1305.2799","created_at":"2026-05-18T01:19:00.675614+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.2799v2","created_at":"2026-05-18T01:19:00.675614+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2799","created_at":"2026-05-18T01:19:00.675614+00:00"},{"alias_kind":"pith_short_12","alias_value":"P3SNXAYRZALP","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"P3SNXAYRZALP3PCJ","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"P3SNXAYR","created_at":"2026-05-18T12:27:54.935989+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/P3SNXAYRZALP3PCJL7BDFHAH5K","json":"https://pith.science/pith/P3SNXAYRZALP3PCJL7BDFHAH5K.json","graph_json":"https://pith.science/api/pith-number/P3SNXAYRZALP3PCJL7BDFHAH5K/graph.json","events_json":"https://pith.science/api/pith-number/P3SNXAYRZALP3PCJL7BDFHAH5K/events.json","paper":"https://pith.science/paper/P3SNXAYR"},"agent_actions":{"view_html":"https://pith.science/pith/P3SNXAYRZALP3PCJL7BDFHAH5K","download_json":"https://pith.science/pith/P3SNXAYRZALP3PCJL7BDFHAH5K.json","view_paper":"https://pith.science/paper/P3SNXAYR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.2799&json=true","fetch_graph":"https://pith.science/api/pith-number/P3SNXAYRZALP3PCJL7BDFHAH5K/graph.json","fetch_events":"https://pith.science/api/pith-number/P3SNXAYRZALP3PCJL7BDFHAH5K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P3SNXAYRZALP3PCJL7BDFHAH5K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P3SNXAYRZALP3PCJL7BDFHAH5K/action/storage_attestation","attest_author":"https://pith.science/pith/P3SNXAYRZALP3PCJL7BDFHAH5K/action/author_attestation","sign_citation":"https://pith.science/pith/P3SNXAYRZALP3PCJL7BDFHAH5K/action/citation_signature","submit_replication":"https://pith.science/pith/P3SNXAYRZALP3PCJL7BDFHAH5K/action/replication_record"}},"created_at":"2026-05-18T01:19:00.675614+00:00","updated_at":"2026-05-18T01:19:00.675614+00:00"}