{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:23QDGSLN2QMIWWFNSRRN54ENQY","short_pith_number":"pith:23QDGSLN","canonical_record":{"source":{"id":"1307.1664","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-05T17:04:15Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"02cd13a049cc63a9cde4938c4702984884eee466c9a0ef2fa9480a72551c2bea","abstract_canon_sha256":"231d8d21998543dcaac32a3599824f449591e18c5b977d8389a11ae9be3116ce"},"schema_version":"1.0"},"canonical_sha256":"d6e033496dd4188b58ad9462def08d86039c942a32e77c85b82b295f5a914e5b","source":{"kind":"arxiv","id":"1307.1664","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1664","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1664v2","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1664","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"23QDGSLN2QMI","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"23QDGSLN2QMIWWFN","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"23QDGSLN","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:23QDGSLN2QMIWWFNSRRN54ENQY","target":"record","payload":{"canonical_record":{"source":{"id":"1307.1664","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-05T17:04:15Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"02cd13a049cc63a9cde4938c4702984884eee466c9a0ef2fa9480a72551c2bea","abstract_canon_sha256":"231d8d21998543dcaac32a3599824f449591e18c5b977d8389a11ae9be3116ce"},"schema_version":"1.0"},"canonical_sha256":"d6e033496dd4188b58ad9462def08d86039c942a32e77c85b82b295f5a914e5b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:35.485934Z","signature_b64":"WWjWaSk/DoO4jMjWaGODWAuy+1VkZ6GIBjiKKS0AqoBfNzpqqPITqb7Y9cHBM6+AAxlfx8vjrnhFc2sNHVupBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6e033496dd4188b58ad9462def08d86039c942a32e77c85b82b295f5a914e5b","last_reissued_at":"2026-05-17T23:53:35.485119Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:35.485119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.1664","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EUgT6hK+PdpP7xPLQon6LwalpxWYysQOZoMXD21NvLMao5IRTngMdkB0rL/FSpmB+MhViv76iGskYJKAheaFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T20:24:17.239520Z"},"content_sha256":"4a8828e915d595635e5e54a3897c07ba439d9df33ece2c7dddfa8f81e3c61686","schema_version":"1.0","event_id":"sha256:4a8828e915d595635e5e54a3897c07ba439d9df33ece2c7dddfa8f81e3c61686"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:23QDGSLN2QMIWWFNSRRN54ENQY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On non-contractible periodic orbits for surface homeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DS","authors_text":"Fabio Armando Tal","submitted_at":"2013-07-05T17:04:15Z","abstract_excerpt":"In this work we study homeomorphisms of closed orientable surfaces homotopic to the identity, focusing on the existence of non-contractible periodic orbits. We show that, if $g$ is such a homeomorphism, and if $\\hat g$ is its lift to the universal covering of $S$ that commutes with the deck transformations, then one of the following three conditions must be satisfied: (1) The set of fixed points for $\\hat g$ projects to a closed subset $F$ which contains an essential continuum, (2) $g$ has non-contratible periodic points of every sufficiently large period, or (3) there exists an uniform bound "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1664","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RI54bd6jNpK+2b8AWf4XCsfHJjufKAmL4kLNC8d064fKk6tiHCqAi4UHOg+ZF/QXfO7F1ZRlUnafEfrTXqJjDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T20:24:17.239862Z"},"content_sha256":"8097fe0a48494e855e5cc168cbd99f8c527229363e7db600b8b1c733e7ae2bf8","schema_version":"1.0","event_id":"sha256:8097fe0a48494e855e5cc168cbd99f8c527229363e7db600b8b1c733e7ae2bf8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/23QDGSLN2QMIWWFNSRRN54ENQY/bundle.json","state_url":"https://pith.science/pith/23QDGSLN2QMIWWFNSRRN54ENQY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/23QDGSLN2QMIWWFNSRRN54ENQY/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":"2026-06-23T20:24:17Z","links":{"resolver":"https://pith.science/pith/23QDGSLN2QMIWWFNSRRN54ENQY","bundle":"https://pith.science/pith/23QDGSLN2QMIWWFNSRRN54ENQY/bundle.json","state":"https://pith.science/pith/23QDGSLN2QMIWWFNSRRN54ENQY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/23QDGSLN2QMIWWFNSRRN54ENQY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:23QDGSLN2QMIWWFNSRRN54ENQY","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":"231d8d21998543dcaac32a3599824f449591e18c5b977d8389a11ae9be3116ce","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-05T17:04:15Z","title_canon_sha256":"02cd13a049cc63a9cde4938c4702984884eee466c9a0ef2fa9480a72551c2bea"},"schema_version":"1.0","source":{"id":"1307.1664","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1664","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1664v2","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1664","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"23QDGSLN2QMI","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"23QDGSLN2QMIWWFN","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"23QDGSLN","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:8097fe0a48494e855e5cc168cbd99f8c527229363e7db600b8b1c733e7ae2bf8","target":"graph","created_at":"2026-05-17T23:53:35Z","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":"In this work we study homeomorphisms of closed orientable surfaces homotopic to the identity, focusing on the existence of non-contractible periodic orbits. We show that, if $g$ is such a homeomorphism, and if $\\hat g$ is its lift to the universal covering of $S$ that commutes with the deck transformations, then one of the following three conditions must be satisfied: (1) The set of fixed points for $\\hat g$ projects to a closed subset $F$ which contains an essential continuum, (2) $g$ has non-contratible periodic points of every sufficiently large period, or (3) there exists an uniform bound ","authors_text":"Fabio Armando Tal","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-05T17:04:15Z","title":"On non-contractible periodic orbits for surface homeomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1664","kind":"arxiv","version":2},"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":"sha256:4a8828e915d595635e5e54a3897c07ba439d9df33ece2c7dddfa8f81e3c61686","target":"record","created_at":"2026-05-17T23:53:35Z","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":"231d8d21998543dcaac32a3599824f449591e18c5b977d8389a11ae9be3116ce","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-05T17:04:15Z","title_canon_sha256":"02cd13a049cc63a9cde4938c4702984884eee466c9a0ef2fa9480a72551c2bea"},"schema_version":"1.0","source":{"id":"1307.1664","kind":"arxiv","version":2}},"canonical_sha256":"d6e033496dd4188b58ad9462def08d86039c942a32e77c85b82b295f5a914e5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6e033496dd4188b58ad9462def08d86039c942a32e77c85b82b295f5a914e5b","first_computed_at":"2026-05-17T23:53:35.485119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:35.485119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WWjWaSk/DoO4jMjWaGODWAuy+1VkZ6GIBjiKKS0AqoBfNzpqqPITqb7Y9cHBM6+AAxlfx8vjrnhFc2sNHVupBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:35.485934Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.1664","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a8828e915d595635e5e54a3897c07ba439d9df33ece2c7dddfa8f81e3c61686","sha256:8097fe0a48494e855e5cc168cbd99f8c527229363e7db600b8b1c733e7ae2bf8"],"state_sha256":"af9dc19b569a9f8d0ba73b5b0722590739030d59eb648c4e544affa39a5a703d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jF4FKgkv5r51zq5kOLwSbILryb07/6WYpmIcLzMXU0R41aEPweE/MchE44GpKwjVPnsNPQ2yLcT0sG7gmqMXCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T20:24:17.241801Z","bundle_sha256":"52266979d1b3141b1aafcb27cd3603738da17b0e1448daca726da8025d883c0d"}}