{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CHFSYEYXXM4XTD6NZBXRIEGYKR","short_pith_number":"pith:CHFSYEYX","canonical_record":{"source":{"id":"1401.1356","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-01-07T12:32:25Z","cross_cats_sorted":[],"title_canon_sha256":"80fa897a657ae2547ec33d40c914b344addbb8c70b7b2703876775c8e577bd78","abstract_canon_sha256":"7bf3757828908a0daf9766b348b8f07e552f7bff0fb241ecae80a8889f77a3ed"},"schema_version":"1.0"},"canonical_sha256":"11cb2c1317bb39798fcdc86f1410d8545424bce2083994099800454ef068cc89","source":{"kind":"arxiv","id":"1401.1356","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1356","created_at":"2026-05-18T00:01:23Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1356v2","created_at":"2026-05-18T00:01:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1356","created_at":"2026-05-18T00:01:23Z"},{"alias_kind":"pith_short_12","alias_value":"CHFSYEYXXM4X","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CHFSYEYXXM4XTD6N","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CHFSYEYX","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CHFSYEYXXM4XTD6NZBXRIEGYKR","target":"record","payload":{"canonical_record":{"source":{"id":"1401.1356","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-01-07T12:32:25Z","cross_cats_sorted":[],"title_canon_sha256":"80fa897a657ae2547ec33d40c914b344addbb8c70b7b2703876775c8e577bd78","abstract_canon_sha256":"7bf3757828908a0daf9766b348b8f07e552f7bff0fb241ecae80a8889f77a3ed"},"schema_version":"1.0"},"canonical_sha256":"11cb2c1317bb39798fcdc86f1410d8545424bce2083994099800454ef068cc89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:23.814456Z","signature_b64":"qHeZ6d387cTjHYBNYRsge45rX5uX/wqqnCrd0tWQ5Mr9rm7qRM+bxLFSd4e0PbNXilE/Nei/1S6ogENTWkE9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11cb2c1317bb39798fcdc86f1410d8545424bce2083994099800454ef068cc89","last_reissued_at":"2026-05-18T00:01:23.814074Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:23.814074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.1356","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":"2026-05-18T00:01:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rFrzcDALVPEBHOftULdRHnKq1rFG6AL3htBippc+9Q4+XIDZ7DfN+khQdVw41S2I6HYyNp071in2SNfYqX3FDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:40:31.482634Z"},"content_sha256":"d182095971026c9dcaf21cb97a006a321d15e46a1a4241623046a1bba85738a5","schema_version":"1.0","event_id":"sha256:d182095971026c9dcaf21cb97a006a321d15e46a1a4241623046a1bba85738a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CHFSYEYXXM4XTD6NZBXRIEGYKR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetric periodic orbits and uniruled real Liouville domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Otto van Koert, Urs Frauenfelder","submitted_at":"2014-01-07T12:32:25Z","abstract_excerpt":"A real Liouville domain is a Liouville domain together with an exact anti-symplectic involution. We call a real Liouville domain uniruled if there exists an invariant finite energy plane through every real point. Asymptotically an invariant finite energy plane converges to a symmetric periodic orbit. In this note we work out a criterion which guarantees uniruledness for real Liouville domains."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1356","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":"2026-05-18T00:01:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UgX1ILEGiaSmS6knlKpG/n8IM1L2bA5W6X+YYWTdt70T1lfysSf4sg2mimiM4r0ZbVypcCtksCkU3lw+Yxo3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:40:31.483150Z"},"content_sha256":"55f67b02e85e7c580d5ecf37cfc3be3eed0ed8ba04588ccd1c9bbf61fb254a4a","schema_version":"1.0","event_id":"sha256:55f67b02e85e7c580d5ecf37cfc3be3eed0ed8ba04588ccd1c9bbf61fb254a4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CHFSYEYXXM4XTD6NZBXRIEGYKR/bundle.json","state_url":"https://pith.science/pith/CHFSYEYXXM4XTD6NZBXRIEGYKR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CHFSYEYXXM4XTD6NZBXRIEGYKR/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":"2026-05-27T05:40:31Z","links":{"resolver":"https://pith.science/pith/CHFSYEYXXM4XTD6NZBXRIEGYKR","bundle":"https://pith.science/pith/CHFSYEYXXM4XTD6NZBXRIEGYKR/bundle.json","state":"https://pith.science/pith/CHFSYEYXXM4XTD6NZBXRIEGYKR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CHFSYEYXXM4XTD6NZBXRIEGYKR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CHFSYEYXXM4XTD6NZBXRIEGYKR","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":"7bf3757828908a0daf9766b348b8f07e552f7bff0fb241ecae80a8889f77a3ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-01-07T12:32:25Z","title_canon_sha256":"80fa897a657ae2547ec33d40c914b344addbb8c70b7b2703876775c8e577bd78"},"schema_version":"1.0","source":{"id":"1401.1356","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1356","created_at":"2026-05-18T00:01:23Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1356v2","created_at":"2026-05-18T00:01:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1356","created_at":"2026-05-18T00:01:23Z"},{"alias_kind":"pith_short_12","alias_value":"CHFSYEYXXM4X","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CHFSYEYXXM4XTD6N","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CHFSYEYX","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:55f67b02e85e7c580d5ecf37cfc3be3eed0ed8ba04588ccd1c9bbf61fb254a4a","target":"graph","created_at":"2026-05-18T00:01:23Z","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":"A real Liouville domain is a Liouville domain together with an exact anti-symplectic involution. We call a real Liouville domain uniruled if there exists an invariant finite energy plane through every real point. Asymptotically an invariant finite energy plane converges to a symmetric periodic orbit. In this note we work out a criterion which guarantees uniruledness for real Liouville domains.","authors_text":"Otto van Koert, Urs Frauenfelder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-01-07T12:32:25Z","title":"Symmetric periodic orbits and uniruled real Liouville domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1356","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:d182095971026c9dcaf21cb97a006a321d15e46a1a4241623046a1bba85738a5","target":"record","created_at":"2026-05-18T00:01:23Z","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":"7bf3757828908a0daf9766b348b8f07e552f7bff0fb241ecae80a8889f77a3ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-01-07T12:32:25Z","title_canon_sha256":"80fa897a657ae2547ec33d40c914b344addbb8c70b7b2703876775c8e577bd78"},"schema_version":"1.0","source":{"id":"1401.1356","kind":"arxiv","version":2}},"canonical_sha256":"11cb2c1317bb39798fcdc86f1410d8545424bce2083994099800454ef068cc89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11cb2c1317bb39798fcdc86f1410d8545424bce2083994099800454ef068cc89","first_computed_at":"2026-05-18T00:01:23.814074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:23.814074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qHeZ6d387cTjHYBNYRsge45rX5uX/wqqnCrd0tWQ5Mr9rm7qRM+bxLFSd4e0PbNXilE/Nei/1S6ogENTWkE9AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:23.814456Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.1356","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d182095971026c9dcaf21cb97a006a321d15e46a1a4241623046a1bba85738a5","sha256:55f67b02e85e7c580d5ecf37cfc3be3eed0ed8ba04588ccd1c9bbf61fb254a4a"],"state_sha256":"37a84eadd35e10be7122e6d598eefa225bf847d0c44163f30e93023675728e17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hU76j369DsfVkMXRkqnzvBFNdzX1uP2ydYRT1AAPtWzMnFeKxyh76ya0BdaAPWr5q9OWY6I0PBJUZMX40RTDBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T05:40:31.486779Z","bundle_sha256":"7ab6288ec28cd8658fc3ab3181e3200fd3634bae4e84800f6985fd4a1720939a"}}