{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:CGSWCELL5CA5NA26MPXS4PUCJN","short_pith_number":"pith:CGSWCELL","canonical_record":{"source":{"id":"2206.15152","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-06-30T09:35:25Z","cross_cats_sorted":["math.DS","math.SG"],"title_canon_sha256":"07e595d59f835473cd85d0f934dfaf08d516967c360bf67421982674fcdd2d7c","abstract_canon_sha256":"b7244294b84254031fb970aa3ec2849684a64eb8260b9c859f4c373e87cf5b7d"},"schema_version":"1.0"},"canonical_sha256":"11a561116be881d6835e63ef2e3e824b6d970ab3666e8acde6a671ef35c89998","source":{"kind":"arxiv","id":"2206.15152","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.15152","created_at":"2026-07-05T11:32:11Z"},{"alias_kind":"arxiv_version","alias_value":"2206.15152v3","created_at":"2026-07-05T11:32:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.15152","created_at":"2026-07-05T11:32:11Z"},{"alias_kind":"pith_short_12","alias_value":"CGSWCELL5CA5","created_at":"2026-07-05T11:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"CGSWCELL5CA5NA26","created_at":"2026-07-05T11:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"CGSWCELL","created_at":"2026-07-05T11:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:CGSWCELL5CA5NA26MPXS4PUCJN","target":"record","payload":{"canonical_record":{"source":{"id":"2206.15152","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-06-30T09:35:25Z","cross_cats_sorted":["math.DS","math.SG"],"title_canon_sha256":"07e595d59f835473cd85d0f934dfaf08d516967c360bf67421982674fcdd2d7c","abstract_canon_sha256":"b7244294b84254031fb970aa3ec2849684a64eb8260b9c859f4c373e87cf5b7d"},"schema_version":"1.0"},"canonical_sha256":"11a561116be881d6835e63ef2e3e824b6d970ab3666e8acde6a671ef35c89998","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:32:11.901989Z","signature_b64":"weAqMXbLJBSGGe9CyBaZglvmJTJ7+fOT6aZPf7BIWxrKNQfK8cFoWnzcYIIi6FJHsmAz/NssdNAvaZZBRZmqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11a561116be881d6835e63ef2e3e824b6d970ab3666e8acde6a671ef35c89998","last_reissued_at":"2026-07-05T11:32:11.901508Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:32:11.901508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.15152","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":"2026-07-05T11:32:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7W9oBQNLEM56QiabANVRxRs+WR9opyoy8nHnOW3eK3fcwJlBMwi9Qb473iFJRf5N+wuXRYECH4/ZLi9rkXRgBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T10:49:27.465632Z"},"content_sha256":"ac5d524779b1e135ad88e27e0e0e92d5ca79a927f34b96f9348352d6fa4746e9","schema_version":"1.0","event_id":"sha256:ac5d524779b1e135ad88e27e0e0e92d5ca79a927f34b96f9348352d6fa4746e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:CGSWCELL5CA5NA26MPXS4PUCJN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equidistributed Closed Geodesics on Closed Finsler and Riemannian Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.SG"],"primary_cat":"math.DG","authors_text":"Hui Liu, Lei Liu","submitted_at":"2022-06-30T09:35:25Z","abstract_excerpt":"In this paper, we establish the existence of an equidistributed sequence of nondegenerate closed geodesics for generic Finsler, symmetric Finsler and Riemannian metrics on every closed surface. The proof relies on the volume property of embedded contact homology, established by Cristofaro-Gardiner, Hutchings and Ramos, along with specific local variational constructions and transversality arguments. Our approach is motivated by Irie's equidistribution result in [19] for three-dimensional Reeb flows and the analogous result presented by Marques, Neves and Song [27] for embedded minimal hypersur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.15152","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.15152/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:32:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Z86/S+H3DEnM9MiTgBf7kRE9erefmB/qSuY2Jrelimc5g8wIFM6mCMXPDtu3do8yifGSjx8fRUwDs0MSMHcAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T10:49:27.466581Z"},"content_sha256":"937d3b6606af55d8a5f9fb143920f114a0d622e1792cf5507c79af58b53363f8","schema_version":"1.0","event_id":"sha256:937d3b6606af55d8a5f9fb143920f114a0d622e1792cf5507c79af58b53363f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CGSWCELL5CA5NA26MPXS4PUCJN/bundle.json","state_url":"https://pith.science/pith/CGSWCELL5CA5NA26MPXS4PUCJN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CGSWCELL5CA5NA26MPXS4PUCJN/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":"2026-08-06T10:49:27Z","links":{"resolver":"https://pith.science/pith/CGSWCELL5CA5NA26MPXS4PUCJN","bundle":"https://pith.science/pith/CGSWCELL5CA5NA26MPXS4PUCJN/bundle.json","state":"https://pith.science/pith/CGSWCELL5CA5NA26MPXS4PUCJN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CGSWCELL5CA5NA26MPXS4PUCJN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:CGSWCELL5CA5NA26MPXS4PUCJN","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":"b7244294b84254031fb970aa3ec2849684a64eb8260b9c859f4c373e87cf5b7d","cross_cats_sorted":["math.DS","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-06-30T09:35:25Z","title_canon_sha256":"07e595d59f835473cd85d0f934dfaf08d516967c360bf67421982674fcdd2d7c"},"schema_version":"1.0","source":{"id":"2206.15152","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.15152","created_at":"2026-07-05T11:32:11Z"},{"alias_kind":"arxiv_version","alias_value":"2206.15152v3","created_at":"2026-07-05T11:32:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.15152","created_at":"2026-07-05T11:32:11Z"},{"alias_kind":"pith_short_12","alias_value":"CGSWCELL5CA5","created_at":"2026-07-05T11:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"CGSWCELL5CA5NA26","created_at":"2026-07-05T11:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"CGSWCELL","created_at":"2026-07-05T11:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:937d3b6606af55d8a5f9fb143920f114a0d622e1792cf5507c79af58b53363f8","target":"graph","created_at":"2026-07-05T11:32:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2206.15152/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we establish the existence of an equidistributed sequence of nondegenerate closed geodesics for generic Finsler, symmetric Finsler and Riemannian metrics on every closed surface. The proof relies on the volume property of embedded contact homology, established by Cristofaro-Gardiner, Hutchings and Ramos, along with specific local variational constructions and transversality arguments. Our approach is motivated by Irie's equidistribution result in [19] for three-dimensional Reeb flows and the analogous result presented by Marques, Neves and Song [27] for embedded minimal hypersur","authors_text":"Hui Liu, Lei Liu","cross_cats":["math.DS","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-06-30T09:35:25Z","title":"Equidistributed Closed Geodesics on Closed Finsler and Riemannian Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.15152","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:ac5d524779b1e135ad88e27e0e0e92d5ca79a927f34b96f9348352d6fa4746e9","target":"record","created_at":"2026-07-05T11:32:11Z","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":"b7244294b84254031fb970aa3ec2849684a64eb8260b9c859f4c373e87cf5b7d","cross_cats_sorted":["math.DS","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-06-30T09:35:25Z","title_canon_sha256":"07e595d59f835473cd85d0f934dfaf08d516967c360bf67421982674fcdd2d7c"},"schema_version":"1.0","source":{"id":"2206.15152","kind":"arxiv","version":3}},"canonical_sha256":"11a561116be881d6835e63ef2e3e824b6d970ab3666e8acde6a671ef35c89998","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11a561116be881d6835e63ef2e3e824b6d970ab3666e8acde6a671ef35c89998","first_computed_at":"2026-07-05T11:32:11.901508Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:32:11.901508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"weAqMXbLJBSGGe9CyBaZglvmJTJ7+fOT6aZPf7BIWxrKNQfK8cFoWnzcYIIi6FJHsmAz/NssdNAvaZZBRZmqBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:32:11.901989Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.15152","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac5d524779b1e135ad88e27e0e0e92d5ca79a927f34b96f9348352d6fa4746e9","sha256:937d3b6606af55d8a5f9fb143920f114a0d622e1792cf5507c79af58b53363f8"],"state_sha256":"1e3dc72d5c856fc284b50023209ff0c19d77d181276db0cd6725de8316843463"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GjN2pTudLiVqQnieVyo3uvV6Yp+OxOaE6oQUX4K5RpYUqw+mZGqDZFpC+thbMZcu4O3PTDwhm7tJtIA4rIj9Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T10:49:27.472754Z","bundle_sha256":"15e4205e1f9c21ffd3f86aff05f5840fa97765a6f938b6e9dbe4622c88712aa1"}}