{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:RGVSJSDX64O2RL3ZUUPFPWLLJ7","short_pith_number":"pith:RGVSJSDX","canonical_record":{"source":{"id":"1903.07060","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-17T11:49:34Z","cross_cats_sorted":[],"title_canon_sha256":"f3023deb43f1eb7716d3907b58fd8b7c9b2be80d80628420a1ce614266814bf0","abstract_canon_sha256":"95e6b7964e80da67ae2072b562f30ec8f427cd96e544909096e14a1003e327e1"},"schema_version":"1.0"},"canonical_sha256":"89ab24c877f71da8af79a51e57d96b4ff2dc10bddca97419b2f5ed00d53b1ba0","source":{"kind":"arxiv","id":"1903.07060","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07060","created_at":"2026-07-05T00:42:18Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07060v4","created_at":"2026-07-05T00:42:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07060","created_at":"2026-07-05T00:42:18Z"},{"alias_kind":"pith_short_12","alias_value":"RGVSJSDX64O2","created_at":"2026-07-05T00:42:18Z"},{"alias_kind":"pith_short_16","alias_value":"RGVSJSDX64O2RL3Z","created_at":"2026-07-05T00:42:18Z"},{"alias_kind":"pith_short_8","alias_value":"RGVSJSDX","created_at":"2026-07-05T00:42:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:RGVSJSDX64O2RL3ZUUPFPWLLJ7","target":"record","payload":{"canonical_record":{"source":{"id":"1903.07060","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-17T11:49:34Z","cross_cats_sorted":[],"title_canon_sha256":"f3023deb43f1eb7716d3907b58fd8b7c9b2be80d80628420a1ce614266814bf0","abstract_canon_sha256":"95e6b7964e80da67ae2072b562f30ec8f427cd96e544909096e14a1003e327e1"},"schema_version":"1.0"},"canonical_sha256":"89ab24c877f71da8af79a51e57d96b4ff2dc10bddca97419b2f5ed00d53b1ba0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:42:18.611599Z","signature_b64":"k08cGCV9FW32vii0+1ce1HdQpYlFqopQ1BhJu/kW7aceijC0kT080ZQBGJSjduMAA/G97b/8DY1UMMfJYjpWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89ab24c877f71da8af79a51e57d96b4ff2dc10bddca97419b2f5ed00d53b1ba0","last_reissued_at":"2026-07-05T00:42:18.611160Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:42:18.611160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.07060","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:42:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ivzDAlL0VKEd+K7pbymAUCpZYQ+j8uqxJwz2WCjWbtDC1GKSQc7v3cHkvu2jKsJuUILeE2XY8kYVpQOVnrlHBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T04:09:56.008071Z"},"content_sha256":"4068403891cecc3ce9a3572aaf8b042815668ad13b746cad7a7ea8bfa9efd238","schema_version":"1.0","event_id":"sha256:4068403891cecc3ce9a3572aaf8b042815668ad13b746cad7a7ea8bfa9efd238"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:RGVSJSDX64O2RL3ZUUPFPWLLJ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Euler-genus distributions of cubic Halin graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jinlian Zhang, Xuhui Peng","submitted_at":"2019-03-17T11:49:34Z","abstract_excerpt":"Gross derived an $O(n^2)$-time algorithm to calculate the genus distribution of a given cubic Halin graph.\n  In this paper, with the help of overlap matrix, we get a recurrence relation for the Euler-genus polynomial of cubic caterpillar-Halin graphs.\n  Explicit formulas for the embeddings of cubic caterpillar-Halin graph into a surface with Euler-genus 0, 1 and 2 are also obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07060","kind":"arxiv","version":4},"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/1903.07060/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":"2026-07-05T00:42:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mIwCdaWWhNAF86zddJON8KumFIrakE+aM5m9zaAUVArgyytuA+Y9Ctx5I53FkK5DWrY5ef95g8coXHT6NpRFAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T04:09:56.008411Z"},"content_sha256":"99da3c51370c9e8ff7fa4edd0c82b98756f87d3ce540198c1fd375932bf720f7","schema_version":"1.0","event_id":"sha256:99da3c51370c9e8ff7fa4edd0c82b98756f87d3ce540198c1fd375932bf720f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RGVSJSDX64O2RL3ZUUPFPWLLJ7/bundle.json","state_url":"https://pith.science/pith/RGVSJSDX64O2RL3ZUUPFPWLLJ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RGVSJSDX64O2RL3ZUUPFPWLLJ7/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":"2026-08-24T04:09:56Z","links":{"resolver":"https://pith.science/pith/RGVSJSDX64O2RL3ZUUPFPWLLJ7","bundle":"https://pith.science/pith/RGVSJSDX64O2RL3ZUUPFPWLLJ7/bundle.json","state":"https://pith.science/pith/RGVSJSDX64O2RL3ZUUPFPWLLJ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RGVSJSDX64O2RL3ZUUPFPWLLJ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RGVSJSDX64O2RL3ZUUPFPWLLJ7","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":"95e6b7964e80da67ae2072b562f30ec8f427cd96e544909096e14a1003e327e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-17T11:49:34Z","title_canon_sha256":"f3023deb43f1eb7716d3907b58fd8b7c9b2be80d80628420a1ce614266814bf0"},"schema_version":"1.0","source":{"id":"1903.07060","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07060","created_at":"2026-07-05T00:42:18Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07060v4","created_at":"2026-07-05T00:42:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07060","created_at":"2026-07-05T00:42:18Z"},{"alias_kind":"pith_short_12","alias_value":"RGVSJSDX64O2","created_at":"2026-07-05T00:42:18Z"},{"alias_kind":"pith_short_16","alias_value":"RGVSJSDX64O2RL3Z","created_at":"2026-07-05T00:42:18Z"},{"alias_kind":"pith_short_8","alias_value":"RGVSJSDX","created_at":"2026-07-05T00:42:18Z"}],"graph_snapshots":[{"event_id":"sha256:99da3c51370c9e8ff7fa4edd0c82b98756f87d3ce540198c1fd375932bf720f7","target":"graph","created_at":"2026-07-05T00:42:18Z","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/1903.07060/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gross derived an $O(n^2)$-time algorithm to calculate the genus distribution of a given cubic Halin graph.\n  In this paper, with the help of overlap matrix, we get a recurrence relation for the Euler-genus polynomial of cubic caterpillar-Halin graphs.\n  Explicit formulas for the embeddings of cubic caterpillar-Halin graph into a surface with Euler-genus 0, 1 and 2 are also obtained.","authors_text":"Jinlian Zhang, Xuhui Peng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-17T11:49:34Z","title":"Euler-genus distributions of cubic Halin graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07060","kind":"arxiv","version":4},"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":"sha256:4068403891cecc3ce9a3572aaf8b042815668ad13b746cad7a7ea8bfa9efd238","target":"record","created_at":"2026-07-05T00:42:18Z","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":"95e6b7964e80da67ae2072b562f30ec8f427cd96e544909096e14a1003e327e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-17T11:49:34Z","title_canon_sha256":"f3023deb43f1eb7716d3907b58fd8b7c9b2be80d80628420a1ce614266814bf0"},"schema_version":"1.0","source":{"id":"1903.07060","kind":"arxiv","version":4}},"canonical_sha256":"89ab24c877f71da8af79a51e57d96b4ff2dc10bddca97419b2f5ed00d53b1ba0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89ab24c877f71da8af79a51e57d96b4ff2dc10bddca97419b2f5ed00d53b1ba0","first_computed_at":"2026-07-05T00:42:18.611160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:42:18.611160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k08cGCV9FW32vii0+1ce1HdQpYlFqopQ1BhJu/kW7aceijC0kT080ZQBGJSjduMAA/G97b/8DY1UMMfJYjpWAg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:42:18.611599Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.07060","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4068403891cecc3ce9a3572aaf8b042815668ad13b746cad7a7ea8bfa9efd238","sha256:99da3c51370c9e8ff7fa4edd0c82b98756f87d3ce540198c1fd375932bf720f7"],"state_sha256":"effdc9a129364702cbf4b8d8a076332c3dee49a954c6d31f4cb4e58d2fb6af6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C7x0oRitefAbwtqwJY7ZKwrVgLlm0b0g9YgBar44/JJPGnyk8vbegHYUHyPKZNHAw5Bkr+l5HIBERNeHIQ/xCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-24T04:09:56.011819Z","bundle_sha256":"ff30e7a7951295c26bf49a5a9108caeacfdd40f8f6959a71a433151edb1a8bf2"}}