{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:L5I3W35LJRV53AU5EUSYCMELRI","short_pith_number":"pith:L5I3W35L","canonical_record":{"source":{"id":"1302.0972","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-05T09:34:45Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"7629c396837da1b8c90770ce1bd742da8fecd252bb8ea31cd816020ce4710a62","abstract_canon_sha256":"eac198f0b8cd2b0ed918b397539df54f5310293a985663aa9811039d2ecb47bc"},"schema_version":"1.0"},"canonical_sha256":"5f51bb6fab4c6bdd829d252581308b8a3cfd917644e9dd49332e4e2a9d46cd50","source":{"kind":"arxiv","id":"1302.0972","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0972","created_at":"2026-05-18T03:34:26Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0972v1","created_at":"2026-05-18T03:34:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0972","created_at":"2026-05-18T03:34:26Z"},{"alias_kind":"pith_short_12","alias_value":"L5I3W35LJRV5","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"L5I3W35LJRV53AU5","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"L5I3W35L","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:L5I3W35LJRV53AU5EUSYCMELRI","target":"record","payload":{"canonical_record":{"source":{"id":"1302.0972","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-05T09:34:45Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"7629c396837da1b8c90770ce1bd742da8fecd252bb8ea31cd816020ce4710a62","abstract_canon_sha256":"eac198f0b8cd2b0ed918b397539df54f5310293a985663aa9811039d2ecb47bc"},"schema_version":"1.0"},"canonical_sha256":"5f51bb6fab4c6bdd829d252581308b8a3cfd917644e9dd49332e4e2a9d46cd50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:26.608283Z","signature_b64":"lxast3lkNrmw1GTXUdMCuoarT/zHUgWEtefxZwPHRnC6/PZf4aeDXXaA2VlfkFBNngV/yzf+Dm397Ajxk6pADw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f51bb6fab4c6bdd829d252581308b8a3cfd917644e9dd49332e4e2a9d46cd50","last_reissued_at":"2026-05-18T03:34:26.607514Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:26.607514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.0972","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:34:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TsCMY3D/dpGTnnXB4HOLBnWtN0/IE1d2vyTXnsYIoHtgg7nI5+8+Z3xcedGn87GO/hNEygZKRngPmnSno4s9AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T06:39:53.114104Z"},"content_sha256":"e455bba9099de8fe955f20c6e09b2f33a5e3e605e8de882aba4bae9ec1420f79","schema_version":"1.0","event_id":"sha256:e455bba9099de8fe955f20c6e09b2f33a5e3e605e8de882aba4bae9ec1420f79"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:L5I3W35LJRV53AU5EUSYCMELRI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Embedding periodic maps on surfaces into those on $S^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Chao Wang, Shicheng Wang, Yimu Zhang, Yu Guo","submitted_at":"2013-02-05T09:34:45Z","abstract_excerpt":"Call a periodic map $h$ on the closed orientable surface $\\Sigma_g$ extendable if $h$ extends to a periodic map over the pair $(S^3, \\Sigma_g)$ for possible embeddings $e: \\Sigma_g\\to S^3$.\n  We determine the extendabilities for all periodical maps on $\\Sigma_2$. The results involve various orientation preserving/reversing behalves of the periodical maps on the pair $(S^3, \\Sigma_g)$. To do this we first list all periodic maps on $\\Sigma_2$, and indeed we exhibit each of them as a composition of primary and explicit symmetries, like rotations, reflections and antipodal maps, which itself shoul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0972","kind":"arxiv","version":1},"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":"2026-05-18T03:34:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DqD6KJmXZT0bHARhEKt2ODJB/+J1jGOk9PpekdHnqYyFRGWRFP8Qfi70l36Q6RuasE9xpOCmQsAcy9J9ANf3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T06:39:53.114753Z"},"content_sha256":"043687f142be99ec8e88a506bda47a7bdefc0a9337d773f9b0d0336698c44d8e","schema_version":"1.0","event_id":"sha256:043687f142be99ec8e88a506bda47a7bdefc0a9337d773f9b0d0336698c44d8e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L5I3W35LJRV53AU5EUSYCMELRI/bundle.json","state_url":"https://pith.science/pith/L5I3W35LJRV53AU5EUSYCMELRI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L5I3W35LJRV53AU5EUSYCMELRI/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":"2026-05-25T06:39:53Z","links":{"resolver":"https://pith.science/pith/L5I3W35LJRV53AU5EUSYCMELRI","bundle":"https://pith.science/pith/L5I3W35LJRV53AU5EUSYCMELRI/bundle.json","state":"https://pith.science/pith/L5I3W35LJRV53AU5EUSYCMELRI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L5I3W35LJRV53AU5EUSYCMELRI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:L5I3W35LJRV53AU5EUSYCMELRI","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":"eac198f0b8cd2b0ed918b397539df54f5310293a985663aa9811039d2ecb47bc","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-05T09:34:45Z","title_canon_sha256":"7629c396837da1b8c90770ce1bd742da8fecd252bb8ea31cd816020ce4710a62"},"schema_version":"1.0","source":{"id":"1302.0972","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0972","created_at":"2026-05-18T03:34:26Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0972v1","created_at":"2026-05-18T03:34:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0972","created_at":"2026-05-18T03:34:26Z"},{"alias_kind":"pith_short_12","alias_value":"L5I3W35LJRV5","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"L5I3W35LJRV53AU5","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"L5I3W35L","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:043687f142be99ec8e88a506bda47a7bdefc0a9337d773f9b0d0336698c44d8e","target":"graph","created_at":"2026-05-18T03:34:26Z","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":"Call a periodic map $h$ on the closed orientable surface $\\Sigma_g$ extendable if $h$ extends to a periodic map over the pair $(S^3, \\Sigma_g)$ for possible embeddings $e: \\Sigma_g\\to S^3$.\n  We determine the extendabilities for all periodical maps on $\\Sigma_2$. The results involve various orientation preserving/reversing behalves of the periodical maps on the pair $(S^3, \\Sigma_g)$. To do this we first list all periodic maps on $\\Sigma_2$, and indeed we exhibit each of them as a composition of primary and explicit symmetries, like rotations, reflections and antipodal maps, which itself shoul","authors_text":"Chao Wang, Shicheng Wang, Yimu Zhang, Yu Guo","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-05T09:34:45Z","title":"Embedding periodic maps on surfaces into those on $S^3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0972","kind":"arxiv","version":1},"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:e455bba9099de8fe955f20c6e09b2f33a5e3e605e8de882aba4bae9ec1420f79","target":"record","created_at":"2026-05-18T03:34:26Z","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":"eac198f0b8cd2b0ed918b397539df54f5310293a985663aa9811039d2ecb47bc","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-05T09:34:45Z","title_canon_sha256":"7629c396837da1b8c90770ce1bd742da8fecd252bb8ea31cd816020ce4710a62"},"schema_version":"1.0","source":{"id":"1302.0972","kind":"arxiv","version":1}},"canonical_sha256":"5f51bb6fab4c6bdd829d252581308b8a3cfd917644e9dd49332e4e2a9d46cd50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f51bb6fab4c6bdd829d252581308b8a3cfd917644e9dd49332e4e2a9d46cd50","first_computed_at":"2026-05-18T03:34:26.607514Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:26.607514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lxast3lkNrmw1GTXUdMCuoarT/zHUgWEtefxZwPHRnC6/PZf4aeDXXaA2VlfkFBNngV/yzf+Dm397Ajxk6pADw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:26.608283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0972","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e455bba9099de8fe955f20c6e09b2f33a5e3e605e8de882aba4bae9ec1420f79","sha256:043687f142be99ec8e88a506bda47a7bdefc0a9337d773f9b0d0336698c44d8e"],"state_sha256":"869c9b54664d61403a3bc0e91d33fd6fa02acf45c0a73b28099663961b2c8d0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z058GloqturXGBYd6SlmserWt0fLG/SDkfkvBQQneeVSBG7pAQ44SBg+9kPttjIrQ9rWUoLEtuGP/3uQOSYuBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T06:39:53.118176Z","bundle_sha256":"711102aa8cff90b36df785e0d9d2c7d73d951d6d33b8803f2432f747f70979d8"}}