{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HLRFT43JMHAZQTO5UIDCHDCWLY","short_pith_number":"pith:HLRFT43J","canonical_record":{"source":{"id":"1803.05116","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-14T02:56:23Z","cross_cats_sorted":[],"title_canon_sha256":"53f56a3550e714654555f18154471c37bc2cd2cbd21bf544d413f68cbca44a34","abstract_canon_sha256":"18b0ed1d9f97cab7730f1667007216983d3eec9b18284701fd5a25bc1f502ec7"},"schema_version":"1.0"},"canonical_sha256":"3ae259f36961c1984ddda206238c565e34457b954bfa9b882940aa258ef74de1","source":{"kind":"arxiv","id":"1803.05116","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05116","created_at":"2026-05-17T23:47:44Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05116v3","created_at":"2026-05-17T23:47:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05116","created_at":"2026-05-17T23:47:44Z"},{"alias_kind":"pith_short_12","alias_value":"HLRFT43JMHAZ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HLRFT43JMHAZQTO5","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HLRFT43J","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HLRFT43JMHAZQTO5UIDCHDCWLY","target":"record","payload":{"canonical_record":{"source":{"id":"1803.05116","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-14T02:56:23Z","cross_cats_sorted":[],"title_canon_sha256":"53f56a3550e714654555f18154471c37bc2cd2cbd21bf544d413f68cbca44a34","abstract_canon_sha256":"18b0ed1d9f97cab7730f1667007216983d3eec9b18284701fd5a25bc1f502ec7"},"schema_version":"1.0"},"canonical_sha256":"3ae259f36961c1984ddda206238c565e34457b954bfa9b882940aa258ef74de1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:44.355223Z","signature_b64":"53Hp0c9QEt14vr3sJjx33t7WpCU2PGzCJ/Z1MHnSrFZqG8X5HwM1jXGKLGOJLUGHB4HiubtyWOCqU6V97xgQDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ae259f36961c1984ddda206238c565e34457b954bfa9b882940aa258ef74de1","last_reissued_at":"2026-05-17T23:47:44.354765Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:44.354765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.05116","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":"2026-05-17T23:47:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BUsEce78Im/HOvWV6onLCsHP6paPRDnTdqyShpNnUaiH4BUgMDOdLr7/MfKiTsgJsgvOixr/D0dEeus0lSu7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:55:33.250763Z"},"content_sha256":"1a022ad75de07f8641990a4c4da8a65975198f0740d06598c3d3259927fb85f2","schema_version":"1.0","event_id":"sha256:1a022ad75de07f8641990a4c4da8a65975198f0740d06598c3d3259927fb85f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HLRFT43JMHAZQTO5UIDCHDCWLY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extending automorphisms of the genus-2 surface over the 3-sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kenta Funayoshi, Yuya Koda","submitted_at":"2018-03-14T02:56:23Z","abstract_excerpt":"An automorphism $f$ of a closed orientable surface $\\Sigma$ is said to be extendable over the 3-sphere $S^3$ if $f$ extends to an automorphism of the pair $(S^3, \\Sigma)$ with respect to some embedding $\\Sigma \\hookrightarrow S^3$. We prove that if an automorphism of a genus-2 surface $\\Sigma$ is extendable over $S^3$, then $f$ extends to an automorphism of the pair $(S^3, \\Sigma)$ with respect to an embedding $\\Sigma \\hookrightarrow S^3$ such that $\\Sigma$ bounds genus-2 handlebodies on both sides. The classification of essential annuli in the exterior of genus-2 handlebodies embedded in $S^3"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05116","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":""},"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":"2026-05-17T23:47:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kDraDgX9p2ylsP60ry62b632nFYqF+IhCsjxknh+S42FWd5VAWtfdZf/viJkyOTBRaIeDfCy25F9JPzigzEOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:55:33.251108Z"},"content_sha256":"468357947c3d8bb12eaabe623f5b04206d56405898be8318c33f12639644b740","schema_version":"1.0","event_id":"sha256:468357947c3d8bb12eaabe623f5b04206d56405898be8318c33f12639644b740"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HLRFT43JMHAZQTO5UIDCHDCWLY/bundle.json","state_url":"https://pith.science/pith/HLRFT43JMHAZQTO5UIDCHDCWLY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HLRFT43JMHAZQTO5UIDCHDCWLY/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":"2026-06-20T04:55:33Z","links":{"resolver":"https://pith.science/pith/HLRFT43JMHAZQTO5UIDCHDCWLY","bundle":"https://pith.science/pith/HLRFT43JMHAZQTO5UIDCHDCWLY/bundle.json","state":"https://pith.science/pith/HLRFT43JMHAZQTO5UIDCHDCWLY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HLRFT43JMHAZQTO5UIDCHDCWLY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HLRFT43JMHAZQTO5UIDCHDCWLY","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":"18b0ed1d9f97cab7730f1667007216983d3eec9b18284701fd5a25bc1f502ec7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-14T02:56:23Z","title_canon_sha256":"53f56a3550e714654555f18154471c37bc2cd2cbd21bf544d413f68cbca44a34"},"schema_version":"1.0","source":{"id":"1803.05116","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05116","created_at":"2026-05-17T23:47:44Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05116v3","created_at":"2026-05-17T23:47:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05116","created_at":"2026-05-17T23:47:44Z"},{"alias_kind":"pith_short_12","alias_value":"HLRFT43JMHAZ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HLRFT43JMHAZQTO5","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HLRFT43J","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:468357947c3d8bb12eaabe623f5b04206d56405898be8318c33f12639644b740","target":"graph","created_at":"2026-05-17T23:47:44Z","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":"An automorphism $f$ of a closed orientable surface $\\Sigma$ is said to be extendable over the 3-sphere $S^3$ if $f$ extends to an automorphism of the pair $(S^3, \\Sigma)$ with respect to some embedding $\\Sigma \\hookrightarrow S^3$. We prove that if an automorphism of a genus-2 surface $\\Sigma$ is extendable over $S^3$, then $f$ extends to an automorphism of the pair $(S^3, \\Sigma)$ with respect to an embedding $\\Sigma \\hookrightarrow S^3$ such that $\\Sigma$ bounds genus-2 handlebodies on both sides. The classification of essential annuli in the exterior of genus-2 handlebodies embedded in $S^3","authors_text":"Kenta Funayoshi, Yuya Koda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-14T02:56:23Z","title":"Extending automorphisms of the genus-2 surface over the 3-sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05116","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":"sha256:1a022ad75de07f8641990a4c4da8a65975198f0740d06598c3d3259927fb85f2","target":"record","created_at":"2026-05-17T23:47:44Z","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":"18b0ed1d9f97cab7730f1667007216983d3eec9b18284701fd5a25bc1f502ec7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-14T02:56:23Z","title_canon_sha256":"53f56a3550e714654555f18154471c37bc2cd2cbd21bf544d413f68cbca44a34"},"schema_version":"1.0","source":{"id":"1803.05116","kind":"arxiv","version":3}},"canonical_sha256":"3ae259f36961c1984ddda206238c565e34457b954bfa9b882940aa258ef74de1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ae259f36961c1984ddda206238c565e34457b954bfa9b882940aa258ef74de1","first_computed_at":"2026-05-17T23:47:44.354765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:44.354765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"53Hp0c9QEt14vr3sJjx33t7WpCU2PGzCJ/Z1MHnSrFZqG8X5HwM1jXGKLGOJLUGHB4HiubtyWOCqU6V97xgQDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:44.355223Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.05116","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a022ad75de07f8641990a4c4da8a65975198f0740d06598c3d3259927fb85f2","sha256:468357947c3d8bb12eaabe623f5b04206d56405898be8318c33f12639644b740"],"state_sha256":"517a7e62f1ae59976b65c432230e49bb650f15de94ec4d2b2c31df97f2ec8c1a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qjXFBCCZ8qvrPvyJjCUjclfDPvVRHYWKLiedRdGGIWN/1rREvlWm9N6ZcvhivMp6OaFrggAwmmlGwmRwRKrfBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T04:55:33.253008Z","bundle_sha256":"342ccbd07a75b90cbfd73b7b90bf4085cbc9bd662e5a2d6cac1a89699752bc86"}}