{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:54CF5CI2SUFLMXHGQ7LAQJWMDO","short_pith_number":"pith:54CF5CI2","canonical_record":{"source":{"id":"math/9706222","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"1997-06-30T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"07cfb1fc03a0942e432cf2faba7c8a747dd574c6955477adf8ea06ed8e909638","abstract_canon_sha256":"c08566e13d3404fb8aef87f4956f72b8269d4cc80bdce2f82cdc4de56abeb564"},"schema_version":"1.0"},"canonical_sha256":"ef045e891a950ab65ce687d60826cc1b83d9b1fea2bde8a610dcba5b793f472d","source":{"kind":"arxiv","id":"math/9706222","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9706222","created_at":"2026-05-18T01:05:35Z"},{"alias_kind":"arxiv_version","alias_value":"math/9706222v1","created_at":"2026-05-18T01:05:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9706222","created_at":"2026-05-18T01:05:35Z"},{"alias_kind":"pith_short_12","alias_value":"54CF5CI2SUFL","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"54CF5CI2SUFLMXHG","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"54CF5CI2","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:54CF5CI2SUFLMXHGQ7LAQJWMDO","target":"record","payload":{"canonical_record":{"source":{"id":"math/9706222","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"1997-06-30T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"07cfb1fc03a0942e432cf2faba7c8a747dd574c6955477adf8ea06ed8e909638","abstract_canon_sha256":"c08566e13d3404fb8aef87f4956f72b8269d4cc80bdce2f82cdc4de56abeb564"},"schema_version":"1.0"},"canonical_sha256":"ef045e891a950ab65ce687d60826cc1b83d9b1fea2bde8a610dcba5b793f472d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:35.138809Z","signature_b64":"QtOyrhA+PDDiSqpsCxgq2xYNB71M5xC8CqkZALd/+/30/1GXuKueB7lGJsuQQ2qocnblEjvHU7YjONy0vSLeCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef045e891a950ab65ce687d60826cc1b83d9b1fea2bde8a610dcba5b793f472d","last_reissued_at":"2026-05-18T01:05:35.138097Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:35.138097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9706222","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":"2026-05-18T01:05:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fuaYfDOB4im7gTs4Y4F8Aq9byl8lFkf2ShIPt6igw0IgsL5E4K4wqcaS24izg5KTG53iTGl5SUXnkkDMAzNjDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T06:22:43.149249Z"},"content_sha256":"68f1c03e8fb2faca4c160d0f3b35f5839038a2de0dd92f24f111c13ba79969d2","schema_version":"1.0","event_id":"sha256:68f1c03e8fb2faca4c160d0f3b35f5839038a2de0dd92f24f111c13ba79969d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:54CF5CI2SUFLMXHGQ7LAQJWMDO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extension of incompressible surfaces on the boundary of 3-manifolds","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Hugh Howards, Michael Freedman, Ying-Qing Wu","submitted_at":"1997-06-30T00:00:00Z","abstract_excerpt":"An incompressible surface $F$ on the boundary of a compact orientable 3-manifold $M$ is arc-extendible if there is an arc $\\gamma$ on $\\partial M - $ Int $F$ such that $F \\cup N(\\gamma)$ is incompressible, where $N(\\gamma)$ is a regular neighborhood of $\\gamma$ in $\\partial M$. Suppose for simplicity that $M$ is irreducible, and $F$ has no disk components. If $M$ is a product $F\\times I$, or if $\\partial M - F$ is a set of annuli, then clearly $F$ is not arc-extendible. The main theorem of this paper shows that these are the only obstructions for $F$ to be arc-extendible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9706222","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":"2026-05-18T01:05:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ROHYPls1NboLtdDbe88hQJdNpgDvztMfW9QkpWESC165pOuYvWd61abk7cp1KONs1uXRtSvIE7D5FcR5BJJIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T06:22:43.149953Z"},"content_sha256":"e3715cf683e8c37a434bb284a8f15546a83ebde71fbffbc5485e7fde10580297","schema_version":"1.0","event_id":"sha256:e3715cf683e8c37a434bb284a8f15546a83ebde71fbffbc5485e7fde10580297"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/54CF5CI2SUFLMXHGQ7LAQJWMDO/bundle.json","state_url":"https://pith.science/pith/54CF5CI2SUFLMXHGQ7LAQJWMDO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/54CF5CI2SUFLMXHGQ7LAQJWMDO/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":"2026-05-24T06:22:43Z","links":{"resolver":"https://pith.science/pith/54CF5CI2SUFLMXHGQ7LAQJWMDO","bundle":"https://pith.science/pith/54CF5CI2SUFLMXHGQ7LAQJWMDO/bundle.json","state":"https://pith.science/pith/54CF5CI2SUFLMXHGQ7LAQJWMDO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/54CF5CI2SUFLMXHGQ7LAQJWMDO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:54CF5CI2SUFLMXHGQ7LAQJWMDO","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":"c08566e13d3404fb8aef87f4956f72b8269d4cc80bdce2f82cdc4de56abeb564","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"1997-06-30T00:00:00Z","title_canon_sha256":"07cfb1fc03a0942e432cf2faba7c8a747dd574c6955477adf8ea06ed8e909638"},"schema_version":"1.0","source":{"id":"math/9706222","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9706222","created_at":"2026-05-18T01:05:35Z"},{"alias_kind":"arxiv_version","alias_value":"math/9706222v1","created_at":"2026-05-18T01:05:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9706222","created_at":"2026-05-18T01:05:35Z"},{"alias_kind":"pith_short_12","alias_value":"54CF5CI2SUFL","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"54CF5CI2SUFLMXHG","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"54CF5CI2","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:e3715cf683e8c37a434bb284a8f15546a83ebde71fbffbc5485e7fde10580297","target":"graph","created_at":"2026-05-18T01:05:35Z","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 incompressible surface $F$ on the boundary of a compact orientable 3-manifold $M$ is arc-extendible if there is an arc $\\gamma$ on $\\partial M - $ Int $F$ such that $F \\cup N(\\gamma)$ is incompressible, where $N(\\gamma)$ is a regular neighborhood of $\\gamma$ in $\\partial M$. Suppose for simplicity that $M$ is irreducible, and $F$ has no disk components. If $M$ is a product $F\\times I$, or if $\\partial M - F$ is a set of annuli, then clearly $F$ is not arc-extendible. The main theorem of this paper shows that these are the only obstructions for $F$ to be arc-extendible.","authors_text":"Hugh Howards, Michael Freedman, Ying-Qing Wu","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"1997-06-30T00:00:00Z","title":"Extension of incompressible surfaces on the boundary of 3-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9706222","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":"sha256:68f1c03e8fb2faca4c160d0f3b35f5839038a2de0dd92f24f111c13ba79969d2","target":"record","created_at":"2026-05-18T01:05:35Z","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":"c08566e13d3404fb8aef87f4956f72b8269d4cc80bdce2f82cdc4de56abeb564","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"1997-06-30T00:00:00Z","title_canon_sha256":"07cfb1fc03a0942e432cf2faba7c8a747dd574c6955477adf8ea06ed8e909638"},"schema_version":"1.0","source":{"id":"math/9706222","kind":"arxiv","version":1}},"canonical_sha256":"ef045e891a950ab65ce687d60826cc1b83d9b1fea2bde8a610dcba5b793f472d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef045e891a950ab65ce687d60826cc1b83d9b1fea2bde8a610dcba5b793f472d","first_computed_at":"2026-05-18T01:05:35.138097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:35.138097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QtOyrhA+PDDiSqpsCxgq2xYNB71M5xC8CqkZALd/+/30/1GXuKueB7lGJsuQQ2qocnblEjvHU7YjONy0vSLeCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:35.138809Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9706222","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68f1c03e8fb2faca4c160d0f3b35f5839038a2de0dd92f24f111c13ba79969d2","sha256:e3715cf683e8c37a434bb284a8f15546a83ebde71fbffbc5485e7fde10580297"],"state_sha256":"a43ab276c718f525f1e6acb8ca442ebbbda8a3eea001ef121373d0a8113f24c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/AE4f3+Nd5qv5tUQXkI/AThPDIu/tEi1RqYTtZGxjsUVBtQ0ZLlWXopFyoZ6SCoBJLnCFGqAnR5hlH3lL9rMCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T06:22:43.153572Z","bundle_sha256":"3771b3d063dbdef7f6c7beacbae9353ce3e837d633ef091854da37e50a6bae01"}}