{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:7CJL324IALMQJDGA4UP3IDH6UZ","short_pith_number":"pith:7CJL324I","canonical_record":{"source":{"id":"math/0604358","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2006-04-16T20:29:43Z","cross_cats_sorted":[],"title_canon_sha256":"19bc645f3dbb2086433850eaffc8600d0df5a50b06c9f459fe7f8655b8fafc1b","abstract_canon_sha256":"2db8413d2f0057464c7f8535c34d9ac103aa1f4584b793e134350b2ef3092433"},"schema_version":"1.0"},"canonical_sha256":"f892bdeb8802d9048cc0e51fb40cfea642a9c92a7309078eb5b966e97c885c05","source":{"kind":"arxiv","id":"math/0604358","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0604358","created_at":"2026-07-04T15:41:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0604358v2","created_at":"2026-07-04T15:41:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0604358","created_at":"2026-07-04T15:41:38Z"},{"alias_kind":"pith_short_12","alias_value":"7CJL324IALMQ","created_at":"2026-07-04T15:41:38Z"},{"alias_kind":"pith_short_16","alias_value":"7CJL324IALMQJDGA","created_at":"2026-07-04T15:41:38Z"},{"alias_kind":"pith_short_8","alias_value":"7CJL324I","created_at":"2026-07-04T15:41:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:7CJL324IALMQJDGA4UP3IDH6UZ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0604358","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2006-04-16T20:29:43Z","cross_cats_sorted":[],"title_canon_sha256":"19bc645f3dbb2086433850eaffc8600d0df5a50b06c9f459fe7f8655b8fafc1b","abstract_canon_sha256":"2db8413d2f0057464c7f8535c34d9ac103aa1f4584b793e134350b2ef3092433"},"schema_version":"1.0"},"canonical_sha256":"f892bdeb8802d9048cc0e51fb40cfea642a9c92a7309078eb5b966e97c885c05","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:41:38.975716Z","signature_b64":"AiGbJNjB73XOUaVY4EzgzSqZAR59QDuRNyH9lDLf1gR4wfgCdVPERAqZj6/8FEZI2ly4kxUtMbRCAuKjkVG+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f892bdeb8802d9048cc0e51fb40cfea642a9c92a7309078eb5b966e97c885c05","last_reissued_at":"2026-07-04T15:41:38.975339Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:41:38.975339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0604358","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:41:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xBHqQeirIbUgfinokavlYveWu9n5eyfjRCrqQ1iY4J/jiChXrotydyAoUw/fcNbuDhWYbuBv1SIn0Nd10WTGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T07:36:17.806658Z"},"content_sha256":"30a8e30873822f63057bb21f622b80fc77f011adec44a4b8ac5e105e9d1f4d80","schema_version":"1.0","event_id":"sha256:30a8e30873822f63057bb21f622b80fc77f011adec44a4b8ac5e105e9d1f4d80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:7CJL324IALMQJDGA4UP3IDH6UZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homeomorphisms which are Dehn twists on the boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Darryl McCullough","submitted_at":"2006-04-16T20:29:43Z","abstract_excerpt":"A homeomorphism of a 3-manifold M is said to be Dehn twists on the boundary when its restriction to the boundary of M is isotopic to the identity on the complement of a collection of disjoint simple closed curves in the boundary of M. In this paper, we give various results about such collections of curves and the associated homeomorphisms. In particular, if M is compact, orientable, irreducible and the boundary of M is a single torus, and M admits a homeomorphism which is a nontrivial Dehn twist on the boundary of M, then M must be a solid torus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604358","kind":"arxiv","version":2},"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/math/0604358/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":"2026-07-04T15:41:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mlSZLo8TobaukT1cRdIHZC4jRz7qmIN3EvuD9n9lmK3WGyuI25GYV6P7AuYPR6A17+QrWX3dE48vPrBWmcLTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T07:36:17.807036Z"},"content_sha256":"3f4b153184d9dfd2c3e41cb59dfd1b4e40eafaf15add068a277f98012242737e","schema_version":"1.0","event_id":"sha256:3f4b153184d9dfd2c3e41cb59dfd1b4e40eafaf15add068a277f98012242737e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7CJL324IALMQJDGA4UP3IDH6UZ/bundle.json","state_url":"https://pith.science/pith/7CJL324IALMQJDGA4UP3IDH6UZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7CJL324IALMQJDGA4UP3IDH6UZ/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":"2026-08-04T07:36:17Z","links":{"resolver":"https://pith.science/pith/7CJL324IALMQJDGA4UP3IDH6UZ","bundle":"https://pith.science/pith/7CJL324IALMQJDGA4UP3IDH6UZ/bundle.json","state":"https://pith.science/pith/7CJL324IALMQJDGA4UP3IDH6UZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7CJL324IALMQJDGA4UP3IDH6UZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:7CJL324IALMQJDGA4UP3IDH6UZ","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":"2db8413d2f0057464c7f8535c34d9ac103aa1f4584b793e134350b2ef3092433","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2006-04-16T20:29:43Z","title_canon_sha256":"19bc645f3dbb2086433850eaffc8600d0df5a50b06c9f459fe7f8655b8fafc1b"},"schema_version":"1.0","source":{"id":"math/0604358","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0604358","created_at":"2026-07-04T15:41:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0604358v2","created_at":"2026-07-04T15:41:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0604358","created_at":"2026-07-04T15:41:38Z"},{"alias_kind":"pith_short_12","alias_value":"7CJL324IALMQ","created_at":"2026-07-04T15:41:38Z"},{"alias_kind":"pith_short_16","alias_value":"7CJL324IALMQJDGA","created_at":"2026-07-04T15:41:38Z"},{"alias_kind":"pith_short_8","alias_value":"7CJL324I","created_at":"2026-07-04T15:41:38Z"}],"graph_snapshots":[{"event_id":"sha256:3f4b153184d9dfd2c3e41cb59dfd1b4e40eafaf15add068a277f98012242737e","target":"graph","created_at":"2026-07-04T15:41:38Z","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/math/0604358/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A homeomorphism of a 3-manifold M is said to be Dehn twists on the boundary when its restriction to the boundary of M is isotopic to the identity on the complement of a collection of disjoint simple closed curves in the boundary of M. In this paper, we give various results about such collections of curves and the associated homeomorphisms. In particular, if M is compact, orientable, irreducible and the boundary of M is a single torus, and M admits a homeomorphism which is a nontrivial Dehn twist on the boundary of M, then M must be a solid torus.","authors_text":"Darryl McCullough","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2006-04-16T20:29:43Z","title":"Homeomorphisms which are Dehn twists on the boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604358","kind":"arxiv","version":2},"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":"sha256:30a8e30873822f63057bb21f622b80fc77f011adec44a4b8ac5e105e9d1f4d80","target":"record","created_at":"2026-07-04T15:41:38Z","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":"2db8413d2f0057464c7f8535c34d9ac103aa1f4584b793e134350b2ef3092433","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2006-04-16T20:29:43Z","title_canon_sha256":"19bc645f3dbb2086433850eaffc8600d0df5a50b06c9f459fe7f8655b8fafc1b"},"schema_version":"1.0","source":{"id":"math/0604358","kind":"arxiv","version":2}},"canonical_sha256":"f892bdeb8802d9048cc0e51fb40cfea642a9c92a7309078eb5b966e97c885c05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f892bdeb8802d9048cc0e51fb40cfea642a9c92a7309078eb5b966e97c885c05","first_computed_at":"2026-07-04T15:41:38.975339Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:41:38.975339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AiGbJNjB73XOUaVY4EzgzSqZAR59QDuRNyH9lDLf1gR4wfgCdVPERAqZj6/8FEZI2ly4kxUtMbRCAuKjkVG+BQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:41:38.975716Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0604358","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30a8e30873822f63057bb21f622b80fc77f011adec44a4b8ac5e105e9d1f4d80","sha256:3f4b153184d9dfd2c3e41cb59dfd1b4e40eafaf15add068a277f98012242737e"],"state_sha256":"cc4a41020dc5d81505b9f7e4c737a3889f66c133953c0498fd397794ff407328"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qU3ccX/YX87mEJ8aX/Jl7iqUz2QpWFsXtYohqbv8uU7vKuYfEI3sBFIY/nzqvCJJ+2Q+nVe+BZW/z8WDJZoIAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T07:36:17.809784Z","bundle_sha256":"cdd921e3fa11dfbeac5d47b3b6f9b1677c106255913e560442ea34e60c1c0250"}}