{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:MEABW37VDINVE4N65AOGCHY775","short_pith_number":"pith:MEABW37V","canonical_record":{"source":{"id":"2105.08904","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-05-19T03:35:27Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"ea3a4412c1a16d79bfef22dfba8f20546e6c6edc92283201889c1d487331f76c","abstract_canon_sha256":"9b149493662026c843e7158f69100dd56d7d77f3568375e95b3a44b9af80cdd7"},"schema_version":"1.0"},"canonical_sha256":"61001b6ff51a1b5271bee81c611f1fff402a9ea07b21c3d7bfa9c503e0d55c59","source":{"kind":"arxiv","id":"2105.08904","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.08904","created_at":"2026-07-05T09:52:06Z"},{"alias_kind":"arxiv_version","alias_value":"2105.08904v3","created_at":"2026-07-05T09:52:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.08904","created_at":"2026-07-05T09:52:06Z"},{"alias_kind":"pith_short_12","alias_value":"MEABW37VDINV","created_at":"2026-07-05T09:52:06Z"},{"alias_kind":"pith_short_16","alias_value":"MEABW37VDINVE4N6","created_at":"2026-07-05T09:52:06Z"},{"alias_kind":"pith_short_8","alias_value":"MEABW37V","created_at":"2026-07-05T09:52:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:MEABW37VDINVE4N65AOGCHY775","target":"record","payload":{"canonical_record":{"source":{"id":"2105.08904","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-05-19T03:35:27Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"ea3a4412c1a16d79bfef22dfba8f20546e6c6edc92283201889c1d487331f76c","abstract_canon_sha256":"9b149493662026c843e7158f69100dd56d7d77f3568375e95b3a44b9af80cdd7"},"schema_version":"1.0"},"canonical_sha256":"61001b6ff51a1b5271bee81c611f1fff402a9ea07b21c3d7bfa9c503e0d55c59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:52:06.181001Z","signature_b64":"U4yvHtnsrBo7hBi4z+vbjNqHZDFks6RCjX6MqhHf5aFAwYGAgVoMsFBfYWfFChMyBhwRvKBeC7YCghxXOF69Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61001b6ff51a1b5271bee81c611f1fff402a9ea07b21c3d7bfa9c503e0d55c59","last_reissued_at":"2026-07-05T09:52:06.180657Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:52:06.180657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.08904","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":"2026-07-05T09:52:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DW+hjDFMlyPw7Aopa3334v0UykocD7Lvk/twblsxddjl3MH54pVmUUHDa0TRg9TZj93CiBIx55MY46h7eLpUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:02:11.678665Z"},"content_sha256":"3339fadd144202da02362928a2963564dde9eebfb3baba92948268c308e87eeb","schema_version":"1.0","event_id":"sha256:3339fadd144202da02362928a2963564dde9eebfb3baba92948268c308e87eeb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:MEABW37VDINVE4N65AOGCHY775","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Torelli groups and Dehn twists of smooth 4-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Alexander Kupers, Manuel Krannich","submitted_at":"2021-05-19T03:35:27Z","abstract_excerpt":"This note has two related but independent parts. Firstly, we prove a generalisation of a recent result of Gay on the smooth mapping class group of $S^4$. Secondly, we give an alternative proof of a consequence of work of Saeki, namely that the Dehn twist along the boundary sphere of a simply-connected closed smooth $4$-manifold $X$ with $\\partial X\\cong S^3$ is trivial after taking connected sums with enough copies of $S^2\\times S^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.08904","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2105.08904/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":"2026-07-05T09:52:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gs8Pvp3gR0WxW0gTFn8gTM/sVIkpe3m5UpLf6HaDkYdgdRIMO+1DR8htCI8+Mxfk60grw5IgPyjnOala+JXpBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:02:11.679170Z"},"content_sha256":"6ced222dbc6020131d71700dc56e9c0b160ac930600f0a92567ff0709047dfab","schema_version":"1.0","event_id":"sha256:6ced222dbc6020131d71700dc56e9c0b160ac930600f0a92567ff0709047dfab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MEABW37VDINVE4N65AOGCHY775/bundle.json","state_url":"https://pith.science/pith/MEABW37VDINVE4N65AOGCHY775/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MEABW37VDINVE4N65AOGCHY775/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":"2026-07-07T13:02:11Z","links":{"resolver":"https://pith.science/pith/MEABW37VDINVE4N65AOGCHY775","bundle":"https://pith.science/pith/MEABW37VDINVE4N65AOGCHY775/bundle.json","state":"https://pith.science/pith/MEABW37VDINVE4N65AOGCHY775/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MEABW37VDINVE4N65AOGCHY775/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:MEABW37VDINVE4N65AOGCHY775","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":"9b149493662026c843e7158f69100dd56d7d77f3568375e95b3a44b9af80cdd7","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-05-19T03:35:27Z","title_canon_sha256":"ea3a4412c1a16d79bfef22dfba8f20546e6c6edc92283201889c1d487331f76c"},"schema_version":"1.0","source":{"id":"2105.08904","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.08904","created_at":"2026-07-05T09:52:06Z"},{"alias_kind":"arxiv_version","alias_value":"2105.08904v3","created_at":"2026-07-05T09:52:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.08904","created_at":"2026-07-05T09:52:06Z"},{"alias_kind":"pith_short_12","alias_value":"MEABW37VDINV","created_at":"2026-07-05T09:52:06Z"},{"alias_kind":"pith_short_16","alias_value":"MEABW37VDINVE4N6","created_at":"2026-07-05T09:52:06Z"},{"alias_kind":"pith_short_8","alias_value":"MEABW37V","created_at":"2026-07-05T09:52:06Z"}],"graph_snapshots":[{"event_id":"sha256:6ced222dbc6020131d71700dc56e9c0b160ac930600f0a92567ff0709047dfab","target":"graph","created_at":"2026-07-05T09:52:06Z","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/2105.08904/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This note has two related but independent parts. Firstly, we prove a generalisation of a recent result of Gay on the smooth mapping class group of $S^4$. Secondly, we give an alternative proof of a consequence of work of Saeki, namely that the Dehn twist along the boundary sphere of a simply-connected closed smooth $4$-manifold $X$ with $\\partial X\\cong S^3$ is trivial after taking connected sums with enough copies of $S^2\\times S^2$.","authors_text":"Alexander Kupers, Manuel Krannich","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-05-19T03:35:27Z","title":"On Torelli groups and Dehn twists of smooth 4-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.08904","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":"sha256:3339fadd144202da02362928a2963564dde9eebfb3baba92948268c308e87eeb","target":"record","created_at":"2026-07-05T09:52:06Z","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":"9b149493662026c843e7158f69100dd56d7d77f3568375e95b3a44b9af80cdd7","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2021-05-19T03:35:27Z","title_canon_sha256":"ea3a4412c1a16d79bfef22dfba8f20546e6c6edc92283201889c1d487331f76c"},"schema_version":"1.0","source":{"id":"2105.08904","kind":"arxiv","version":3}},"canonical_sha256":"61001b6ff51a1b5271bee81c611f1fff402a9ea07b21c3d7bfa9c503e0d55c59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61001b6ff51a1b5271bee81c611f1fff402a9ea07b21c3d7bfa9c503e0d55c59","first_computed_at":"2026-07-05T09:52:06.180657Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:52:06.180657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U4yvHtnsrBo7hBi4z+vbjNqHZDFks6RCjX6MqhHf5aFAwYGAgVoMsFBfYWfFChMyBhwRvKBeC7YCghxXOF69Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:52:06.181001Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.08904","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3339fadd144202da02362928a2963564dde9eebfb3baba92948268c308e87eeb","sha256:6ced222dbc6020131d71700dc56e9c0b160ac930600f0a92567ff0709047dfab"],"state_sha256":"07539cbd58df27644b2134e1c7165ce404b94457b92c3042184d52520559c76b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6sRHRAenBZ8vJyTWmtCu7BKPdlEdq0e1wjMF4H4E6bE+dyoFaXeIBaJWNVRwwypS4jRZXTls1Vyls4R5q1EiBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T13:02:11.682454Z","bundle_sha256":"c1b7e04a9ab132dbc5034b6f63bcc09fac6183ff081fc2730b18fe875f828a3e"}}