{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:PFANUEHZFBNAHWLWGQJCLWREDH","short_pith_number":"pith:PFANUEHZ","canonical_record":{"source":{"id":"1007.3606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-07-21T10:29:38Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"066a57d00d10a35260e1a9184a0eda884de7591a2656b9c581527b7925475cf6","abstract_canon_sha256":"1ab9e4f02ab69356c508df117ca7b060eb9471938755b38e3d9be9e5f907789e"},"schema_version":"1.0"},"canonical_sha256":"7940da10f9285a03d976341225da2419e3f4cdbe7311a4197007d0478ac60fac","source":{"kind":"arxiv","id":"1007.3606","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.3606","created_at":"2026-05-17T23:51:50Z"},{"alias_kind":"arxiv_version","alias_value":"1007.3606v1","created_at":"2026-05-17T23:51:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3606","created_at":"2026-05-17T23:51:50Z"},{"alias_kind":"pith_short_12","alias_value":"PFANUEHZFBNA","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PFANUEHZFBNAHWLW","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PFANUEHZ","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:PFANUEHZFBNAHWLWGQJCLWREDH","target":"record","payload":{"canonical_record":{"source":{"id":"1007.3606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-07-21T10:29:38Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"066a57d00d10a35260e1a9184a0eda884de7591a2656b9c581527b7925475cf6","abstract_canon_sha256":"1ab9e4f02ab69356c508df117ca7b060eb9471938755b38e3d9be9e5f907789e"},"schema_version":"1.0"},"canonical_sha256":"7940da10f9285a03d976341225da2419e3f4cdbe7311a4197007d0478ac60fac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:50.054079Z","signature_b64":"61SF9UzFUHBkVErmV4pX7w1X7utRmaSNld28FwR8qgVau6DBzKeiFIi0HZc5XEP9TgIdqacYoE3QLc3XOTeICA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7940da10f9285a03d976341225da2419e3f4cdbe7311a4197007d0478ac60fac","last_reissued_at":"2026-05-17T23:51:50.053352Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:50.053352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.3606","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":"2026-05-17T23:51:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s5jOcs1Kf3yGVUze2HsSPqmtHX+D4KmxHY9cL0OLD/qntFJRQFidlA/AvZ9O25iELSWDxW8eAdid3AMl1tS+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:38:33.926491Z"},"content_sha256":"48d5802431db49d556b47c563076481d3475b236750b23f495eb4229087436b8","schema_version":"1.0","event_id":"sha256:48d5802431db49d556b47c563076481d3475b236750b23f495eb4229087436b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:PFANUEHZFBNAHWLWGQJCLWREDH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eliashberg's proof of Cerf's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Hansj\\\"org Geiges, Kai Zehmisch","submitted_at":"2010-07-21T10:29:38Z","abstract_excerpt":"Following a line of reasoning suggested by Eliashberg, we prove Cerf's theorem that any diffeomorphism of the 3-sphere extends over the 4-ball. To this end we develop a moduli-theoretic version of Eliashberg's filling-with-holomorphic-discs method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3606","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":"2026-05-17T23:51:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XP/mMFAzTkyz/+NPDQ4peiFOU8EbPhjgnTpnDBQygz+7D0QC8KJyybK8tKyyhvVLGoihNkFPMD7/D+Aw97CoBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:38:33.926826Z"},"content_sha256":"4f8e159daf2e10c20c31142c03f26d06bff67d5cab133cede771c9e86c9888a9","schema_version":"1.0","event_id":"sha256:4f8e159daf2e10c20c31142c03f26d06bff67d5cab133cede771c9e86c9888a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PFANUEHZFBNAHWLWGQJCLWREDH/bundle.json","state_url":"https://pith.science/pith/PFANUEHZFBNAHWLWGQJCLWREDH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PFANUEHZFBNAHWLWGQJCLWREDH/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":"2026-06-21T23:38:33Z","links":{"resolver":"https://pith.science/pith/PFANUEHZFBNAHWLWGQJCLWREDH","bundle":"https://pith.science/pith/PFANUEHZFBNAHWLWGQJCLWREDH/bundle.json","state":"https://pith.science/pith/PFANUEHZFBNAHWLWGQJCLWREDH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PFANUEHZFBNAHWLWGQJCLWREDH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PFANUEHZFBNAHWLWGQJCLWREDH","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":"1ab9e4f02ab69356c508df117ca7b060eb9471938755b38e3d9be9e5f907789e","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-07-21T10:29:38Z","title_canon_sha256":"066a57d00d10a35260e1a9184a0eda884de7591a2656b9c581527b7925475cf6"},"schema_version":"1.0","source":{"id":"1007.3606","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.3606","created_at":"2026-05-17T23:51:50Z"},{"alias_kind":"arxiv_version","alias_value":"1007.3606v1","created_at":"2026-05-17T23:51:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3606","created_at":"2026-05-17T23:51:50Z"},{"alias_kind":"pith_short_12","alias_value":"PFANUEHZFBNA","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PFANUEHZFBNAHWLW","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PFANUEHZ","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:4f8e159daf2e10c20c31142c03f26d06bff67d5cab133cede771c9e86c9888a9","target":"graph","created_at":"2026-05-17T23:51:50Z","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":"Following a line of reasoning suggested by Eliashberg, we prove Cerf's theorem that any diffeomorphism of the 3-sphere extends over the 4-ball. To this end we develop a moduli-theoretic version of Eliashberg's filling-with-holomorphic-discs method.","authors_text":"Hansj\\\"org Geiges, Kai Zehmisch","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-07-21T10:29:38Z","title":"Eliashberg's proof of Cerf's theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3606","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":"sha256:48d5802431db49d556b47c563076481d3475b236750b23f495eb4229087436b8","target":"record","created_at":"2026-05-17T23:51:50Z","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":"1ab9e4f02ab69356c508df117ca7b060eb9471938755b38e3d9be9e5f907789e","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-07-21T10:29:38Z","title_canon_sha256":"066a57d00d10a35260e1a9184a0eda884de7591a2656b9c581527b7925475cf6"},"schema_version":"1.0","source":{"id":"1007.3606","kind":"arxiv","version":1}},"canonical_sha256":"7940da10f9285a03d976341225da2419e3f4cdbe7311a4197007d0478ac60fac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7940da10f9285a03d976341225da2419e3f4cdbe7311a4197007d0478ac60fac","first_computed_at":"2026-05-17T23:51:50.053352Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:50.053352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"61SF9UzFUHBkVErmV4pX7w1X7utRmaSNld28FwR8qgVau6DBzKeiFIi0HZc5XEP9TgIdqacYoE3QLc3XOTeICA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:50.054079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.3606","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48d5802431db49d556b47c563076481d3475b236750b23f495eb4229087436b8","sha256:4f8e159daf2e10c20c31142c03f26d06bff67d5cab133cede771c9e86c9888a9"],"state_sha256":"fbe56bb446efaeeca7a8e1cc2c18db248d2291c60ce1e1ddf3b41f3e30a19c05"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5LpYsqLT98MP8BLKLnH7DZUZtBdDb0pgc+TKTWWLbFtrFMIijAQOngCUx8D7p7xMl1qKmE8mD5GLv8AX7cDTDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T23:38:33.928724Z","bundle_sha256":"f099741b65fba9232178b3b8c2bd495e8a7717bb8e25e46943969d6e151e3178"}}