{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:B4WEL7YPLJSJAVMC7ALAX3J2OC","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":"026c372c4681fe580d9d863f7ab134df455f723f289a106a06c3151da1d1220b","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-05-01T15:36:21Z","title_canon_sha256":"6a6c672709bc9a5dcf27db63ccb4cd3a05448e673c163e73168d1ecbc9c9a11e"},"schema_version":"1.0","source":{"id":"0905.0104","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.0104","created_at":"2026-05-18T04:40:57Z"},{"alias_kind":"arxiv_version","alias_value":"0905.0104v3","created_at":"2026-05-18T04:40:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.0104","created_at":"2026-05-18T04:40:57Z"},{"alias_kind":"pith_short_12","alias_value":"B4WEL7YPLJSJ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"B4WEL7YPLJSJAVMC","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"B4WEL7YP","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:f9d512b8e0a911f2e88624c1ed50a39e97c5f2fe38d926c2769c4faab5b3e145","target":"graph","created_at":"2026-05-18T04:40:57Z","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":"The Wall surgery obstruction groups have two interesting geometrically defined subgroups, consisting of the surgery obstructions between closed manifolds, and the inertial elements. We show that the inertia group $I_{n+1}(\\pi,w)$ and the closed manifold subgroup $C_{n+1}(\\pi,w)$ are equal in dimensions $n+1\\geq 6$, for any finitely-presented group $\\pi$ and any orientation character $w\\colon \\pi \\to \\cy 2$.","authors_text":"Ian Hambleton","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-05-01T15:36:21Z","title":"Surgery obstructions on closed manifolds and the Inertia subgroup"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.0104","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":"sha256:69d9edad77eac3c90d38e75cc63ae1b4e1fe9c722f6723f35539e6abae2d926d","target":"record","created_at":"2026-05-18T04:40:57Z","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":"026c372c4681fe580d9d863f7ab134df455f723f289a106a06c3151da1d1220b","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-05-01T15:36:21Z","title_canon_sha256":"6a6c672709bc9a5dcf27db63ccb4cd3a05448e673c163e73168d1ecbc9c9a11e"},"schema_version":"1.0","source":{"id":"0905.0104","kind":"arxiv","version":3}},"canonical_sha256":"0f2c45ff0f5a64905582f8160bed3a708e8193535a1fd9e536581b7b3f67a230","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f2c45ff0f5a64905582f8160bed3a708e8193535a1fd9e536581b7b3f67a230","first_computed_at":"2026-05-18T04:40:57.407384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:57.407384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p1YrjJMgh6bxZNuuwmWCttDXvagv7ylMvCqHR1wKEQWovOy+Wpt4R7WMgwcb8h/R6r+B5pOKggYC+o61e8h1Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:57.407824Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.0104","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69d9edad77eac3c90d38e75cc63ae1b4e1fe9c722f6723f35539e6abae2d926d","sha256:f9d512b8e0a911f2e88624c1ed50a39e97c5f2fe38d926c2769c4faab5b3e145"],"state_sha256":"3ad2cafab06824c0152a8f187fca2e17efa69a91aecc7cfd96c093e3416af1da"}