{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:7ZPXMVA2NV2UC5MELNKM55ESUV","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":"a53c906798631ebbc78cf7328cd4f01fce003f3ae4d9a168077b3ce2f59f3597","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-02-04T11:37:46Z","title_canon_sha256":"4f94a6b2d79a12d5b637b1b11efc3b8f63150399c28303d2ddc0ce6f241792ab"},"schema_version":"1.0","source":{"id":"0902.0705","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.0705","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"0902.0705v1","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0705","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"7ZPXMVA2NV2U","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7ZPXMVA2NV2UC5ME","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7ZPXMVA2","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:68a0615bc88313450f248b55b7ddb81d5492c2d52d52d7af98056952b1c29b4a","target":"graph","created_at":"2026-05-18T02:41:51Z","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":"In this paper we introduce an open-closed cobordism category with maps to a background space. We identify the classifying space of this category for certain classes of background space. The key ingredient is the homology stability of mapping class groups with twisted coefficients.","authors_text":"Elizabeth Hanbury","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-02-04T11:37:46Z","title":"An open-closed cobordism category with background space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0705","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":"sha256:23d9a97cb9eb41b2601f963f58c0fe7a3a6ba67d0b042a41fe49aaf223a69e5c","target":"record","created_at":"2026-05-18T02:41:51Z","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":"a53c906798631ebbc78cf7328cd4f01fce003f3ae4d9a168077b3ce2f59f3597","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-02-04T11:37:46Z","title_canon_sha256":"4f94a6b2d79a12d5b637b1b11efc3b8f63150399c28303d2ddc0ce6f241792ab"},"schema_version":"1.0","source":{"id":"0902.0705","kind":"arxiv","version":1}},"canonical_sha256":"fe5f76541a6d754175845b54cef492a57547422747284e2e742d0724d8486530","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe5f76541a6d754175845b54cef492a57547422747284e2e742d0724d8486530","first_computed_at":"2026-05-18T02:41:51.366441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:51.366441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+kAZVACGx9YGgdQUAOzYivfVUPPsVTAXYDKoEYyMHpPRm+KgopNhTuPp1FDaDaNSZ2XC9SauzIquWWvFd/G/Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:51.366871Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.0705","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23d9a97cb9eb41b2601f963f58c0fe7a3a6ba67d0b042a41fe49aaf223a69e5c","sha256:68a0615bc88313450f248b55b7ddb81d5492c2d52d52d7af98056952b1c29b4a"],"state_sha256":"7fd55d72d23a12383dd9b856bc388ef0389f5acea0d3e144b6111822225943e6"}