{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TRFZRT3YQORC2RQ6VIKR2Y2NCR","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":"479b06dc6a0f8fe5be65e30caeff2e5fca63cdae7690919c732b6de5ed6a99b3","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-26T14:14:42Z","title_canon_sha256":"8429b620efba8933d0082c2f5706dbb9b5184edacdf6f335434c61d2f3b362c8"},"schema_version":"1.0","source":{"id":"1303.6502","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6502","created_at":"2026-05-18T03:29:26Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6502v3","created_at":"2026-05-18T03:29:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6502","created_at":"2026-05-18T03:29:26Z"},{"alias_kind":"pith_short_12","alias_value":"TRFZRT3YQORC","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TRFZRT3YQORC2RQ6","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TRFZRT3Y","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:38c642dd1c924c1c30a4baab032c81d7f2bca9ab2f55a8b33b18b1a86717195f","target":"graph","created_at":"2026-05-18T03:29:26Z","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 the paper \\cite{wall_1}, C.T.C. Wall proved that two smooth closed simply connected 4-manifolds which are homeomorphic are in fact stably diffeomorphic. We prove a similar result which states that two smooth closed 4-manifolds satisfying certain properties are stably diffeomorphic if and only if their signatures agree. The manifolds in question are obtained by surgery on loops. The methods we use are modified surgery of Kreck \\cite{kreck} and Kirby calculus.","authors_text":"Wojciech Politarczyk","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-26T14:14:42Z","title":"4-manifolds, surgery on loops and geometric realization of Tietze transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6502","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":"sha256:5e7833c6abb64d853f1bc77efec89638fc2a799ec5bca5367200cfa2cdad8610","target":"record","created_at":"2026-05-18T03:29:26Z","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":"479b06dc6a0f8fe5be65e30caeff2e5fca63cdae7690919c732b6de5ed6a99b3","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-03-26T14:14:42Z","title_canon_sha256":"8429b620efba8933d0082c2f5706dbb9b5184edacdf6f335434c61d2f3b362c8"},"schema_version":"1.0","source":{"id":"1303.6502","kind":"arxiv","version":3}},"canonical_sha256":"9c4b98cf7883a22d461eaa151d634d14430891d9a1c7070232f27feccd90244c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c4b98cf7883a22d461eaa151d634d14430891d9a1c7070232f27feccd90244c","first_computed_at":"2026-05-18T03:29:26.411398Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:26.411398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"47Rpk2dyNBbJDo0Pf0O8P+kcg72kji1Pd9mMon7XGC2+KEOWqpQWxMzxEDQNlGPu8NwBm7/TYQEQalX5YytMAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:26.412209Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.6502","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e7833c6abb64d853f1bc77efec89638fc2a799ec5bca5367200cfa2cdad8610","sha256:38c642dd1c924c1c30a4baab032c81d7f2bca9ab2f55a8b33b18b1a86717195f"],"state_sha256":"910219501409b0099a40461d374bd1c8ee25b37e332a085dafc811bacd1d7441"}