{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4NUDSF6F4F4OZWV6QDXKMMB2MA","short_pith_number":"pith:4NUDSF6F","canonical_record":{"source":{"id":"1702.04417","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-02-14T23:10:58Z","cross_cats_sorted":["math.AP","math.DG"],"title_canon_sha256":"f8a2b7ae59f27164bb115428a5c8e39222ea2d9aa76527807fa2761f96f9b020","abstract_canon_sha256":"e552d573706d31f1d8133e84c70aff866c6caeb8b45ddad8f02426da8e7a0c3c"},"schema_version":"1.0"},"canonical_sha256":"e3683917c5e178ecdabe80eea6303a6037024c193f5d56f97cedc42293d6acc1","source":{"kind":"arxiv","id":"1702.04417","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04417","created_at":"2026-05-18T00:13:32Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04417v2","created_at":"2026-05-18T00:13:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04417","created_at":"2026-05-18T00:13:32Z"},{"alias_kind":"pith_short_12","alias_value":"4NUDSF6F4F4O","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4NUDSF6F4F4OZWV6","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4NUDSF6F","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4NUDSF6F4F4OZWV6QDXKMMB2MA","target":"record","payload":{"canonical_record":{"source":{"id":"1702.04417","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-02-14T23:10:58Z","cross_cats_sorted":["math.AP","math.DG"],"title_canon_sha256":"f8a2b7ae59f27164bb115428a5c8e39222ea2d9aa76527807fa2761f96f9b020","abstract_canon_sha256":"e552d573706d31f1d8133e84c70aff866c6caeb8b45ddad8f02426da8e7a0c3c"},"schema_version":"1.0"},"canonical_sha256":"e3683917c5e178ecdabe80eea6303a6037024c193f5d56f97cedc42293d6acc1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:32.829194Z","signature_b64":"AZh6WJih7YoqhAWHinh0rktq6D3DB0nu+188r17PCP8S9py3vk6JFBVIz6scUXXABvhzLGGAazxw0+nckLcyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3683917c5e178ecdabe80eea6303a6037024c193f5d56f97cedc42293d6acc1","last_reissued_at":"2026-05-18T00:13:32.828720Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:32.828720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.04417","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:13:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jryPMSh2szNuqGtyt6i6AqwtXOshlH2DPFJqYZbWXhGtYbgtSVdlVqmepCXPE11uC3BrH66B2rzs9cSXJDYTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:49:11.981324Z"},"content_sha256":"b260172938d5219d50af60930767b9001d77b18a4247687d83212b3e401dea2b","schema_version":"1.0","event_id":"sha256:b260172938d5219d50af60930767b9001d77b18a4247687d83212b3e401dea2b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4NUDSF6F4F4OZWV6QDXKMMB2MA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A splitting theorem for the Seiberg-Witten invariant of a homology $S^1 \\times S^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG"],"primary_cat":"math.GT","authors_text":"Daniel Ruberman, Jianfeng Lin, Nikolai Saveliev","submitted_at":"2017-02-14T23:10:58Z","abstract_excerpt":"We study the Seiberg-Witten invariant $\\lambda_{\\rm{SW}} (X)$ of smooth spin $4$-manifolds $X$ with integral homology of $S^1\\times S^3$ defined by Mrowka, Ruberman, and Saveliev as a signed count of irreducible monopoles amended by an index-theoretic correction term. We prove a splitting formula for this invariant in terms of the Fr{\\o}yshov invariant $h(X)$ and a certain Lefschetz number in the reduced monopole Floer homology of Kronheimer and Mrowka. We apply this formula to obstruct existence of metrics of positive scalar curvature on certain 4-manifolds, and to exhibit new classes of inte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04417","kind":"arxiv","version":2},"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":"2026-05-18T00:13:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ALZBpNLyeOqF8t/ztJsnCezHPf6iUBFjdx+aRsH3qMGwxvXol+06XRL4f06LZmnO8G704XqLG4GHWXSKZGKyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:49:11.981667Z"},"content_sha256":"e3778902c82ba955e2decd379cea85cc7f53e8939e1220c81207f1986619a935","schema_version":"1.0","event_id":"sha256:e3778902c82ba955e2decd379cea85cc7f53e8939e1220c81207f1986619a935"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4NUDSF6F4F4OZWV6QDXKMMB2MA/bundle.json","state_url":"https://pith.science/pith/4NUDSF6F4F4OZWV6QDXKMMB2MA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4NUDSF6F4F4OZWV6QDXKMMB2MA/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":"2026-06-25T10:49:11Z","links":{"resolver":"https://pith.science/pith/4NUDSF6F4F4OZWV6QDXKMMB2MA","bundle":"https://pith.science/pith/4NUDSF6F4F4OZWV6QDXKMMB2MA/bundle.json","state":"https://pith.science/pith/4NUDSF6F4F4OZWV6QDXKMMB2MA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4NUDSF6F4F4OZWV6QDXKMMB2MA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4NUDSF6F4F4OZWV6QDXKMMB2MA","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":"e552d573706d31f1d8133e84c70aff866c6caeb8b45ddad8f02426da8e7a0c3c","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-02-14T23:10:58Z","title_canon_sha256":"f8a2b7ae59f27164bb115428a5c8e39222ea2d9aa76527807fa2761f96f9b020"},"schema_version":"1.0","source":{"id":"1702.04417","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04417","created_at":"2026-05-18T00:13:32Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04417v2","created_at":"2026-05-18T00:13:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04417","created_at":"2026-05-18T00:13:32Z"},{"alias_kind":"pith_short_12","alias_value":"4NUDSF6F4F4O","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4NUDSF6F4F4OZWV6","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4NUDSF6F","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:e3778902c82ba955e2decd379cea85cc7f53e8939e1220c81207f1986619a935","target":"graph","created_at":"2026-05-18T00:13:32Z","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":"We study the Seiberg-Witten invariant $\\lambda_{\\rm{SW}} (X)$ of smooth spin $4$-manifolds $X$ with integral homology of $S^1\\times S^3$ defined by Mrowka, Ruberman, and Saveliev as a signed count of irreducible monopoles amended by an index-theoretic correction term. We prove a splitting formula for this invariant in terms of the Fr{\\o}yshov invariant $h(X)$ and a certain Lefschetz number in the reduced monopole Floer homology of Kronheimer and Mrowka. We apply this formula to obstruct existence of metrics of positive scalar curvature on certain 4-manifolds, and to exhibit new classes of inte","authors_text":"Daniel Ruberman, Jianfeng Lin, Nikolai Saveliev","cross_cats":["math.AP","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-02-14T23:10:58Z","title":"A splitting theorem for the Seiberg-Witten invariant of a homology $S^1 \\times S^3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04417","kind":"arxiv","version":2},"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:b260172938d5219d50af60930767b9001d77b18a4247687d83212b3e401dea2b","target":"record","created_at":"2026-05-18T00:13:32Z","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":"e552d573706d31f1d8133e84c70aff866c6caeb8b45ddad8f02426da8e7a0c3c","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-02-14T23:10:58Z","title_canon_sha256":"f8a2b7ae59f27164bb115428a5c8e39222ea2d9aa76527807fa2761f96f9b020"},"schema_version":"1.0","source":{"id":"1702.04417","kind":"arxiv","version":2}},"canonical_sha256":"e3683917c5e178ecdabe80eea6303a6037024c193f5d56f97cedc42293d6acc1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3683917c5e178ecdabe80eea6303a6037024c193f5d56f97cedc42293d6acc1","first_computed_at":"2026-05-18T00:13:32.828720Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:32.828720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AZh6WJih7YoqhAWHinh0rktq6D3DB0nu+188r17PCP8S9py3vk6JFBVIz6scUXXABvhzLGGAazxw0+nckLcyCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:32.829194Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.04417","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b260172938d5219d50af60930767b9001d77b18a4247687d83212b3e401dea2b","sha256:e3778902c82ba955e2decd379cea85cc7f53e8939e1220c81207f1986619a935"],"state_sha256":"58b918ea82e2274153d14216f8b747031cc94a948a5dc09c61a758e8375edd3a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5GJPGoxYkeB1n5yRp7vTg9DKoefNtfjp0msWAPBuCS58RJgVAKCaciJ3w7MjSMDoy6HfFb6F4iFVF1svcOeVDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T10:49:11.983563Z","bundle_sha256":"4df09dac320b64a98bdcc3b36ccb556e2bab13184ac06212baec32c816daa890"}}