{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7FPKATKVUDYM4MNQ23HH2WAYWG","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":"5818e2827c97805fdefe345ac62961aa31a6d96de103dca9a32ef169ba97aa9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-02-20T23:21:14Z","title_canon_sha256":"6a643229a2b6c1a4a2612440b80e681cde1da93b52a461b2174b21f5f8d663c9"},"schema_version":"1.0","source":{"id":"1502.06035","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06035","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06035v3","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06035","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"pith_short_12","alias_value":"7FPKATKVUDYM","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7FPKATKVUDYM4MNQ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7FPKATKV","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:e827a78c635da6f3a6f2c49fcdce21c364fbfc54788dd4bac6c7196ad6ce1581","target":"graph","created_at":"2026-05-18T00:40:01Z","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":"A crucial step in the surgery-theoretic program to classify smooth manifolds is that of representing a middle--dimensional homology class by a smoothly embedded sphere. This step fails even for the simple 4-manifolds obtained from the 4-ball by adding a 2-handle with framing r along some knot K in S^3. An r-shake slice knot is one for which a generator of the second homology of this 4-manifold can be represented by a smoothly embedded 2-sphere. It is not known whether there exist 0-shake slice knots that are not slice. We define a relative notion of shake sliceness of knots, which we call shak","authors_text":"Arunima Ray, Tim D. Cochran","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-02-20T23:21:14Z","title":"Shake slice and shake concordant knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06035","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":"sha256:96c59f11eed3bdd5233dd2ebf85e501350d63b63aec1d7d0f993283faf7ee38c","target":"record","created_at":"2026-05-18T00:40:01Z","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":"5818e2827c97805fdefe345ac62961aa31a6d96de103dca9a32ef169ba97aa9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-02-20T23:21:14Z","title_canon_sha256":"6a643229a2b6c1a4a2612440b80e681cde1da93b52a461b2174b21f5f8d663c9"},"schema_version":"1.0","source":{"id":"1502.06035","kind":"arxiv","version":3}},"canonical_sha256":"f95ea04d55a0f0ce31b0d6ce7d5818b18093de7fc177e3b32fcec200d8225c03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f95ea04d55a0f0ce31b0d6ce7d5818b18093de7fc177e3b32fcec200d8225c03","first_computed_at":"2026-05-18T00:40:01.435865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:01.435865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sxJBXL6p3Q6NZ3lfrw1dtUsOb/RU3x/Y1G0PcwkJg4aUOpLkePtLOojGrrvBvk6qYGUhruEQi9BZsXi0S5GnBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:01.436478Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.06035","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96c59f11eed3bdd5233dd2ebf85e501350d63b63aec1d7d0f993283faf7ee38c","sha256:e827a78c635da6f3a6f2c49fcdce21c364fbfc54788dd4bac6c7196ad6ce1581"],"state_sha256":"0083f7f838cf2b58f094242e068464d3f976032479a13570804cab340909a126"}