{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YBTB4T6PGOKAJQQAOW42VBYBCL","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":"b44194ba0fec6c1b9c67cdea746e5b0a9ce48feb2c0ebd92936054381d20e73f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-09-09T11:54:38Z","title_canon_sha256":"e46a773fdaffd6cb5265c298284c0f8e12ea067bdcca036ed55fdf89be9873d0"},"schema_version":"1.0","source":{"id":"1509.02738","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02738","created_at":"2026-05-18T00:53:26Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02738v2","created_at":"2026-05-18T00:53:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02738","created_at":"2026-05-18T00:53:26Z"},{"alias_kind":"pith_short_12","alias_value":"YBTB4T6PGOKA","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YBTB4T6PGOKAJQQA","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YBTB4T6P","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:9d64faaa656dd87060db69e96cb579b9a3d6ada3b3fdcd51086ca5bc76f57a26","target":"graph","created_at":"2026-05-18T00:53:26Z","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":"We show that a decorated knot concordance $C$ from $K$ to $K'$ induces a homomorphism $F_C$ on knot Floer homology that preserves the Alexander and Maslov gradings. Furthermore, it induces a morphism of the spectral sequences to $\\widehat{HF}(S^3) \\cong \\mathbb{Z}_2$ that agrees with $F_C$ on the $E^1$ page and is the identity on the $E^\\infty$ page. It follows that $F_C$ is non-vanishing on $\\widehat{HFK}_0(K, \\tau(K))$. We also obtain an invariant of slice disks in homology 4-balls bounding $S^3$. If $C$ is invertible, then $F_C$ is injective, hence $\\dim \\widehat{HFK}_j(K,i) \\le \\dim \\wideh","authors_text":"Andras Juhasz, Marco Marengon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-09-09T11:54:38Z","title":"Concordance maps in knot Floer homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02738","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":"sha256:8f9e5bd773088c39d3d9e0d852fa2c839e1c2b79e57a13dca3712a9418f3e26b","target":"record","created_at":"2026-05-18T00:53:26Z","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":"b44194ba0fec6c1b9c67cdea746e5b0a9ce48feb2c0ebd92936054381d20e73f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-09-09T11:54:38Z","title_canon_sha256":"e46a773fdaffd6cb5265c298284c0f8e12ea067bdcca036ed55fdf89be9873d0"},"schema_version":"1.0","source":{"id":"1509.02738","kind":"arxiv","version":2}},"canonical_sha256":"c0661e4fcf339404c20075b9aa870112e25401743113bd6a6add113b86304419","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0661e4fcf339404c20075b9aa870112e25401743113bd6a6add113b86304419","first_computed_at":"2026-05-18T00:53:26.341019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:26.341019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gsotwkv9dhxIyNQ/IyGv0LHNT5p0JjfUeVj9+zzlwuO6Nu5uLoPKipUrX4SImDetB0lFjIlZ4SIofN4P/qZ6Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:26.341412Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.02738","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f9e5bd773088c39d3d9e0d852fa2c839e1c2b79e57a13dca3712a9418f3e26b","sha256:9d64faaa656dd87060db69e96cb579b9a3d6ada3b3fdcd51086ca5bc76f57a26"],"state_sha256":"446ef08d18f010e91682eb6e90dfe6d787f9f63bdf07fe66eddb0c8851efc385"}