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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.02738","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-09-09T11:54:38Z","cross_cats_sorted":[],"title_canon_sha256":"e46a773fdaffd6cb5265c298284c0f8e12ea067bdcca036ed55fdf89be9873d0","abstract_canon_sha256":"b44194ba0fec6c1b9c67cdea746e5b0a9ce48feb2c0ebd92936054381d20e73f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:26.341412Z","signature_b64":"gsotwkv9dhxIyNQ/IyGv0LHNT5p0JjfUeVj9+zzlwuO6Nu5uLoPKipUrX4SImDetB0lFjIlZ4SIofN4P/qZ6Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0661e4fcf339404c20075b9aa870112e25401743113bd6a6add113b86304419","last_reissued_at":"2026-05-18T00:53:26.341019Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:26.341019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Concordance maps in knot Floer homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Andras Juhasz, Marco Marengon","submitted_at":"2015-09-09T11:54:38Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02738","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1509.02738","created_at":"2026-05-18T00:53:26.341080+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.02738v2","created_at":"2026-05-18T00:53:26.341080+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02738","created_at":"2026-05-18T00:53:26.341080+00:00"},{"alias_kind":"pith_short_12","alias_value":"YBTB4T6PGOKA","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"YBTB4T6PGOKAJQQA","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"YBTB4T6P","created_at":"2026-05-18T12:29:50.041715+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YBTB4T6PGOKAJQQAOW42VBYBCL","json":"https://pith.science/pith/YBTB4T6PGOKAJQQAOW42VBYBCL.json","graph_json":"https://pith.science/api/pith-number/YBTB4T6PGOKAJQQAOW42VBYBCL/graph.json","events_json":"https://pith.science/api/pith-number/YBTB4T6PGOKAJQQAOW42VBYBCL/events.json","paper":"https://pith.science/paper/YBTB4T6P"},"agent_actions":{"view_html":"https://pith.science/pith/YBTB4T6PGOKAJQQAOW42VBYBCL","download_json":"https://pith.science/pith/YBTB4T6PGOKAJQQAOW42VBYBCL.json","view_paper":"https://pith.science/paper/YBTB4T6P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.02738&json=true","fetch_graph":"https://pith.science/api/pith-number/YBTB4T6PGOKAJQQAOW42VBYBCL/graph.json","fetch_events":"https://pith.science/api/pith-number/YBTB4T6PGOKAJQQAOW42VBYBCL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YBTB4T6PGOKAJQQAOW42VBYBCL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YBTB4T6PGOKAJQQAOW42VBYBCL/action/storage_attestation","attest_author":"https://pith.science/pith/YBTB4T6PGOKAJQQAOW42VBYBCL/action/author_attestation","sign_citation":"https://pith.science/pith/YBTB4T6PGOKAJQQAOW42VBYBCL/action/citation_signature","submit_replication":"https://pith.science/pith/YBTB4T6PGOKAJQQAOW42VBYBCL/action/replication_record"}},"created_at":"2026-05-18T00:53:26.341080+00:00","updated_at":"2026-05-18T00:53:26.341080+00:00"}