{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IR4FUQ5GM7ESSOJ56DUBMO74M2","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":"1dbbf2e567b5257d321e25edd58596bcb5f9c5bbdd0c3ed78677e19c568042b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-09-03T08:47:06Z","title_canon_sha256":"4113c840fb4ac06188dc1139f2bce377f474186ada928114ff3d068292f2c568"},"schema_version":"1.0","source":{"id":"1509.00987","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00987","created_at":"2026-05-18T00:17:24Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00987v2","created_at":"2026-05-18T00:17:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00987","created_at":"2026-05-18T00:17:24Z"},{"alias_kind":"pith_short_12","alias_value":"IR4FUQ5GM7ES","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IR4FUQ5GM7ESSOJ5","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IR4FUQ5G","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:89cbe8bb88b64c6824fccf0ff6addc7a5cba0ed9d49a897e15f9f6828b5cc07a","target":"graph","created_at":"2026-05-18T00:17:24Z","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 present paper, we study regularity of the Andersson-Samuelsson Koppelman integral operator on affine cones over smooth projective complete intersections. Particularly, we prove $L^p$- and $C^\\alpha$-estimates, and compactness of the operator, when the degree is sufficiently small. As applications, we obtain homotopy formulas for different $\\overline{\\partial}$-operators acting on $L^p$-spaces of forms, including the case $p=2$ if the varieties have canonical singularities. We also prove that the $\\mathcal{A}$-forms introduced by Andersson-Samuelsson are $C^\\alpha$ for $\\alpha < 1$.","authors_text":"Jean Ruppenthal, Richard L\\\"ark\\\"ang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-09-03T08:47:06Z","title":"Koppelman formulas on affine cones over smooth projective complete intersections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00987","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:de16b9de809f843f088ead87537d6c292fb36d583d5c8f89c6aa7ab736805e50","target":"record","created_at":"2026-05-18T00:17:24Z","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":"1dbbf2e567b5257d321e25edd58596bcb5f9c5bbdd0c3ed78677e19c568042b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-09-03T08:47:06Z","title_canon_sha256":"4113c840fb4ac06188dc1139f2bce377f474186ada928114ff3d068292f2c568"},"schema_version":"1.0","source":{"id":"1509.00987","kind":"arxiv","version":2}},"canonical_sha256":"44785a43a667c929393df0e8163bfc66833c92a684d7288f1b19728ff02658a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44785a43a667c929393df0e8163bfc66833c92a684d7288f1b19728ff02658a0","first_computed_at":"2026-05-18T00:17:24.612426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:24.612426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7WUZg079zUKko7qEBu3QgFz+1xhIxRSusx0uJy0NqpATDlDiSRto0r7sNtsRqDHqbmjDr+ajE0qGc3VmZ2tFBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:24.613046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.00987","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de16b9de809f843f088ead87537d6c292fb36d583d5c8f89c6aa7ab736805e50","sha256:89cbe8bb88b64c6824fccf0ff6addc7a5cba0ed9d49a897e15f9f6828b5cc07a"],"state_sha256":"a9914af7b2c6a88df04917893645148eef08f6f47e0f3bb6dcec2bd98c9d7807"}