{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:Y2B3HWGVZZKA2H3GNAKEQQTLKY","short_pith_number":"pith:Y2B3HWGV","schema_version":"1.0","canonical_sha256":"c683b3d8d5ce540d1f66681448426b560dac05f42e5c3bc9b8470e87e20763de","source":{"kind":"arxiv","id":"1111.0278","version":1},"attestation_state":"computed","paper":{"title":"Quasi-potentials and regularization of currents, and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Tuyen Trung Truong","submitted_at":"2011-11-01T19:20:33Z","abstract_excerpt":"Let $Y$ be a compact K\\\"ahler manifold. We show that the weak regularization $K_n$ of Dinh and Sibony for the diagonal $\\Delta_Y$ (see Section 2 for more detail) is compatible with wedge product in the following sense:\n  If $T$ is a positive $dd^c$-closed $(p,p)$ current and $\\theta$ is a smooth $(q,q)$ form then there is a sequence of positive $dd^c$-closed $(p+q,p+q)$ currents $S_n$ whose masses converge to 0 so that $-S_n\\leq K_n(T\\wedge \\theta)-K_n(T)\\wedge \\theta \\leq S_n$ for all $n$.\n  We also prove a result concerning the quasi-potentials of positive closed currents. We give two applic"},"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":"1111.0278","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-11-01T19:20:33Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"652d82a8c9ede255ba70679171d7192c980ba644da68321a485633f4ce605c95","abstract_canon_sha256":"ebb1e5040aa2a7cdf7ea88e24a7c1fdcf8e424ec1aeb6e99895ef99e21dd05b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:46.075253Z","signature_b64":"N6xA4cmQv6tL6YvLN+kERMebHKTvQJ29ngq7/gLnW4zvXuS8M0AO6ggeo3BnUNRPOc9j/N3qU1f1+V9gnyhSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c683b3d8d5ce540d1f66681448426b560dac05f42e5c3bc9b8470e87e20763de","last_reissued_at":"2026-05-18T04:09:46.074861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:46.074861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasi-potentials and regularization of currents, and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Tuyen Trung Truong","submitted_at":"2011-11-01T19:20:33Z","abstract_excerpt":"Let $Y$ be a compact K\\\"ahler manifold. We show that the weak regularization $K_n$ of Dinh and Sibony for the diagonal $\\Delta_Y$ (see Section 2 for more detail) is compatible with wedge product in the following sense:\n  If $T$ is a positive $dd^c$-closed $(p,p)$ current and $\\theta$ is a smooth $(q,q)$ form then there is a sequence of positive $dd^c$-closed $(p+q,p+q)$ currents $S_n$ whose masses converge to 0 so that $-S_n\\leq K_n(T\\wedge \\theta)-K_n(T)\\wedge \\theta \\leq S_n$ for all $n$.\n  We also prove a result concerning the quasi-potentials of positive closed currents. We give two applic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0278","kind":"arxiv","version":1},"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":"1111.0278","created_at":"2026-05-18T04:09:46.074924+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.0278v1","created_at":"2026-05-18T04:09:46.074924+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0278","created_at":"2026-05-18T04:09:46.074924+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y2B3HWGVZZKA","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y2B3HWGVZZKA2H3G","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y2B3HWGV","created_at":"2026-05-18T12:26:47.523578+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/Y2B3HWGVZZKA2H3GNAKEQQTLKY","json":"https://pith.science/pith/Y2B3HWGVZZKA2H3GNAKEQQTLKY.json","graph_json":"https://pith.science/api/pith-number/Y2B3HWGVZZKA2H3GNAKEQQTLKY/graph.json","events_json":"https://pith.science/api/pith-number/Y2B3HWGVZZKA2H3GNAKEQQTLKY/events.json","paper":"https://pith.science/paper/Y2B3HWGV"},"agent_actions":{"view_html":"https://pith.science/pith/Y2B3HWGVZZKA2H3GNAKEQQTLKY","download_json":"https://pith.science/pith/Y2B3HWGVZZKA2H3GNAKEQQTLKY.json","view_paper":"https://pith.science/paper/Y2B3HWGV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.0278&json=true","fetch_graph":"https://pith.science/api/pith-number/Y2B3HWGVZZKA2H3GNAKEQQTLKY/graph.json","fetch_events":"https://pith.science/api/pith-number/Y2B3HWGVZZKA2H3GNAKEQQTLKY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y2B3HWGVZZKA2H3GNAKEQQTLKY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y2B3HWGVZZKA2H3GNAKEQQTLKY/action/storage_attestation","attest_author":"https://pith.science/pith/Y2B3HWGVZZKA2H3GNAKEQQTLKY/action/author_attestation","sign_citation":"https://pith.science/pith/Y2B3HWGVZZKA2H3GNAKEQQTLKY/action/citation_signature","submit_replication":"https://pith.science/pith/Y2B3HWGVZZKA2H3GNAKEQQTLKY/action/replication_record"}},"created_at":"2026-05-18T04:09:46.074924+00:00","updated_at":"2026-05-18T04:09:46.074924+00:00"}