{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NACNS5HI3OHKIKLMEOBDZ5FUXV","short_pith_number":"pith:NACNS5HI","canonical_record":{"source":{"id":"1107.1743","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-08T22:13:40Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"c9e2ef269c8e7900108a594fc6a8f403ef96f7345c716887cd55f6754360a7ce","abstract_canon_sha256":"a64cdccdaa5a6b6df5dadc726060a8e2c53bafcc9386b7b448517c796959bc44"},"schema_version":"1.0"},"canonical_sha256":"6804d974e8db8ea4296c23823cf4b4bd488b96abb7a53a38f7e8e1fcdac91ba5","source":{"kind":"arxiv","id":"1107.1743","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1743","created_at":"2026-05-18T04:09:46Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1743v2","created_at":"2026-05-18T04:09:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1743","created_at":"2026-05-18T04:09:46Z"},{"alias_kind":"pith_short_12","alias_value":"NACNS5HI3OHK","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NACNS5HI3OHKIKLM","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NACNS5HI","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NACNS5HI3OHKIKLMEOBDZ5FUXV","target":"record","payload":{"canonical_record":{"source":{"id":"1107.1743","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-08T22:13:40Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"c9e2ef269c8e7900108a594fc6a8f403ef96f7345c716887cd55f6754360a7ce","abstract_canon_sha256":"a64cdccdaa5a6b6df5dadc726060a8e2c53bafcc9386b7b448517c796959bc44"},"schema_version":"1.0"},"canonical_sha256":"6804d974e8db8ea4296c23823cf4b4bd488b96abb7a53a38f7e8e1fcdac91ba5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:46.823516Z","signature_b64":"rBZwtBjp+S8Er2Rkk+S+q9lFmiqi7DMq9UY0FXnFe420LzlcXEQ8w8FGcsZHbqQs3KWjXEil3pn5sB+YjrwEAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6804d974e8db8ea4296c23823cf4b4bd488b96abb7a53a38f7e8e1fcdac91ba5","last_reissued_at":"2026-05-18T04:09:46.822983Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:46.822983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.1743","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:09:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VPNhgb7ymC9DjCZ5pdu00FqIFmVzc+VAkoWxLDbVcTURb6u7HBIxryNYs4ScRsUhkCVh9WoH4YrxguNfUK50Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:49:09.854128Z"},"content_sha256":"3375abb4aaf6db316011f1da91fd378f63c7294c236cbf5a189e749925159824","schema_version":"1.0","event_id":"sha256:3375abb4aaf6db316011f1da91fd378f63c7294c236cbf5a189e749925159824"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NACNS5HI3OHKIKLMEOBDZ5FUXV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pull-back of currents by meromorphic maps","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":"2011-07-08T22:13:40Z","abstract_excerpt":"Let $X$ and $Y$ be compact K\\\"ahler manifolds, and let $f:X\\rightarrow Y$ be a dominant meromorphic map. Base upon a regularization theorem of Dinh and Sibony for DSH currents, we define a pullback operator $f^{\\sharp}$ for currents of bidegrees $(p,p)$ of finite order on $Y$ (and thus for {\\it any} current, since $Y$ is compact). This operator has good properties as may be expected.\n  Our definition and results are compatible to those of various previous works of Meo, Russakovskii and Shiffman, Alessandrini and Bassanelli, Dinh and Sibony, and can be readily extended to the case of meromorphi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1743","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:09:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JWNamD9+v71yjcSUhm+GmOoC4SghW3iQzSsiW88pfiK6nccfHk3fdZX7k4R+CC6ofgVdpyn2wxr75MppVASzDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:49:09.854911Z"},"content_sha256":"be4df812e13c525b409ce883ed31e889f15a63b1ea822ff389d20d481da2957a","schema_version":"1.0","event_id":"sha256:be4df812e13c525b409ce883ed31e889f15a63b1ea822ff389d20d481da2957a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NACNS5HI3OHKIKLMEOBDZ5FUXV/bundle.json","state_url":"https://pith.science/pith/NACNS5HI3OHKIKLMEOBDZ5FUXV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NACNS5HI3OHKIKLMEOBDZ5FUXV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T07:49:09Z","links":{"resolver":"https://pith.science/pith/NACNS5HI3OHKIKLMEOBDZ5FUXV","bundle":"https://pith.science/pith/NACNS5HI3OHKIKLMEOBDZ5FUXV/bundle.json","state":"https://pith.science/pith/NACNS5HI3OHKIKLMEOBDZ5FUXV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NACNS5HI3OHKIKLMEOBDZ5FUXV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NACNS5HI3OHKIKLMEOBDZ5FUXV","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":"a64cdccdaa5a6b6df5dadc726060a8e2c53bafcc9386b7b448517c796959bc44","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-08T22:13:40Z","title_canon_sha256":"c9e2ef269c8e7900108a594fc6a8f403ef96f7345c716887cd55f6754360a7ce"},"schema_version":"1.0","source":{"id":"1107.1743","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1743","created_at":"2026-05-18T04:09:46Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1743v2","created_at":"2026-05-18T04:09:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1743","created_at":"2026-05-18T04:09:46Z"},{"alias_kind":"pith_short_12","alias_value":"NACNS5HI3OHK","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NACNS5HI3OHKIKLM","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NACNS5HI","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:be4df812e13c525b409ce883ed31e889f15a63b1ea822ff389d20d481da2957a","target":"graph","created_at":"2026-05-18T04:09:46Z","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":"Let $X$ and $Y$ be compact K\\\"ahler manifolds, and let $f:X\\rightarrow Y$ be a dominant meromorphic map. Base upon a regularization theorem of Dinh and Sibony for DSH currents, we define a pullback operator $f^{\\sharp}$ for currents of bidegrees $(p,p)$ of finite order on $Y$ (and thus for {\\it any} current, since $Y$ is compact). This operator has good properties as may be expected.\n  Our definition and results are compatible to those of various previous works of Meo, Russakovskii and Shiffman, Alessandrini and Bassanelli, Dinh and Sibony, and can be readily extended to the case of meromorphi","authors_text":"Tuyen Trung Truong","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-08T22:13:40Z","title":"Pull-back of currents by meromorphic maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1743","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":"sha256:3375abb4aaf6db316011f1da91fd378f63c7294c236cbf5a189e749925159824","target":"record","created_at":"2026-05-18T04:09:46Z","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":"a64cdccdaa5a6b6df5dadc726060a8e2c53bafcc9386b7b448517c796959bc44","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-08T22:13:40Z","title_canon_sha256":"c9e2ef269c8e7900108a594fc6a8f403ef96f7345c716887cd55f6754360a7ce"},"schema_version":"1.0","source":{"id":"1107.1743","kind":"arxiv","version":2}},"canonical_sha256":"6804d974e8db8ea4296c23823cf4b4bd488b96abb7a53a38f7e8e1fcdac91ba5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6804d974e8db8ea4296c23823cf4b4bd488b96abb7a53a38f7e8e1fcdac91ba5","first_computed_at":"2026-05-18T04:09:46.822983Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:46.822983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rBZwtBjp+S8Er2Rkk+S+q9lFmiqi7DMq9UY0FXnFe420LzlcXEQ8w8FGcsZHbqQs3KWjXEil3pn5sB+YjrwEAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:46.823516Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1743","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3375abb4aaf6db316011f1da91fd378f63c7294c236cbf5a189e749925159824","sha256:be4df812e13c525b409ce883ed31e889f15a63b1ea822ff389d20d481da2957a"],"state_sha256":"94e3b91e780f172e7f684ecdb87ea8eabe6ee6fc5d64b431a4169e88bdbb51fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RvoxpKlXWXWCTcmCfBa0k5sZZ6HIX2iFH+7C+29f8fTeS8QxUInmnUaDb16zpZR/POtqcY8ELm9lqX/PTxmTAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:49:09.859088Z","bundle_sha256":"ddcb6d54da70d47aff7591a16eff5b506ae03f18f9718d7b4ff9820365fac2d0"}}