{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YJR2WVDQJ5V2YT3QYU5BOKL2SN","short_pith_number":"pith:YJR2WVDQ","canonical_record":{"source":{"id":"1404.2875","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-04-10T16:43:13Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"06218bb0ea12f46fe8cb0da95f7e4c3b88bd6d59d8c53900d6881f87174bf24f","abstract_canon_sha256":"aea1af9a6b80bdb35fd94133310bfce891e36cd7510be5d4a2a13f8a6b03570c"},"schema_version":"1.0"},"canonical_sha256":"c263ab54704f6bac4f70c53a17297a935bcb55e27c6293bc2cde60cd1ff418c6","source":{"kind":"arxiv","id":"1404.2875","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2875","created_at":"2026-05-18T02:54:06Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2875v2","created_at":"2026-05-18T02:54:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2875","created_at":"2026-05-18T02:54:06Z"},{"alias_kind":"pith_short_12","alias_value":"YJR2WVDQJ5V2","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YJR2WVDQJ5V2YT3Q","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YJR2WVDQ","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YJR2WVDQJ5V2YT3QYU5BOKL2SN","target":"record","payload":{"canonical_record":{"source":{"id":"1404.2875","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-04-10T16:43:13Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"06218bb0ea12f46fe8cb0da95f7e4c3b88bd6d59d8c53900d6881f87174bf24f","abstract_canon_sha256":"aea1af9a6b80bdb35fd94133310bfce891e36cd7510be5d4a2a13f8a6b03570c"},"schema_version":"1.0"},"canonical_sha256":"c263ab54704f6bac4f70c53a17297a935bcb55e27c6293bc2cde60cd1ff418c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:06.446757Z","signature_b64":"va2zwMHCyFdD1k6LfBn+5S0hNvRCzBKe3VC/SFTqepWDeKaP1xFpCYY1OCLVWZysMjIWBy7Hc8MRk6cRyeE0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c263ab54704f6bac4f70c53a17297a935bcb55e27c6293bc2cde60cd1ff418c6","last_reissued_at":"2026-05-18T02:54:06.445999Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:06.445999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.2875","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":"2026-05-18T02:54:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0HFZq/dtEp8yLZ78/M3Ypwu/yKZHd79FFVkHfuU0naLc4u9Jds8yvqycPweVGMLThQeAdM0pe/t7+sv2dfh5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:46:57.495178Z"},"content_sha256":"30de5e01fb8d6a1e034cc0ddfa3b446bffc90b995bbff87437dad9a10fd6595a","schema_version":"1.0","event_id":"sha256:30de5e01fb8d6a1e034cc0ddfa3b446bffc90b995bbff87437dad9a10fd6595a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YJR2WVDQJ5V2YT3QYU5BOKL2SN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Least negative intersections of positive closed currents on compact K\\\"ahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Tuyen Trung Truong","submitted_at":"2014-04-10T16:43:13Z","abstract_excerpt":"Let $X$ be a compact K\\\"ahler manifold of dimension $k$. Let $R$ be a positive closed $(p,p)$ current on $X$, and $T_1,\\ldots ,T_{k-p}$ be positive closed $(1,1)$ currents on $X$. We define a so-called least negative intersection of the currents $T_1,T_2,\\ldots ,T_{k-p}$ and $R$, as a sublinear bounded operator \\begin{eqnarray*} \\bigwedge (T_1,\\ldots ,T_{k-p},R):~C^0(X)\\rightarrow \\mathbb{R}. \\end{eqnarray*} This operator is {\\bf symmetric} in $T_1,\\ldots ,T_{k-p}$. It is {\\bf independent} of the choice of a quasi-potential $u_i$ of $T_i$, of the choice of a smooth closed $(1,1)$ form $\\theta "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2875","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":"2026-05-18T02:54:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vr9HNqhkFCQKVhlZ6uM4CPzLMWkBg9q2AfLjtEWraRVLXV0womR//jCSl240lMGaj3dgOUPgD4axf4Q1VwLwBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:46:57.495830Z"},"content_sha256":"bb72a8bee6ca39bb236b4d21d493f1a45dc5cda4cf0584a24c8a9f3a84e0529d","schema_version":"1.0","event_id":"sha256:bb72a8bee6ca39bb236b4d21d493f1a45dc5cda4cf0584a24c8a9f3a84e0529d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YJR2WVDQJ5V2YT3QYU5BOKL2SN/bundle.json","state_url":"https://pith.science/pith/YJR2WVDQJ5V2YT3QYU5BOKL2SN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YJR2WVDQJ5V2YT3QYU5BOKL2SN/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":"2026-06-09T11:46:57Z","links":{"resolver":"https://pith.science/pith/YJR2WVDQJ5V2YT3QYU5BOKL2SN","bundle":"https://pith.science/pith/YJR2WVDQJ5V2YT3QYU5BOKL2SN/bundle.json","state":"https://pith.science/pith/YJR2WVDQJ5V2YT3QYU5BOKL2SN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YJR2WVDQJ5V2YT3QYU5BOKL2SN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YJR2WVDQJ5V2YT3QYU5BOKL2SN","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":"aea1af9a6b80bdb35fd94133310bfce891e36cd7510be5d4a2a13f8a6b03570c","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-04-10T16:43:13Z","title_canon_sha256":"06218bb0ea12f46fe8cb0da95f7e4c3b88bd6d59d8c53900d6881f87174bf24f"},"schema_version":"1.0","source":{"id":"1404.2875","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2875","created_at":"2026-05-18T02:54:06Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2875v2","created_at":"2026-05-18T02:54:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2875","created_at":"2026-05-18T02:54:06Z"},{"alias_kind":"pith_short_12","alias_value":"YJR2WVDQJ5V2","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YJR2WVDQJ5V2YT3Q","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YJR2WVDQ","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:bb72a8bee6ca39bb236b4d21d493f1a45dc5cda4cf0584a24c8a9f3a84e0529d","target":"graph","created_at":"2026-05-18T02:54:06Z","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 $X$ be a compact K\\\"ahler manifold of dimension $k$. Let $R$ be a positive closed $(p,p)$ current on $X$, and $T_1,\\ldots ,T_{k-p}$ be positive closed $(1,1)$ currents on $X$. We define a so-called least negative intersection of the currents $T_1,T_2,\\ldots ,T_{k-p}$ and $R$, as a sublinear bounded operator \\begin{eqnarray*} \\bigwedge (T_1,\\ldots ,T_{k-p},R):~C^0(X)\\rightarrow \\mathbb{R}. \\end{eqnarray*} This operator is {\\bf symmetric} in $T_1,\\ldots ,T_{k-p}$. It is {\\bf independent} of the choice of a quasi-potential $u_i$ of $T_i$, of the choice of a smooth closed $(1,1)$ form $\\theta ","authors_text":"Tuyen Trung Truong","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-04-10T16:43:13Z","title":"Least negative intersections of positive closed currents on compact K\\\"ahler manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2875","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":"sha256:30de5e01fb8d6a1e034cc0ddfa3b446bffc90b995bbff87437dad9a10fd6595a","target":"record","created_at":"2026-05-18T02:54:06Z","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":"aea1af9a6b80bdb35fd94133310bfce891e36cd7510be5d4a2a13f8a6b03570c","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-04-10T16:43:13Z","title_canon_sha256":"06218bb0ea12f46fe8cb0da95f7e4c3b88bd6d59d8c53900d6881f87174bf24f"},"schema_version":"1.0","source":{"id":"1404.2875","kind":"arxiv","version":2}},"canonical_sha256":"c263ab54704f6bac4f70c53a17297a935bcb55e27c6293bc2cde60cd1ff418c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c263ab54704f6bac4f70c53a17297a935bcb55e27c6293bc2cde60cd1ff418c6","first_computed_at":"2026-05-18T02:54:06.445999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:06.445999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"va2zwMHCyFdD1k6LfBn+5S0hNvRCzBKe3VC/SFTqepWDeKaP1xFpCYY1OCLVWZysMjIWBy7Hc8MRk6cRyeE0Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:06.446757Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.2875","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30de5e01fb8d6a1e034cc0ddfa3b446bffc90b995bbff87437dad9a10fd6595a","sha256:bb72a8bee6ca39bb236b4d21d493f1a45dc5cda4cf0584a24c8a9f3a84e0529d"],"state_sha256":"2ec787bc92c9429ff0d3ff8ca358e09dc07084121b173c6f182f4e873d2ec9ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rxVzzQUyUKHwnbqTx8U667Ju+M7c4bgz3pvO4t3CCrQQWBpvrU9bbonJjps37Si5BzEXZ19jS5fHhCyMqEcADQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T11:46:57.500122Z","bundle_sha256":"1990e49d7f76d418519556e824289c23fdb865454f4a7e4f6430cfd3e4ffa410"}}