{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QZSNVY4DYHHOU545KCXPSKBYRD","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":"54c928f5ade066cf90f5be78f84985c5b8db73eb5bf14e4d647c1f55e386bdd3","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-20T02:39:47Z","title_canon_sha256":"3a0c6a334dcf2eadd64c050eaef532e25e9ab5aa4c3be0d02574b6d35c613370"},"schema_version":"1.0","source":{"id":"1707.06349","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06349","created_at":"2026-05-18T00:39:54Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06349v1","created_at":"2026-05-18T00:39:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06349","created_at":"2026-05-18T00:39:54Z"},{"alias_kind":"pith_short_12","alias_value":"QZSNVY4DYHHO","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QZSNVY4DYHHOU545","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QZSNVY4D","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:5dd397e1b3eee8cc5c4e86aceb8ff4d5e52b9c198e1b5ffb0a3e2035cca8127c","target":"graph","created_at":"2026-05-18T00:39:54Z","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":"Using the duality of positive cones, we show that applying the polar transform from convex analysis to local positivity invariants for divisors gives interesting and new local positivity invariants for curves. These new invariants have nice properties similar to those for divisors. In particular, this enables us to give a characterization of the divisorial components of the non-Kahler locus of a big class.","authors_text":"Jian Xiao, Nicholas McCleerey","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-20T02:39:47Z","title":"Polar Transform and Local Positivity for Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06349","kind":"arxiv","version":1},"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":"sha256:027086e42259c3b33d3fe8e86c3a6cb6ee2522c129e4275d9bb8b0a2f1e4a8e2","target":"record","created_at":"2026-05-18T00:39:54Z","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":"54c928f5ade066cf90f5be78f84985c5b8db73eb5bf14e4d647c1f55e386bdd3","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-20T02:39:47Z","title_canon_sha256":"3a0c6a334dcf2eadd64c050eaef532e25e9ab5aa4c3be0d02574b6d35c613370"},"schema_version":"1.0","source":{"id":"1707.06349","kind":"arxiv","version":1}},"canonical_sha256":"8664dae383c1ceea779d50aef9283888d414a2d9225b73f0fd888575df25077b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8664dae383c1ceea779d50aef9283888d414a2d9225b73f0fd888575df25077b","first_computed_at":"2026-05-18T00:39:54.071635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:54.071635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CWqeTykiEmFbQK/CWD3loo1/g0bJSYDI0RbenXNSMdAAMg64McVF+iEpz0r8qY2SGMfL1B0jZXxyoUZdD6I+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:54.072150Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.06349","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:027086e42259c3b33d3fe8e86c3a6cb6ee2522c129e4275d9bb8b0a2f1e4a8e2","sha256:5dd397e1b3eee8cc5c4e86aceb8ff4d5e52b9c198e1b5ffb0a3e2035cca8127c"],"state_sha256":"2827f093f64d2c43eb25cd6e3ccd99b2f6f050ddc96c9850233b641059938137"}