{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6DDYALHHT4Q5GQQSOGGOT7JSBM","short_pith_number":"pith:6DDYALHH","canonical_record":{"source":{"id":"1607.06989","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-07-24T01:24:01Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"1a4fedd08aaf1f26754a52f20722938b58b7191e5364447e3de0dc2d7760adf9","abstract_canon_sha256":"5d2e901f382134ad4c400f632fcf114a37565420b762134865e0c645563ffd33"},"schema_version":"1.0"},"canonical_sha256":"f0c7802ce79f21d34212718ce9fd320b397c7441b705b6389e328eb69e8c251d","source":{"kind":"arxiv","id":"1607.06989","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06989","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06989v1","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06989","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"pith_short_12","alias_value":"6DDYALHHT4Q5","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6DDYALHHT4Q5GQQS","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6DDYALHH","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6DDYALHHT4Q5GQQSOGGOT7JSBM","target":"record","payload":{"canonical_record":{"source":{"id":"1607.06989","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-07-24T01:24:01Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"1a4fedd08aaf1f26754a52f20722938b58b7191e5364447e3de0dc2d7760adf9","abstract_canon_sha256":"5d2e901f382134ad4c400f632fcf114a37565420b762134865e0c645563ffd33"},"schema_version":"1.0"},"canonical_sha256":"f0c7802ce79f21d34212718ce9fd320b397c7441b705b6389e328eb69e8c251d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:35.230969Z","signature_b64":"sQKpE+p/6yrpCG6FjzbGHb4r84ZQBMeGmJNHRnxP9WT4MzlFIlkVuP+a2Qj2QJhphVGkOiwH+K2Gt1MhKuMZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0c7802ce79f21d34212718ce9fd320b397c7441b705b6389e328eb69e8c251d","last_reissued_at":"2026-05-18T01:10:35.230480Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:35.230480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.06989","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:10:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"axlLJGxIm6HOKp3icgCfBWuql9pv6snguYbE5fqnaS4z+NfGsSac0e0pKhi3lhg2JWYUjWjbbN1cA7wrSuUWAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:55:08.692415Z"},"content_sha256":"840ab615f7797d29b64eea4dc1d5963e1c2f185223cbf0ba83e3bd232f4427c4","schema_version":"1.0","event_id":"sha256:840ab615f7797d29b64eea4dc1d5963e1c2f185223cbf0ba83e3bd232f4427c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6DDYALHHT4Q5GQQSOGGOT7JSBM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eventual positivity of Hermitian algebraic functions and associated integral operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Colin Tan, Wing-Keung To","submitted_at":"2016-07-24T01:24:01Z","abstract_excerpt":"Quillen proved that repeated multiplication of the standard sesquilinear form to a positive Hermitian bihomogeneous polynomial eventually results in a sum of Hermitian squares, which was the first Hermitian analogue of Hilbert's seventeenth problem in the nondegenerate case. Later Catlin-D'Angelo generalized this positivstellensatz of Quillen to the case of Hermitian algebraic functions on holomorphic line bundles over compact complex manifolds by proving the eventual positivity of an associated integral operator. The arguments of Catlin-D'Angelo, as well as that of a subsequent refinement by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06989","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:10:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xEhTKog+xMAMAbYZtWWyk/OCQQFsw0j9PDTJ/yf1AUhv3pNnRbQzAO3Zi2pvoXTp0KPKj40H7obvbMx7/WYDBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:55:08.692764Z"},"content_sha256":"78c689cc6da8ff54e73507cdae45c2084c48805def7f8f2175bf35bee2d187ba","schema_version":"1.0","event_id":"sha256:78c689cc6da8ff54e73507cdae45c2084c48805def7f8f2175bf35bee2d187ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6DDYALHHT4Q5GQQSOGGOT7JSBM/bundle.json","state_url":"https://pith.science/pith/6DDYALHHT4Q5GQQSOGGOT7JSBM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6DDYALHHT4Q5GQQSOGGOT7JSBM/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":"2026-06-08T14:55:08Z","links":{"resolver":"https://pith.science/pith/6DDYALHHT4Q5GQQSOGGOT7JSBM","bundle":"https://pith.science/pith/6DDYALHHT4Q5GQQSOGGOT7JSBM/bundle.json","state":"https://pith.science/pith/6DDYALHHT4Q5GQQSOGGOT7JSBM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6DDYALHHT4Q5GQQSOGGOT7JSBM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6DDYALHHT4Q5GQQSOGGOT7JSBM","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":"5d2e901f382134ad4c400f632fcf114a37565420b762134865e0c645563ffd33","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-07-24T01:24:01Z","title_canon_sha256":"1a4fedd08aaf1f26754a52f20722938b58b7191e5364447e3de0dc2d7760adf9"},"schema_version":"1.0","source":{"id":"1607.06989","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06989","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06989v1","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06989","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"pith_short_12","alias_value":"6DDYALHHT4Q5","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6DDYALHHT4Q5GQQS","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6DDYALHH","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:78c689cc6da8ff54e73507cdae45c2084c48805def7f8f2175bf35bee2d187ba","target":"graph","created_at":"2026-05-18T01:10:35Z","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":"Quillen proved that repeated multiplication of the standard sesquilinear form to a positive Hermitian bihomogeneous polynomial eventually results in a sum of Hermitian squares, which was the first Hermitian analogue of Hilbert's seventeenth problem in the nondegenerate case. Later Catlin-D'Angelo generalized this positivstellensatz of Quillen to the case of Hermitian algebraic functions on holomorphic line bundles over compact complex manifolds by proving the eventual positivity of an associated integral operator. The arguments of Catlin-D'Angelo, as well as that of a subsequent refinement by ","authors_text":"Colin Tan, Wing-Keung To","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-07-24T01:24:01Z","title":"Eventual positivity of Hermitian algebraic functions and associated integral operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06989","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":"sha256:840ab615f7797d29b64eea4dc1d5963e1c2f185223cbf0ba83e3bd232f4427c4","target":"record","created_at":"2026-05-18T01:10:35Z","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":"5d2e901f382134ad4c400f632fcf114a37565420b762134865e0c645563ffd33","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-07-24T01:24:01Z","title_canon_sha256":"1a4fedd08aaf1f26754a52f20722938b58b7191e5364447e3de0dc2d7760adf9"},"schema_version":"1.0","source":{"id":"1607.06989","kind":"arxiv","version":1}},"canonical_sha256":"f0c7802ce79f21d34212718ce9fd320b397c7441b705b6389e328eb69e8c251d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0c7802ce79f21d34212718ce9fd320b397c7441b705b6389e328eb69e8c251d","first_computed_at":"2026-05-18T01:10:35.230480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:35.230480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sQKpE+p/6yrpCG6FjzbGHb4r84ZQBMeGmJNHRnxP9WT4MzlFIlkVuP+a2Qj2QJhphVGkOiwH+K2Gt1MhKuMZCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:35.230969Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.06989","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:840ab615f7797d29b64eea4dc1d5963e1c2f185223cbf0ba83e3bd232f4427c4","sha256:78c689cc6da8ff54e73507cdae45c2084c48805def7f8f2175bf35bee2d187ba"],"state_sha256":"53268d0491d1c906809eecb90fbd330072ad19c5b84272b14e97ca336af531e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fIYGc5092aRcP+RFj04y6Dyt8shLunC1N2/i1iYWZgFpmgAOtb13OE4Up1uYU2VJf8I8QiHYTBlvHwO4RrowDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T14:55:08.694760Z","bundle_sha256":"2d86fc34c231a60e470a3d71786037d57deda6ac128ad8a4fa0a1c0e58da5756"}}