{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HQNJCLQP5VQHSSIBKTNMNOQ6RH","short_pith_number":"pith:HQNJCLQP","canonical_record":{"source":{"id":"1411.1661","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-06T16:57:34Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"97e7a1df863d26c97d9dc40bcbd12cff815adc627779af4ed3f32a6b14c795c3","abstract_canon_sha256":"ff3debd7f25fae77675f2a99267424a80d2147fc045f89e290c84267da0a75a6"},"schema_version":"1.0"},"canonical_sha256":"3c1a912e0fed6079490154dac6ba1e89e8669793c130955acd46dd6f2eab6e5c","source":{"kind":"arxiv","id":"1411.1661","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1661","created_at":"2026-05-18T01:44:11Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1661v2","created_at":"2026-05-18T01:44:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1661","created_at":"2026-05-18T01:44:11Z"},{"alias_kind":"pith_short_12","alias_value":"HQNJCLQP5VQH","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HQNJCLQP5VQHSSIB","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HQNJCLQP","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HQNJCLQP5VQHSSIBKTNMNOQ6RH","target":"record","payload":{"canonical_record":{"source":{"id":"1411.1661","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-06T16:57:34Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"97e7a1df863d26c97d9dc40bcbd12cff815adc627779af4ed3f32a6b14c795c3","abstract_canon_sha256":"ff3debd7f25fae77675f2a99267424a80d2147fc045f89e290c84267da0a75a6"},"schema_version":"1.0"},"canonical_sha256":"3c1a912e0fed6079490154dac6ba1e89e8669793c130955acd46dd6f2eab6e5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:11.689596Z","signature_b64":"F139qH0QgqBdm60oegfRS1R6PHA6gEFEkqYkrDfzeLxFM/3ATb+CzEyIcB3IarF3cCuqiOMrZ9hpVUoN5F1wCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c1a912e0fed6079490154dac6ba1e89e8669793c130955acd46dd6f2eab6e5c","last_reissued_at":"2026-05-18T01:44:11.688795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:11.688795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.1661","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":"2026-05-18T01:44:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LMXIRvMQqVQ6feFlLrdtx8eR8iAnFX3qehS2p2D9FGamIfbxQvk6br/vkc66aUcjx1KFqP/h7/49DJplRd8+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:11:43.210244Z"},"content_sha256":"1479985aaff19388b4198a75704ce8b0622d5da7dfe517aad523e9b6ef17f9b8","schema_version":"1.0","event_id":"sha256:1479985aaff19388b4198a75704ce8b0622d5da7dfe517aad523e9b6ef17f9b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HQNJCLQP5VQHSSIBKTNMNOQ6RH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Definite Determinantal Representations of Ternary Hyperbolic Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AG","authors_text":"Christoph Hanselka","submitted_at":"2014-11-06T16:57:34Z","abstract_excerpt":"We give a new and completely algebraic proof of the Helton-Vinnikov Theorem stating that every hyperbolic polynomial in three variables admits a definite linear determinantal representation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1661","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":"2026-05-18T01:44:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5TMkkRf5v017X+qm8d9/P2tWVLUDEs9pBbsXgFez6/jDrxl6Mfpcn7lfyYR/bBUSBf8KJnGRpFBUCmunD7buCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:11:43.210606Z"},"content_sha256":"d0e29b21ead6eae36e368e411413fb574912236b68524c3c05e9b345e1950fc3","schema_version":"1.0","event_id":"sha256:d0e29b21ead6eae36e368e411413fb574912236b68524c3c05e9b345e1950fc3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HQNJCLQP5VQHSSIBKTNMNOQ6RH/bundle.json","state_url":"https://pith.science/pith/HQNJCLQP5VQHSSIBKTNMNOQ6RH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HQNJCLQP5VQHSSIBKTNMNOQ6RH/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":"2026-06-24T19:11:43Z","links":{"resolver":"https://pith.science/pith/HQNJCLQP5VQHSSIBKTNMNOQ6RH","bundle":"https://pith.science/pith/HQNJCLQP5VQHSSIBKTNMNOQ6RH/bundle.json","state":"https://pith.science/pith/HQNJCLQP5VQHSSIBKTNMNOQ6RH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HQNJCLQP5VQHSSIBKTNMNOQ6RH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HQNJCLQP5VQHSSIBKTNMNOQ6RH","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":"ff3debd7f25fae77675f2a99267424a80d2147fc045f89e290c84267da0a75a6","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-06T16:57:34Z","title_canon_sha256":"97e7a1df863d26c97d9dc40bcbd12cff815adc627779af4ed3f32a6b14c795c3"},"schema_version":"1.0","source":{"id":"1411.1661","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1661","created_at":"2026-05-18T01:44:11Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1661v2","created_at":"2026-05-18T01:44:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1661","created_at":"2026-05-18T01:44:11Z"},{"alias_kind":"pith_short_12","alias_value":"HQNJCLQP5VQH","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HQNJCLQP5VQHSSIB","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HQNJCLQP","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:d0e29b21ead6eae36e368e411413fb574912236b68524c3c05e9b345e1950fc3","target":"graph","created_at":"2026-05-18T01:44:11Z","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":"We give a new and completely algebraic proof of the Helton-Vinnikov Theorem stating that every hyperbolic polynomial in three variables admits a definite linear determinantal representation.","authors_text":"Christoph Hanselka","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-06T16:57:34Z","title":"Definite Determinantal Representations of Ternary Hyperbolic Forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1661","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":"sha256:1479985aaff19388b4198a75704ce8b0622d5da7dfe517aad523e9b6ef17f9b8","target":"record","created_at":"2026-05-18T01:44:11Z","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":"ff3debd7f25fae77675f2a99267424a80d2147fc045f89e290c84267da0a75a6","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-06T16:57:34Z","title_canon_sha256":"97e7a1df863d26c97d9dc40bcbd12cff815adc627779af4ed3f32a6b14c795c3"},"schema_version":"1.0","source":{"id":"1411.1661","kind":"arxiv","version":2}},"canonical_sha256":"3c1a912e0fed6079490154dac6ba1e89e8669793c130955acd46dd6f2eab6e5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c1a912e0fed6079490154dac6ba1e89e8669793c130955acd46dd6f2eab6e5c","first_computed_at":"2026-05-18T01:44:11.688795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:44:11.688795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F139qH0QgqBdm60oegfRS1R6PHA6gEFEkqYkrDfzeLxFM/3ATb+CzEyIcB3IarF3cCuqiOMrZ9hpVUoN5F1wCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:44:11.689596Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.1661","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1479985aaff19388b4198a75704ce8b0622d5da7dfe517aad523e9b6ef17f9b8","sha256:d0e29b21ead6eae36e368e411413fb574912236b68524c3c05e9b345e1950fc3"],"state_sha256":"ef93a5ee969e69cae14a4f05189457cdfd6e00d66abdd3464df2225467ee0908"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4pz+iiC/t2O8ZpKM2q+ezytOxGGfjU7fXJe5Wrz4eq+Pk/yWRKunMjyy63JQzg6Ft7VS94tuM6I52QvdPZd5Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T19:11:43.212445Z","bundle_sha256":"83cc3e8d2f735a2f7d35dfd795d6fba14178a1f1cc95c8db712721167f642e37"}}