{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GRBMDMVDVOK75XEXRIYV2WZFE6","short_pith_number":"pith:GRBMDMVD","canonical_record":{"source":{"id":"1612.07340","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-21T21:20:14Z","cross_cats_sorted":[],"title_canon_sha256":"9276eb69c7d7c1f8fe25c300081ad16c348890b80c67b9027a74c56c728472ab","abstract_canon_sha256":"3251cf2a43df715963c9136dd8a21e96eaae828e0f0a3bb9b1283c126e6787c9"},"schema_version":"1.0"},"canonical_sha256":"3442c1b2a3ab95fedc978a315d5b25279c5521dd234a72a4cbec0cb3ff38c2f9","source":{"kind":"arxiv","id":"1612.07340","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07340","created_at":"2026-05-18T00:24:22Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07340v2","created_at":"2026-05-18T00:24:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07340","created_at":"2026-05-18T00:24:22Z"},{"alias_kind":"pith_short_12","alias_value":"GRBMDMVDVOK7","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GRBMDMVDVOK75XEX","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GRBMDMVD","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GRBMDMVDVOK75XEXRIYV2WZFE6","target":"record","payload":{"canonical_record":{"source":{"id":"1612.07340","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-21T21:20:14Z","cross_cats_sorted":[],"title_canon_sha256":"9276eb69c7d7c1f8fe25c300081ad16c348890b80c67b9027a74c56c728472ab","abstract_canon_sha256":"3251cf2a43df715963c9136dd8a21e96eaae828e0f0a3bb9b1283c126e6787c9"},"schema_version":"1.0"},"canonical_sha256":"3442c1b2a3ab95fedc978a315d5b25279c5521dd234a72a4cbec0cb3ff38c2f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:22.717700Z","signature_b64":"Vgd7Gu3zieZ5/pTOCkqLqOeKRRLNdSzZzAeAm/sFc/iZpfeHgat9ZVY3CvTPrXFYoV37wDS1BN0G0mnoxIUPAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3442c1b2a3ab95fedc978a315d5b25279c5521dd234a72a4cbec0cb3ff38c2f9","last_reissued_at":"2026-05-18T00:24:22.717237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:22.717237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.07340","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":"2026-05-18T00:24:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S3qWAZs0njMyJlmmg3Q+aHS3D5KM5QTdBQUovamcwRM8Gp9Ia9STymaqmKbsWgul6ZIOdu9x01bLdyBssrdiDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:15:22.905155Z"},"content_sha256":"384a858c68c189c4d937eb6437521c62976f205e75f2c410579f954e462ae0b4","schema_version":"1.0","event_id":"sha256:384a858c68c189c4d937eb6437521c62976f205e75f2c410579f954e462ae0b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GRBMDMVDVOK75XEXRIYV2WZFE6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symbolic computation in hyperbolic programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Daniel Plaumann, Simone Naldi","submitted_at":"2016-12-21T21:20:14Z","abstract_excerpt":"Hyperbolic programming is the problem of computing the infimum of a linear function when restricted to the hyperbolicity cone of a hyperbolic polynomial, a generalization of semidefinite programming. We propose an approach based on symbolic computation, relying on the multiplicity structure of the algebraic boundary of the cone, without the assumption of determinantal representability. This allows us to design exact algorithms able to certify the multiplicity of the solution and the optimal value of the linear function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07340","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":"2026-05-18T00:24:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o1sVcFgkufJrUWn67riKd2zneKm25ncx6PL8j4seI6NtufLYXH0yA4cgK+UW2Dtka3SVY9rcC0P95jV1NikvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:15:22.905574Z"},"content_sha256":"2fbbf7c9344ec22d572c1ec27f78288a0f1d1e17715b1ee5913fa0073bc3dc52","schema_version":"1.0","event_id":"sha256:2fbbf7c9344ec22d572c1ec27f78288a0f1d1e17715b1ee5913fa0073bc3dc52"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GRBMDMVDVOK75XEXRIYV2WZFE6/bundle.json","state_url":"https://pith.science/pith/GRBMDMVDVOK75XEXRIYV2WZFE6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GRBMDMVDVOK75XEXRIYV2WZFE6/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":"2026-06-05T08:15:22Z","links":{"resolver":"https://pith.science/pith/GRBMDMVDVOK75XEXRIYV2WZFE6","bundle":"https://pith.science/pith/GRBMDMVDVOK75XEXRIYV2WZFE6/bundle.json","state":"https://pith.science/pith/GRBMDMVDVOK75XEXRIYV2WZFE6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GRBMDMVDVOK75XEXRIYV2WZFE6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GRBMDMVDVOK75XEXRIYV2WZFE6","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":"3251cf2a43df715963c9136dd8a21e96eaae828e0f0a3bb9b1283c126e6787c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-21T21:20:14Z","title_canon_sha256":"9276eb69c7d7c1f8fe25c300081ad16c348890b80c67b9027a74c56c728472ab"},"schema_version":"1.0","source":{"id":"1612.07340","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07340","created_at":"2026-05-18T00:24:22Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07340v2","created_at":"2026-05-18T00:24:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07340","created_at":"2026-05-18T00:24:22Z"},{"alias_kind":"pith_short_12","alias_value":"GRBMDMVDVOK7","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GRBMDMVDVOK75XEX","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GRBMDMVD","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:2fbbf7c9344ec22d572c1ec27f78288a0f1d1e17715b1ee5913fa0073bc3dc52","target":"graph","created_at":"2026-05-18T00:24:22Z","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":"Hyperbolic programming is the problem of computing the infimum of a linear function when restricted to the hyperbolicity cone of a hyperbolic polynomial, a generalization of semidefinite programming. We propose an approach based on symbolic computation, relying on the multiplicity structure of the algebraic boundary of the cone, without the assumption of determinantal representability. This allows us to design exact algorithms able to certify the multiplicity of the solution and the optimal value of the linear function.","authors_text":"Daniel Plaumann, Simone Naldi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-21T21:20:14Z","title":"Symbolic computation in hyperbolic programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07340","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":"sha256:384a858c68c189c4d937eb6437521c62976f205e75f2c410579f954e462ae0b4","target":"record","created_at":"2026-05-18T00:24:22Z","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":"3251cf2a43df715963c9136dd8a21e96eaae828e0f0a3bb9b1283c126e6787c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-12-21T21:20:14Z","title_canon_sha256":"9276eb69c7d7c1f8fe25c300081ad16c348890b80c67b9027a74c56c728472ab"},"schema_version":"1.0","source":{"id":"1612.07340","kind":"arxiv","version":2}},"canonical_sha256":"3442c1b2a3ab95fedc978a315d5b25279c5521dd234a72a4cbec0cb3ff38c2f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3442c1b2a3ab95fedc978a315d5b25279c5521dd234a72a4cbec0cb3ff38c2f9","first_computed_at":"2026-05-18T00:24:22.717237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:22.717237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vgd7Gu3zieZ5/pTOCkqLqOeKRRLNdSzZzAeAm/sFc/iZpfeHgat9ZVY3CvTPrXFYoV37wDS1BN0G0mnoxIUPAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:22.717700Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.07340","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:384a858c68c189c4d937eb6437521c62976f205e75f2c410579f954e462ae0b4","sha256:2fbbf7c9344ec22d572c1ec27f78288a0f1d1e17715b1ee5913fa0073bc3dc52"],"state_sha256":"53163a308f0cf01379fb95de7c41484bf46f1bec0c316800e46ea959a1f67d13"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tZEC/Vx2UCitqSh42Hpy9l8GXDyyDa12TUMSD88eS7u8azMKTYXVmPMf6PEoLUm4T2Akr6Bb5EtmbhwrvTskCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T08:15:22.907531Z","bundle_sha256":"1bd383ccf69e2c464c92eeb2dfccfa43412e8168809c15b24f81487a8279417c"}}