{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KO6KZ5BEIIXZ2UE42FYGE3DNI5","short_pith_number":"pith:KO6KZ5BE","canonical_record":{"source":{"id":"1611.06104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-18T14:40:05Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"d0895931bd5a07588a20ecfdd5a1a38417f7566e20bed895e3a0c1ab3d974ef6","abstract_canon_sha256":"b2a3cefb265edb9e47f8848c0c3184df755932f03635b7c5fafddb4c7d3b9341"},"schema_version":"1.0"},"canonical_sha256":"53bcacf424422f9d509cd170626c6d47453e37e5a0e4d1f80df17570b5d9be13","source":{"kind":"arxiv","id":"1611.06104","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06104","created_at":"2026-05-18T00:57:43Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06104v1","created_at":"2026-05-18T00:57:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06104","created_at":"2026-05-18T00:57:43Z"},{"alias_kind":"pith_short_12","alias_value":"KO6KZ5BEIIXZ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KO6KZ5BEIIXZ2UE4","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KO6KZ5BE","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KO6KZ5BEIIXZ2UE42FYGE3DNI5","target":"record","payload":{"canonical_record":{"source":{"id":"1611.06104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-18T14:40:05Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"d0895931bd5a07588a20ecfdd5a1a38417f7566e20bed895e3a0c1ab3d974ef6","abstract_canon_sha256":"b2a3cefb265edb9e47f8848c0c3184df755932f03635b7c5fafddb4c7d3b9341"},"schema_version":"1.0"},"canonical_sha256":"53bcacf424422f9d509cd170626c6d47453e37e5a0e4d1f80df17570b5d9be13","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:43.084248Z","signature_b64":"YEQ8uO9sCkTkE950SIPjUn0JzQa5aVvHJJxBG8SNqCfUDOZ7kUfgRcW+LQ77vwfRue2L7S6o5rUTz8ywkoF9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53bcacf424422f9d509cd170626c6d47453e37e5a0e4d1f80df17570b5d9be13","last_reissued_at":"2026-05-18T00:57:43.083840Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:43.083840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.06104","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":"2026-05-18T00:57:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S1Mp8Qql/pl96a/js4crOsGhkVf775HgFH3q+ZeC3mf4xsij7zvYmYaaKgSM8bqPl4R3fxEIc9A6I6bgzNWOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:03:50.458867Z"},"content_sha256":"91f8921307dc019618ac207479ca82e2d3803bfbed6510061a69c49a4966a4b1","schema_version":"1.0","event_id":"sha256:91f8921307dc019618ac207479ca82e2d3803bfbed6510061a69c49a4966a4b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KO6KZ5BEIIXZ2UE42FYGE3DNI5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectrahedrality of hyperbolicity cones of multivariate matching polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CO","authors_text":"Nima Amini","submitted_at":"2016-11-18T14:40:05Z","abstract_excerpt":"The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further extended (albeit in a weaker sense) to a multivariate version of the independence polynomial for simplicial graphs. As an application we give a new proof of the conjecture for elementary symmetric polynomials (originally due to Br\\\"and\\'en). Finally we consider a hyperbolic convolution of determinant polynomials generalizing an identity of Godsil and Gutman."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06104","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":"2026-05-18T00:57:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fzExC54Ji11/1iLEIFzDfdXp8vxoFih4UuJivmUKQN2jc/U/e0C4b4u1lKr8OTOhg3sM91b1jn3aZWW7xXSDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:03:50.459585Z"},"content_sha256":"a5ac56e893865df101221a21c1bf47c0387a9a39a098fd39072a5b27e0897166","schema_version":"1.0","event_id":"sha256:a5ac56e893865df101221a21c1bf47c0387a9a39a098fd39072a5b27e0897166"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KO6KZ5BEIIXZ2UE42FYGE3DNI5/bundle.json","state_url":"https://pith.science/pith/KO6KZ5BEIIXZ2UE42FYGE3DNI5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KO6KZ5BEIIXZ2UE42FYGE3DNI5/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":"2026-05-31T19:03:50Z","links":{"resolver":"https://pith.science/pith/KO6KZ5BEIIXZ2UE42FYGE3DNI5","bundle":"https://pith.science/pith/KO6KZ5BEIIXZ2UE42FYGE3DNI5/bundle.json","state":"https://pith.science/pith/KO6KZ5BEIIXZ2UE42FYGE3DNI5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KO6KZ5BEIIXZ2UE42FYGE3DNI5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KO6KZ5BEIIXZ2UE42FYGE3DNI5","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":"b2a3cefb265edb9e47f8848c0c3184df755932f03635b7c5fafddb4c7d3b9341","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-18T14:40:05Z","title_canon_sha256":"d0895931bd5a07588a20ecfdd5a1a38417f7566e20bed895e3a0c1ab3d974ef6"},"schema_version":"1.0","source":{"id":"1611.06104","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06104","created_at":"2026-05-18T00:57:43Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06104v1","created_at":"2026-05-18T00:57:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06104","created_at":"2026-05-18T00:57:43Z"},{"alias_kind":"pith_short_12","alias_value":"KO6KZ5BEIIXZ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KO6KZ5BEIIXZ2UE4","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KO6KZ5BE","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:a5ac56e893865df101221a21c1bf47c0387a9a39a098fd39072a5b27e0897166","target":"graph","created_at":"2026-05-18T00:57:43Z","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":"The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further extended (albeit in a weaker sense) to a multivariate version of the independence polynomial for simplicial graphs. As an application we give a new proof of the conjecture for elementary symmetric polynomials (originally due to Br\\\"and\\'en). Finally we consider a hyperbolic convolution of determinant polynomials generalizing an identity of Godsil and Gutman.","authors_text":"Nima Amini","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-18T14:40:05Z","title":"Spectrahedrality of hyperbolicity cones of multivariate matching polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06104","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":"sha256:91f8921307dc019618ac207479ca82e2d3803bfbed6510061a69c49a4966a4b1","target":"record","created_at":"2026-05-18T00:57:43Z","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":"b2a3cefb265edb9e47f8848c0c3184df755932f03635b7c5fafddb4c7d3b9341","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-18T14:40:05Z","title_canon_sha256":"d0895931bd5a07588a20ecfdd5a1a38417f7566e20bed895e3a0c1ab3d974ef6"},"schema_version":"1.0","source":{"id":"1611.06104","kind":"arxiv","version":1}},"canonical_sha256":"53bcacf424422f9d509cd170626c6d47453e37e5a0e4d1f80df17570b5d9be13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53bcacf424422f9d509cd170626c6d47453e37e5a0e4d1f80df17570b5d9be13","first_computed_at":"2026-05-18T00:57:43.083840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:43.083840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YEQ8uO9sCkTkE950SIPjUn0JzQa5aVvHJJxBG8SNqCfUDOZ7kUfgRcW+LQ77vwfRue2L7S6o5rUTz8ywkoF9DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:43.084248Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.06104","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91f8921307dc019618ac207479ca82e2d3803bfbed6510061a69c49a4966a4b1","sha256:a5ac56e893865df101221a21c1bf47c0387a9a39a098fd39072a5b27e0897166"],"state_sha256":"8b3e3699b79143c28f20283d9e5a7158c983f1cc33e93503792409e34088a9e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FZTKknY9Fs9sYADWbpcUYww9bjE7dUFJETRZegDwH059NVMmCLnIR+vnWP5bXpO5c/CE5oNbZtgE/oXzbvzHAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T19:03:50.463398Z","bundle_sha256":"9c4be53f3efa5b2afd76b0dc896775cae5c49399267349e8dc25ce2068b52471"}}