{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UN67FJNG7T3BARHOO7EEEVF6WB","short_pith_number":"pith:UN67FJNG","canonical_record":{"source":{"id":"1609.00498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-02T08:22:28Z","cross_cats_sorted":["cs.NA","math.AG"],"title_canon_sha256":"4567c589cd0659b38abb0f040bdad005020735f00fe2c55cad0c126ea0ee59d1","abstract_canon_sha256":"cdd8070dba9c57fe226c9fad3369c972ad4153a55cd26d938074f13a8d00b6e6"},"schema_version":"1.0"},"canonical_sha256":"a37df2a5a6fcf61044ee77c84254beb06075704d7e454d1ca2c4d49c1b32b51c","source":{"kind":"arxiv","id":"1609.00498","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00498","created_at":"2026-06-04T18:09:59Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00498v1","created_at":"2026-06-04T18:09:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00498","created_at":"2026-06-04T18:09:59Z"},{"alias_kind":"pith_short_12","alias_value":"UN67FJNG7T3B","created_at":"2026-06-04T18:09:59Z"},{"alias_kind":"pith_short_16","alias_value":"UN67FJNG7T3BARHO","created_at":"2026-06-04T18:09:59Z"},{"alias_kind":"pith_short_8","alias_value":"UN67FJNG","created_at":"2026-06-04T18:09:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UN67FJNG7T3BARHOO7EEEVF6WB","target":"record","payload":{"canonical_record":{"source":{"id":"1609.00498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-02T08:22:28Z","cross_cats_sorted":["cs.NA","math.AG"],"title_canon_sha256":"4567c589cd0659b38abb0f040bdad005020735f00fe2c55cad0c126ea0ee59d1","abstract_canon_sha256":"cdd8070dba9c57fe226c9fad3369c972ad4153a55cd26d938074f13a8d00b6e6"},"schema_version":"1.0"},"canonical_sha256":"a37df2a5a6fcf61044ee77c84254beb06075704d7e454d1ca2c4d49c1b32b51c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T18:09:59.410783Z","signature_b64":"bOn6qnCurDwS85XSHYfcgT2LBvdCoKdvMEBQylqvvcK/G0GyjfWQhdmd3BhodvOIHJcbkPcTXch9B3U6dS+OAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a37df2a5a6fcf61044ee77c84254beb06075704d7e454d1ca2c4d49c1b32b51c","last_reissued_at":"2026-06-04T18:09:59.410282Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T18:09:59.410282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.00498","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":"2026-06-04T18:09:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qln9HuU3QeY3GUsMlYCfJQWLc2+cbVlsBrZMFM0tECG94AKfmegTkpEAp8WXkvrA17mqUdpqkaJTr9ijMlUnBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T05:15:11.250999Z"},"content_sha256":"21f44f6621632bbfbae6543b381fb1640c8eb85ec2f07ad85a8da19e1e1f4809","schema_version":"1.0","event_id":"sha256:21f44f6621632bbfbae6543b381fb1640c8eb85ec2f07ad85a8da19e1e1f4809"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UN67FJNG7T3BARHOO7EEEVF6WB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simple determinantal representations of up to quintic bivariate polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AG"],"primary_cat":"math.NA","authors_text":"Anita Buckley, Bor Plestenjak","submitted_at":"2016-09-02T08:22:28Z","abstract_excerpt":"For bivariate polynomials of degree $n\\le 5$ we give fast numerical constructions of determinantal representations with $n\\times n$ matrices. Unlike some other available constructions, our approach returns matrices of the smallest possible size $n\\times n$ for all polynomials of degree $n$ and does not require any symbolic computation. We can apply these linearizations to numerically compute the roots of a system of two bivariate polynomials by using numerical methods for two-parameter eigenvalue problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00498","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1609.00498/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-04T18:09:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FfTpkjN6VyLygN+Ge2YigF8TtJWy2unZgo3PTXZWtv2RGAoGs0cwF/HF8cFV8pWGFU03vtAfifb2RPe1gQaGAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T05:15:11.251432Z"},"content_sha256":"ac1f99de33de733f370c53f7658660f006a608469f10e5f12c591b3a15cf6c8c","schema_version":"1.0","event_id":"sha256:ac1f99de33de733f370c53f7658660f006a608469f10e5f12c591b3a15cf6c8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UN67FJNG7T3BARHOO7EEEVF6WB/bundle.json","state_url":"https://pith.science/pith/UN67FJNG7T3BARHOO7EEEVF6WB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UN67FJNG7T3BARHOO7EEEVF6WB/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":"2026-06-07T05:15:11Z","links":{"resolver":"https://pith.science/pith/UN67FJNG7T3BARHOO7EEEVF6WB","bundle":"https://pith.science/pith/UN67FJNG7T3BARHOO7EEEVF6WB/bundle.json","state":"https://pith.science/pith/UN67FJNG7T3BARHOO7EEEVF6WB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UN67FJNG7T3BARHOO7EEEVF6WB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UN67FJNG7T3BARHOO7EEEVF6WB","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":"cdd8070dba9c57fe226c9fad3369c972ad4153a55cd26d938074f13a8d00b6e6","cross_cats_sorted":["cs.NA","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-02T08:22:28Z","title_canon_sha256":"4567c589cd0659b38abb0f040bdad005020735f00fe2c55cad0c126ea0ee59d1"},"schema_version":"1.0","source":{"id":"1609.00498","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00498","created_at":"2026-06-04T18:09:59Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00498v1","created_at":"2026-06-04T18:09:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00498","created_at":"2026-06-04T18:09:59Z"},{"alias_kind":"pith_short_12","alias_value":"UN67FJNG7T3B","created_at":"2026-06-04T18:09:59Z"},{"alias_kind":"pith_short_16","alias_value":"UN67FJNG7T3BARHO","created_at":"2026-06-04T18:09:59Z"},{"alias_kind":"pith_short_8","alias_value":"UN67FJNG","created_at":"2026-06-04T18:09:59Z"}],"graph_snapshots":[{"event_id":"sha256:ac1f99de33de733f370c53f7658660f006a608469f10e5f12c591b3a15cf6c8c","target":"graph","created_at":"2026-06-04T18:09:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1609.00498/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For bivariate polynomials of degree $n\\le 5$ we give fast numerical constructions of determinantal representations with $n\\times n$ matrices. Unlike some other available constructions, our approach returns matrices of the smallest possible size $n\\times n$ for all polynomials of degree $n$ and does not require any symbolic computation. We can apply these linearizations to numerically compute the roots of a system of two bivariate polynomials by using numerical methods for two-parameter eigenvalue problems.","authors_text":"Anita Buckley, Bor Plestenjak","cross_cats":["cs.NA","math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-02T08:22:28Z","title":"Simple determinantal representations of up to quintic bivariate polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00498","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":"sha256:21f44f6621632bbfbae6543b381fb1640c8eb85ec2f07ad85a8da19e1e1f4809","target":"record","created_at":"2026-06-04T18:09:59Z","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":"cdd8070dba9c57fe226c9fad3369c972ad4153a55cd26d938074f13a8d00b6e6","cross_cats_sorted":["cs.NA","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-02T08:22:28Z","title_canon_sha256":"4567c589cd0659b38abb0f040bdad005020735f00fe2c55cad0c126ea0ee59d1"},"schema_version":"1.0","source":{"id":"1609.00498","kind":"arxiv","version":1}},"canonical_sha256":"a37df2a5a6fcf61044ee77c84254beb06075704d7e454d1ca2c4d49c1b32b51c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a37df2a5a6fcf61044ee77c84254beb06075704d7e454d1ca2c4d49c1b32b51c","first_computed_at":"2026-06-04T18:09:59.410282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T18:09:59.410282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bOn6qnCurDwS85XSHYfcgT2LBvdCoKdvMEBQylqvvcK/G0GyjfWQhdmd3BhodvOIHJcbkPcTXch9B3U6dS+OAw==","signature_status":"signed_v1","signed_at":"2026-06-04T18:09:59.410783Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.00498","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21f44f6621632bbfbae6543b381fb1640c8eb85ec2f07ad85a8da19e1e1f4809","sha256:ac1f99de33de733f370c53f7658660f006a608469f10e5f12c591b3a15cf6c8c"],"state_sha256":"90bf5d18a19149b10227697722e12884e8022879f5639f6af679a83a935df198"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MV2RefQQdVtJUSUr/Yq3gnRtC4NulhVGr3zTg7MpTC+8H811PiyYTXelgrAe5UVqM/VLbLOio2w6i5XWmV9bDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T05:15:11.253327Z","bundle_sha256":"cdc96bf61f213f551980eb12e8a9065a799054ef2b76ab37cd4db5b9f580c50d"}}