{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ECN4HANY6KE4CNRNHASQHBHXLY","short_pith_number":"pith:ECN4HANY","canonical_record":{"source":{"id":"1108.4380","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-22T17:14:05Z","cross_cats_sorted":["cs.SY","math.OC"],"title_canon_sha256":"66899de995685240287ea8a058295deec7583f9c53868af6dab27715e5345331","abstract_canon_sha256":"3bb83c22a1ed2e2c8314001fbd0100756b24aa8253826246682d3e1ff76d7446"},"schema_version":"1.0"},"canonical_sha256":"209bc381b8f289c1362d38250384f75e0ce4c5512bedceb4c83f2a0cbc5861fa","source":{"kind":"arxiv","id":"1108.4380","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4380","created_at":"2026-05-18T04:14:55Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4380v1","created_at":"2026-05-18T04:14:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4380","created_at":"2026-05-18T04:14:55Z"},{"alias_kind":"pith_short_12","alias_value":"ECN4HANY6KE4","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"ECN4HANY6KE4CNRN","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"ECN4HANY","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ECN4HANY6KE4CNRNHASQHBHXLY","target":"record","payload":{"canonical_record":{"source":{"id":"1108.4380","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-22T17:14:05Z","cross_cats_sorted":["cs.SY","math.OC"],"title_canon_sha256":"66899de995685240287ea8a058295deec7583f9c53868af6dab27715e5345331","abstract_canon_sha256":"3bb83c22a1ed2e2c8314001fbd0100756b24aa8253826246682d3e1ff76d7446"},"schema_version":"1.0"},"canonical_sha256":"209bc381b8f289c1362d38250384f75e0ce4c5512bedceb4c83f2a0cbc5861fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:55.624101Z","signature_b64":"by41YW5KcgqgUUXA5BNhxXZYzw/7t8+wfy/iGnA9AcWzt/aADUmIyxfnc6GWODd1nlCJ8YqHE8FvNvWGBxhEDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"209bc381b8f289c1362d38250384f75e0ce4c5512bedceb4c83f2a0cbc5861fa","last_reissued_at":"2026-05-18T04:14:55.623639Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:55.623639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.4380","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":"2026-05-18T04:14:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7rbex8NJ6D/0i2iggwVnm9KrU6KfvLjjjxkFQNaGnhTyqKfhYvIAt9ed+b51L6BObqc2lUYUqaN3tLeSpRweBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:38:43.260398Z"},"content_sha256":"19e4c57abfa3cf1509f5c603e0818543a1bbf10aa618f76aa2c58169dd9e7ca2","schema_version":"1.0","event_id":"sha256:19e4c57abfa3cf1509f5c603e0818543a1bbf10aa618f76aa2c58169dd9e7ca2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ECN4HANY6KE4CNRNHASQHBHXLY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Determinantal Representations and the Hermite Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.OC"],"primary_cat":"math.AG","authors_text":"Andreas Thom, Daniel Plaumann, Tim Netzer","submitted_at":"2011-08-22T17:14:05Z","abstract_excerpt":"We consider the problem of writing real polynomials as determinants of symmetric linear matrix polynomials. This problem of algebraic geometry, whose roots go back to the nineteenth century, has recently received new attention from the viewpoint of convex optimization. We relate the question to sums of squares decompositions of a certain Hermite matrix. If some power of a polynomial admits a definite determinantal representation, then its Hermite matrix is a sum of squares. Conversely, we show how a determinantal representation can sometimes be constructed from a sums-of-squares decomposition "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4380","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":"2026-05-18T04:14:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8FX2GYBbvj+tOAS4gFU3Rhu8LiGMYynuKgbDTJjw2TLMF7MWZ1tfkALSDQ3x7hjtWx1Rmo0bVMqTJrpp0HGFCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:38:43.260744Z"},"content_sha256":"1c389e65cd1e52817383a7090c4129b6c23071a634c1325f56f0f01f5a129075","schema_version":"1.0","event_id":"sha256:1c389e65cd1e52817383a7090c4129b6c23071a634c1325f56f0f01f5a129075"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ECN4HANY6KE4CNRNHASQHBHXLY/bundle.json","state_url":"https://pith.science/pith/ECN4HANY6KE4CNRNHASQHBHXLY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ECN4HANY6KE4CNRNHASQHBHXLY/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":"2026-06-25T09:38:43Z","links":{"resolver":"https://pith.science/pith/ECN4HANY6KE4CNRNHASQHBHXLY","bundle":"https://pith.science/pith/ECN4HANY6KE4CNRNHASQHBHXLY/bundle.json","state":"https://pith.science/pith/ECN4HANY6KE4CNRNHASQHBHXLY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ECN4HANY6KE4CNRNHASQHBHXLY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ECN4HANY6KE4CNRNHASQHBHXLY","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":"3bb83c22a1ed2e2c8314001fbd0100756b24aa8253826246682d3e1ff76d7446","cross_cats_sorted":["cs.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-22T17:14:05Z","title_canon_sha256":"66899de995685240287ea8a058295deec7583f9c53868af6dab27715e5345331"},"schema_version":"1.0","source":{"id":"1108.4380","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.4380","created_at":"2026-05-18T04:14:55Z"},{"alias_kind":"arxiv_version","alias_value":"1108.4380v1","created_at":"2026-05-18T04:14:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.4380","created_at":"2026-05-18T04:14:55Z"},{"alias_kind":"pith_short_12","alias_value":"ECN4HANY6KE4","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"ECN4HANY6KE4CNRN","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"ECN4HANY","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:1c389e65cd1e52817383a7090c4129b6c23071a634c1325f56f0f01f5a129075","target":"graph","created_at":"2026-05-18T04:14:55Z","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 consider the problem of writing real polynomials as determinants of symmetric linear matrix polynomials. This problem of algebraic geometry, whose roots go back to the nineteenth century, has recently received new attention from the viewpoint of convex optimization. We relate the question to sums of squares decompositions of a certain Hermite matrix. If some power of a polynomial admits a definite determinantal representation, then its Hermite matrix is a sum of squares. Conversely, we show how a determinantal representation can sometimes be constructed from a sums-of-squares decomposition ","authors_text":"Andreas Thom, Daniel Plaumann, Tim Netzer","cross_cats":["cs.SY","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-22T17:14:05Z","title":"Determinantal Representations and the Hermite Matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4380","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":"sha256:19e4c57abfa3cf1509f5c603e0818543a1bbf10aa618f76aa2c58169dd9e7ca2","target":"record","created_at":"2026-05-18T04:14:55Z","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":"3bb83c22a1ed2e2c8314001fbd0100756b24aa8253826246682d3e1ff76d7446","cross_cats_sorted":["cs.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-22T17:14:05Z","title_canon_sha256":"66899de995685240287ea8a058295deec7583f9c53868af6dab27715e5345331"},"schema_version":"1.0","source":{"id":"1108.4380","kind":"arxiv","version":1}},"canonical_sha256":"209bc381b8f289c1362d38250384f75e0ce4c5512bedceb4c83f2a0cbc5861fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"209bc381b8f289c1362d38250384f75e0ce4c5512bedceb4c83f2a0cbc5861fa","first_computed_at":"2026-05-18T04:14:55.623639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:55.623639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"by41YW5KcgqgUUXA5BNhxXZYzw/7t8+wfy/iGnA9AcWzt/aADUmIyxfnc6GWODd1nlCJ8YqHE8FvNvWGBxhEDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:55.624101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.4380","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19e4c57abfa3cf1509f5c603e0818543a1bbf10aa618f76aa2c58169dd9e7ca2","sha256:1c389e65cd1e52817383a7090c4129b6c23071a634c1325f56f0f01f5a129075"],"state_sha256":"b219a46340c1eda9703b4da60c94b60ecf941ce6077b882dc0d7fa86bd6fd5a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z/LaDOIoSAMFbg474edcqSsteCmCe9UAxi1A24nTngzlqNPSRG0+8EdQmqPHptscxa5bSFY3w0oCLP6Ag5m6Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T09:38:43.262632Z","bundle_sha256":"c713a37fc5f8e1f43412607179fedf0aea96f43f439371518a1fdc4e8f0b8495"}}