{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:427GYRH2CV2J64UMU5NGCQE3CN","short_pith_number":"pith:427GYRH2","canonical_record":{"source":{"id":"1203.3775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-16T18:21:57Z","cross_cats_sorted":[],"title_canon_sha256":"4eff4b934b27322c61829436a6fb09fff3bc7b87af7f94a21148b8180cc05326","abstract_canon_sha256":"167c0a4ed1cf52d57abfb775f360c8c44e7e674eb5a7d2f5bb56a1c55b4be406"},"schema_version":"1.0"},"canonical_sha256":"e6be6c44fa15749f728ca75a61409b1340767f51d431cd0907b86cb88557a6ae","source":{"kind":"arxiv","id":"1203.3775","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3775","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3775v1","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3775","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"pith_short_12","alias_value":"427GYRH2CV2J","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"427GYRH2CV2J64UM","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"427GYRH2","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:427GYRH2CV2J64UMU5NGCQE3CN","target":"record","payload":{"canonical_record":{"source":{"id":"1203.3775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-16T18:21:57Z","cross_cats_sorted":[],"title_canon_sha256":"4eff4b934b27322c61829436a6fb09fff3bc7b87af7f94a21148b8180cc05326","abstract_canon_sha256":"167c0a4ed1cf52d57abfb775f360c8c44e7e674eb5a7d2f5bb56a1c55b4be406"},"schema_version":"1.0"},"canonical_sha256":"e6be6c44fa15749f728ca75a61409b1340767f51d431cd0907b86cb88557a6ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:49.919190Z","signature_b64":"gy2xLky5MWJid8XTgMYEH2peqxrzjZ5IVyg9Q3EiA4aTNTb71n9+erTOggxkPy12HykgfhjPmTzI5i5WKLMLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6be6c44fa15749f728ca75a61409b1340767f51d431cd0907b86cb88557a6ae","last_reissued_at":"2026-05-18T03:59:49.918697Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:49.918697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.3775","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":"2026-05-18T03:59:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EM4AicHE6jDtKaMcd9o6AnoFM4/nJTsoFCL9mgQ6fELzmTuwSyUtYYTROTHMXddCtFtt3CspqERGHzJj5fxHDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:29:35.428016Z"},"content_sha256":"43a0483c7ba6b0b978142da3d5d05958c8c2dbcba115617984bbc574b947176c","schema_version":"1.0","event_id":"sha256:43a0483c7ba6b0b978142da3d5d05958c8c2dbcba115617984bbc574b947176c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:427GYRH2CV2J64UMU5NGCQE3CN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive Gorenstein Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Grigoriy Blekherman","submitted_at":"2012-03-16T18:21:57Z","abstract_excerpt":"We introduce positive Gorenstein ideals. These are Gorenstein ideals in the graded ring $\\RR[x]$ with socle in degree 2d, which when viewed as a linear functional on $\\RR[x]_{2d}$ is nonnegative on squares. Equivalently, positive Gorenstein ideals are apolar ideals of forms whose differential operator is nonnegative on squares. Positive Gorenstein ideals arise naturally in the context of nonnegative polynomials and sums of squares, and they provide a powerful framework for studying concrete aspects of sums of squares representations. We present applications of positive Gorenstein ideals in rea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3775","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":"2026-05-18T03:59:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VHf9xY9J4e9f3+7rhQ65t6vZJi0mBmTKRIp3O2rRnnYI8Lk+ja+KzW5Qmav/Y28R2j6mfzhxoeTnhTBMZPT/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:29:35.428374Z"},"content_sha256":"ae394a94caac9d57938d6eaec191e7034f5185f593377115bb576d9a881bfbc1","schema_version":"1.0","event_id":"sha256:ae394a94caac9d57938d6eaec191e7034f5185f593377115bb576d9a881bfbc1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/427GYRH2CV2J64UMU5NGCQE3CN/bundle.json","state_url":"https://pith.science/pith/427GYRH2CV2J64UMU5NGCQE3CN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/427GYRH2CV2J64UMU5NGCQE3CN/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":"2026-06-02T16:29:35Z","links":{"resolver":"https://pith.science/pith/427GYRH2CV2J64UMU5NGCQE3CN","bundle":"https://pith.science/pith/427GYRH2CV2J64UMU5NGCQE3CN/bundle.json","state":"https://pith.science/pith/427GYRH2CV2J64UMU5NGCQE3CN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/427GYRH2CV2J64UMU5NGCQE3CN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:427GYRH2CV2J64UMU5NGCQE3CN","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":"167c0a4ed1cf52d57abfb775f360c8c44e7e674eb5a7d2f5bb56a1c55b4be406","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-16T18:21:57Z","title_canon_sha256":"4eff4b934b27322c61829436a6fb09fff3bc7b87af7f94a21148b8180cc05326"},"schema_version":"1.0","source":{"id":"1203.3775","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3775","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3775v1","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3775","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"pith_short_12","alias_value":"427GYRH2CV2J","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"427GYRH2CV2J64UM","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"427GYRH2","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:ae394a94caac9d57938d6eaec191e7034f5185f593377115bb576d9a881bfbc1","target":"graph","created_at":"2026-05-18T03:59:49Z","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 introduce positive Gorenstein ideals. These are Gorenstein ideals in the graded ring $\\RR[x]$ with socle in degree 2d, which when viewed as a linear functional on $\\RR[x]_{2d}$ is nonnegative on squares. Equivalently, positive Gorenstein ideals are apolar ideals of forms whose differential operator is nonnegative on squares. Positive Gorenstein ideals arise naturally in the context of nonnegative polynomials and sums of squares, and they provide a powerful framework for studying concrete aspects of sums of squares representations. We present applications of positive Gorenstein ideals in rea","authors_text":"Grigoriy Blekherman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-16T18:21:57Z","title":"Positive Gorenstein Ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3775","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":"sha256:43a0483c7ba6b0b978142da3d5d05958c8c2dbcba115617984bbc574b947176c","target":"record","created_at":"2026-05-18T03:59:49Z","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":"167c0a4ed1cf52d57abfb775f360c8c44e7e674eb5a7d2f5bb56a1c55b4be406","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-03-16T18:21:57Z","title_canon_sha256":"4eff4b934b27322c61829436a6fb09fff3bc7b87af7f94a21148b8180cc05326"},"schema_version":"1.0","source":{"id":"1203.3775","kind":"arxiv","version":1}},"canonical_sha256":"e6be6c44fa15749f728ca75a61409b1340767f51d431cd0907b86cb88557a6ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6be6c44fa15749f728ca75a61409b1340767f51d431cd0907b86cb88557a6ae","first_computed_at":"2026-05-18T03:59:49.918697Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:49.918697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gy2xLky5MWJid8XTgMYEH2peqxrzjZ5IVyg9Q3EiA4aTNTb71n9+erTOggxkPy12HykgfhjPmTzI5i5WKLMLBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:49.919190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.3775","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43a0483c7ba6b0b978142da3d5d05958c8c2dbcba115617984bbc574b947176c","sha256:ae394a94caac9d57938d6eaec191e7034f5185f593377115bb576d9a881bfbc1"],"state_sha256":"59c5c898c82c0a59a6912ba30a5b3acdd75701f81566c6fabd932963f61246a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VqsjiTDw5N0A7feryNdurkBDZ5NETIN0vH52RMBCtpApX2DQLXv3KZDHLtHaCg1DXNyIqrXMPwrtTv1F3UelDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T16:29:35.430254Z","bundle_sha256":"2bab2842a9c94d692c3af0cc4be624dc44042b6dffe70fc673c36d3cb532a35c"}}