{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:2LD5VRMBM2SVLXZWMFRIMH5V7I","short_pith_number":"pith:2LD5VRMB","canonical_record":{"source":{"id":"2208.05653","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2022-08-11T06:12:56Z","cross_cats_sorted":[],"title_canon_sha256":"6530314e984de83e785762d2be46db5743823aea1d66f768f8d8ffd8d27d3bea","abstract_canon_sha256":"471cb8469f3319c9096d85cd57c1e91df673b715640f792f24b6ac5584a2c77e"},"schema_version":"1.0"},"canonical_sha256":"d2c7dac58166a555df366162861fb5fa1dbd66287b5711d3656b2a8226412df5","source":{"kind":"arxiv","id":"2208.05653","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.05653","created_at":"2026-07-05T06:19:52Z"},{"alias_kind":"arxiv_version","alias_value":"2208.05653v4","created_at":"2026-07-05T06:19:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.05653","created_at":"2026-07-05T06:19:52Z"},{"alias_kind":"pith_short_12","alias_value":"2LD5VRMBM2SV","created_at":"2026-07-05T06:19:52Z"},{"alias_kind":"pith_short_16","alias_value":"2LD5VRMBM2SVLXZW","created_at":"2026-07-05T06:19:52Z"},{"alias_kind":"pith_short_8","alias_value":"2LD5VRMB","created_at":"2026-07-05T06:19:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:2LD5VRMBM2SVLXZWMFRIMH5V7I","target":"record","payload":{"canonical_record":{"source":{"id":"2208.05653","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2022-08-11T06:12:56Z","cross_cats_sorted":[],"title_canon_sha256":"6530314e984de83e785762d2be46db5743823aea1d66f768f8d8ffd8d27d3bea","abstract_canon_sha256":"471cb8469f3319c9096d85cd57c1e91df673b715640f792f24b6ac5584a2c77e"},"schema_version":"1.0"},"canonical_sha256":"d2c7dac58166a555df366162861fb5fa1dbd66287b5711d3656b2a8226412df5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:19:52.775012Z","signature_b64":"o4uRBTwmOOj7fSZ+nocfIgO5yM7DIeEffPHCiMpyHcYsZWg0cYngoOybvC19fU03yXJTG0BakiJ9qfyIUHFrBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2c7dac58166a555df366162861fb5fa1dbd66287b5711d3656b2a8226412df5","last_reissued_at":"2026-07-05T06:19:52.774554Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:19:52.774554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.05653","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:19:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MlZvCTcjgPUr5otz1qbN1QEiq6UIfSQjJNXjDbdkvyHxRhIb9hJsDDiSEoPx9z8LhmNPxsXq/fEEA+aLiSEfCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T08:50:47.823932Z"},"content_sha256":"d3f883dcea8122a02ee2b698380db611db0f41d73ef5b0995b0861056eb8abff","schema_version":"1.0","event_id":"sha256:d3f883dcea8122a02ee2b698380db611db0f41d73ef5b0995b0861056eb8abff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:2LD5VRMBM2SVLXZWMFRIMH5V7I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher Lorentzian Polynomials, Higher Hessians, and the Hodge-Riemann Property for Graded Oriented Artinian Gorenstein Algebras in Codimension Two","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Alexandra Seceleanu, Chris McDaniel, Junzo Watanabe, Pedro Macias Marques","submitted_at":"2022-08-11T06:12:56Z","abstract_excerpt":"A (standard graded) oriented Artinian Gorenstein algebra over the real numbers is uniquely determined by a real homogeneous polynomial called its Macaulay dual generator. We study the mixed Hodge-Riemann relations on oriented Artinian Gorenstein algebras for which we give a signature criterion on the higher mixed Hessian matrices of its Macaulay dual generator. Inspired by recent work of Br\\\"and\\'en and Huh, we introduce a class of homogeneous polynomials in two variables called $i$-Lorentzian polynomials, and show that these are exactly the Macaulay dual generators of oriented Artinian Gorens"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.05653","kind":"arxiv","version":4},"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/2208.05653/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":"2026-07-05T06:19:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+QorNSENn/37+tGjOrg09DttPOsgIox25X6GUUTmYyTU5TvtkviK6r0ggh5+aISA7ZYInltPLplfrbN9DX4TCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T08:50:47.824442Z"},"content_sha256":"b55193248c03cc2936d01c2dcb24d025be36d8a77289e5ed9629765c65572954","schema_version":"1.0","event_id":"sha256:b55193248c03cc2936d01c2dcb24d025be36d8a77289e5ed9629765c65572954"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2LD5VRMBM2SVLXZWMFRIMH5V7I/bundle.json","state_url":"https://pith.science/pith/2LD5VRMBM2SVLXZWMFRIMH5V7I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2LD5VRMBM2SVLXZWMFRIMH5V7I/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":"2026-08-13T08:50:47Z","links":{"resolver":"https://pith.science/pith/2LD5VRMBM2SVLXZWMFRIMH5V7I","bundle":"https://pith.science/pith/2LD5VRMBM2SVLXZWMFRIMH5V7I/bundle.json","state":"https://pith.science/pith/2LD5VRMBM2SVLXZWMFRIMH5V7I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2LD5VRMBM2SVLXZWMFRIMH5V7I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:2LD5VRMBM2SVLXZWMFRIMH5V7I","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":"471cb8469f3319c9096d85cd57c1e91df673b715640f792f24b6ac5584a2c77e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2022-08-11T06:12:56Z","title_canon_sha256":"6530314e984de83e785762d2be46db5743823aea1d66f768f8d8ffd8d27d3bea"},"schema_version":"1.0","source":{"id":"2208.05653","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.05653","created_at":"2026-07-05T06:19:52Z"},{"alias_kind":"arxiv_version","alias_value":"2208.05653v4","created_at":"2026-07-05T06:19:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.05653","created_at":"2026-07-05T06:19:52Z"},{"alias_kind":"pith_short_12","alias_value":"2LD5VRMBM2SV","created_at":"2026-07-05T06:19:52Z"},{"alias_kind":"pith_short_16","alias_value":"2LD5VRMBM2SVLXZW","created_at":"2026-07-05T06:19:52Z"},{"alias_kind":"pith_short_8","alias_value":"2LD5VRMB","created_at":"2026-07-05T06:19:52Z"}],"graph_snapshots":[{"event_id":"sha256:b55193248c03cc2936d01c2dcb24d025be36d8a77289e5ed9629765c65572954","target":"graph","created_at":"2026-07-05T06:19:52Z","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/2208.05653/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A (standard graded) oriented Artinian Gorenstein algebra over the real numbers is uniquely determined by a real homogeneous polynomial called its Macaulay dual generator. We study the mixed Hodge-Riemann relations on oriented Artinian Gorenstein algebras for which we give a signature criterion on the higher mixed Hessian matrices of its Macaulay dual generator. Inspired by recent work of Br\\\"and\\'en and Huh, we introduce a class of homogeneous polynomials in two variables called $i$-Lorentzian polynomials, and show that these are exactly the Macaulay dual generators of oriented Artinian Gorens","authors_text":"Alexandra Seceleanu, Chris McDaniel, Junzo Watanabe, Pedro Macias Marques","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2022-08-11T06:12:56Z","title":"Higher Lorentzian Polynomials, Higher Hessians, and the Hodge-Riemann Property for Graded Oriented Artinian Gorenstein Algebras in Codimension Two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.05653","kind":"arxiv","version":4},"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:d3f883dcea8122a02ee2b698380db611db0f41d73ef5b0995b0861056eb8abff","target":"record","created_at":"2026-07-05T06:19:52Z","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":"471cb8469f3319c9096d85cd57c1e91df673b715640f792f24b6ac5584a2c77e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2022-08-11T06:12:56Z","title_canon_sha256":"6530314e984de83e785762d2be46db5743823aea1d66f768f8d8ffd8d27d3bea"},"schema_version":"1.0","source":{"id":"2208.05653","kind":"arxiv","version":4}},"canonical_sha256":"d2c7dac58166a555df366162861fb5fa1dbd66287b5711d3656b2a8226412df5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2c7dac58166a555df366162861fb5fa1dbd66287b5711d3656b2a8226412df5","first_computed_at":"2026-07-05T06:19:52.774554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:19:52.774554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o4uRBTwmOOj7fSZ+nocfIgO5yM7DIeEffPHCiMpyHcYsZWg0cYngoOybvC19fU03yXJTG0BakiJ9qfyIUHFrBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:19:52.775012Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.05653","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3f883dcea8122a02ee2b698380db611db0f41d73ef5b0995b0861056eb8abff","sha256:b55193248c03cc2936d01c2dcb24d025be36d8a77289e5ed9629765c65572954"],"state_sha256":"b9dcdc9e1844cf5f49d3412ed08d8f8bfd6c8a9b86aa45ad47143a9de1e3f35a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"90OYA0y2EZdy8Px/Il9dd+1cpOvspKhpgwRiQb4eRIAPg4q8Iv2bTENq77Be0LAshbAqxwlZ3CjFbrfIoRu1BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T08:50:47.829686Z","bundle_sha256":"123d4577e546307238af81bc24511f409a7a3963f6418c5a6eef925bdcc80626"}}