{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:VH6AXZYPOW2HPEGB3KRYWQ7EUS","short_pith_number":"pith:VH6AXZYP","canonical_record":{"source":{"id":"2303.16768","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2023-03-29T15:00:00Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ca7537959904ccd833f00f68616ffff669875b6dad1c92f029da7a7018712e7a","abstract_canon_sha256":"afeb59c6fbf4563dac86b7f0a896943107ce87058aa45d1e8bba90676ec5345f"},"schema_version":"1.0"},"canonical_sha256":"a9fc0be70f75b47790c1daa38b43e4a49cdb7caa0c7f50099c0c9a8c3faaab8e","source":{"kind":"arxiv","id":"2303.16768","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.16768","created_at":"2026-07-05T05:56:10Z"},{"alias_kind":"arxiv_version","alias_value":"2303.16768v1","created_at":"2026-07-05T05:56:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.16768","created_at":"2026-07-05T05:56:10Z"},{"alias_kind":"pith_short_12","alias_value":"VH6AXZYPOW2H","created_at":"2026-07-05T05:56:10Z"},{"alias_kind":"pith_short_16","alias_value":"VH6AXZYPOW2HPEGB","created_at":"2026-07-05T05:56:10Z"},{"alias_kind":"pith_short_8","alias_value":"VH6AXZYP","created_at":"2026-07-05T05:56:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:VH6AXZYPOW2HPEGB3KRYWQ7EUS","target":"record","payload":{"canonical_record":{"source":{"id":"2303.16768","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2023-03-29T15:00:00Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ca7537959904ccd833f00f68616ffff669875b6dad1c92f029da7a7018712e7a","abstract_canon_sha256":"afeb59c6fbf4563dac86b7f0a896943107ce87058aa45d1e8bba90676ec5345f"},"schema_version":"1.0"},"canonical_sha256":"a9fc0be70f75b47790c1daa38b43e4a49cdb7caa0c7f50099c0c9a8c3faaab8e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:56:10.263125Z","signature_b64":"cPwkToswJOvjh/vrdXqtLkUhN4qQA8n6hlh3bGwv/YkFLjY/tuD+AVLFIs3jJ0tfWrSOjpv14Xs68s/DxKj7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9fc0be70f75b47790c1daa38b43e4a49cdb7caa0c7f50099c0c9a8c3faaab8e","last_reissued_at":"2026-07-05T05:56:10.262783Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:56:10.262783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.16768","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":"2026-07-05T05:56:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S9gX3u+YTexAi5z+CyyMgDACO5Dz5aLLSXRpyskHTOHAQfCEJrIh0LnTGzB+9HSOHiVgOq1UBxgrytvE7We5Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T19:30:58.649833Z"},"content_sha256":"5d2c850797aa802df8fdab5cab6c22520d4ee03737781c732b0c4d76f4e618da","schema_version":"1.0","event_id":"sha256:5d2c850797aa802df8fdab5cab6c22520d4ee03737781c732b0c4d76f4e618da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:VH6AXZYPOW2HPEGB3KRYWQ7EUS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hilbert functions and Jordan type of Perazzo Artinian algebras","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Anthony Iarrobino, Emilia Mezzetti, Lisa Nicklasson, Luca Fiorindo, Nancy Abdallah, Nasrin Altafi, Pedro Macias Marques, Pietro De Poi, Rosa M. Mir\\'o-Roig","submitted_at":"2023-03-29T15:00:00Z","abstract_excerpt":"We study Hilbert functions, Lefschetz properties, and Jordan type of Artinian Gorenstein algebras associated to Perazzo hypersurfaces in projective space. The main focus lies on Perazzo threefolds, for which we prove that the Hilbert functions are always unimodal. Further we prove that the Hilbert function determines whether the algebra is weak Lefschetz, and we characterize those Hilbert functions for which the weak Lefschetz property holds. By example, we verify that the Hilbert functions of Perazzo fourfolds are not always unimodal. In the particular case of Perazzo threefolds with the smal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.16768","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/2303.16768/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":"2026-07-05T05:56:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wP7+o4JhZxChasrrEOMRhVKiOkqSdNsRQmO1R3XByJtI9zfnECjTuyS5zu5dAz+AekOoH+oDKJp+u/tlwcL0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T19:30:58.650330Z"},"content_sha256":"c52ea5852e7291689c17bddf4d89df6f1ce59efc1e1766c55392b947d8786b78","schema_version":"1.0","event_id":"sha256:c52ea5852e7291689c17bddf4d89df6f1ce59efc1e1766c55392b947d8786b78"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VH6AXZYPOW2HPEGB3KRYWQ7EUS/bundle.json","state_url":"https://pith.science/pith/VH6AXZYPOW2HPEGB3KRYWQ7EUS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VH6AXZYPOW2HPEGB3KRYWQ7EUS/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":"2026-08-12T19:30:58Z","links":{"resolver":"https://pith.science/pith/VH6AXZYPOW2HPEGB3KRYWQ7EUS","bundle":"https://pith.science/pith/VH6AXZYPOW2HPEGB3KRYWQ7EUS/bundle.json","state":"https://pith.science/pith/VH6AXZYPOW2HPEGB3KRYWQ7EUS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VH6AXZYPOW2HPEGB3KRYWQ7EUS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:VH6AXZYPOW2HPEGB3KRYWQ7EUS","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":"afeb59c6fbf4563dac86b7f0a896943107ce87058aa45d1e8bba90676ec5345f","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2023-03-29T15:00:00Z","title_canon_sha256":"ca7537959904ccd833f00f68616ffff669875b6dad1c92f029da7a7018712e7a"},"schema_version":"1.0","source":{"id":"2303.16768","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.16768","created_at":"2026-07-05T05:56:10Z"},{"alias_kind":"arxiv_version","alias_value":"2303.16768v1","created_at":"2026-07-05T05:56:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.16768","created_at":"2026-07-05T05:56:10Z"},{"alias_kind":"pith_short_12","alias_value":"VH6AXZYPOW2H","created_at":"2026-07-05T05:56:10Z"},{"alias_kind":"pith_short_16","alias_value":"VH6AXZYPOW2HPEGB","created_at":"2026-07-05T05:56:10Z"},{"alias_kind":"pith_short_8","alias_value":"VH6AXZYP","created_at":"2026-07-05T05:56:10Z"}],"graph_snapshots":[{"event_id":"sha256:c52ea5852e7291689c17bddf4d89df6f1ce59efc1e1766c55392b947d8786b78","target":"graph","created_at":"2026-07-05T05:56:10Z","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/2303.16768/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study Hilbert functions, Lefschetz properties, and Jordan type of Artinian Gorenstein algebras associated to Perazzo hypersurfaces in projective space. The main focus lies on Perazzo threefolds, for which we prove that the Hilbert functions are always unimodal. Further we prove that the Hilbert function determines whether the algebra is weak Lefschetz, and we characterize those Hilbert functions for which the weak Lefschetz property holds. By example, we verify that the Hilbert functions of Perazzo fourfolds are not always unimodal. In the particular case of Perazzo threefolds with the smal","authors_text":"Anthony Iarrobino, Emilia Mezzetti, Lisa Nicklasson, Luca Fiorindo, Nancy Abdallah, Nasrin Altafi, Pedro Macias Marques, Pietro De Poi, Rosa M. Mir\\'o-Roig","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2023-03-29T15:00:00Z","title":"Hilbert functions and Jordan type of Perazzo Artinian algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.16768","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":"sha256:5d2c850797aa802df8fdab5cab6c22520d4ee03737781c732b0c4d76f4e618da","target":"record","created_at":"2026-07-05T05:56:10Z","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":"afeb59c6fbf4563dac86b7f0a896943107ce87058aa45d1e8bba90676ec5345f","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2023-03-29T15:00:00Z","title_canon_sha256":"ca7537959904ccd833f00f68616ffff669875b6dad1c92f029da7a7018712e7a"},"schema_version":"1.0","source":{"id":"2303.16768","kind":"arxiv","version":1}},"canonical_sha256":"a9fc0be70f75b47790c1daa38b43e4a49cdb7caa0c7f50099c0c9a8c3faaab8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9fc0be70f75b47790c1daa38b43e4a49cdb7caa0c7f50099c0c9a8c3faaab8e","first_computed_at":"2026-07-05T05:56:10.262783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:56:10.262783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cPwkToswJOvjh/vrdXqtLkUhN4qQA8n6hlh3bGwv/YkFLjY/tuD+AVLFIs3jJ0tfWrSOjpv14Xs68s/DxKj7AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:56:10.263125Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.16768","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d2c850797aa802df8fdab5cab6c22520d4ee03737781c732b0c4d76f4e618da","sha256:c52ea5852e7291689c17bddf4d89df6f1ce59efc1e1766c55392b947d8786b78"],"state_sha256":"8478e708eb490eebce5c958c3f593a2cc85a27475a8386b2400d4f86f875f42f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KpPtgf967b09qm4wQLYTk/8GQl9MFFw4At6saqJxUzC6SAHSt/vhUd5cxmLHy9k7Rt19bd9FGG6WT9P+tE5HDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T19:30:58.654780Z","bundle_sha256":"381ebe3a40423f06ded484683df5db85012706f2deba0df3cbd7072caf19858a"}}