{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:K2XOK2VGZ2MGTPJD2D5N6NXP7E","short_pith_number":"pith:K2XOK2VG","canonical_record":{"source":{"id":"1906.00626","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-06-03T08:22:39Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"434a737dc3dd790b7979e3a741874e7bb5852405c625c8343d39f876e44ef3ca","abstract_canon_sha256":"21e5c1f2e6267c5f1190070c3fb715feb65434704b7d82a37cd42ac7c249a514"},"schema_version":"1.0"},"canonical_sha256":"56aee56aa6ce9869bd23d0fadf36eff90b0c8c531d343e73894eee389ba87a50","source":{"kind":"arxiv","id":"1906.00626","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.00626","created_at":"2026-05-17T23:44:24Z"},{"alias_kind":"arxiv_version","alias_value":"1906.00626v1","created_at":"2026-05-17T23:44:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.00626","created_at":"2026-05-17T23:44:24Z"},{"alias_kind":"pith_short_12","alias_value":"K2XOK2VGZ2MG","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"K2XOK2VGZ2MGTPJD","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"K2XOK2VG","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:K2XOK2VGZ2MGTPJD2D5N6NXP7E","target":"record","payload":{"canonical_record":{"source":{"id":"1906.00626","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-06-03T08:22:39Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"434a737dc3dd790b7979e3a741874e7bb5852405c625c8343d39f876e44ef3ca","abstract_canon_sha256":"21e5c1f2e6267c5f1190070c3fb715feb65434704b7d82a37cd42ac7c249a514"},"schema_version":"1.0"},"canonical_sha256":"56aee56aa6ce9869bd23d0fadf36eff90b0c8c531d343e73894eee389ba87a50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:24.301083Z","signature_b64":"qFWGos9nwFAZEhG8MeSgxozudS//FYTKNoPvxGwk8nUYOs1uyzzQ7yE0OHBqCfloCmiBTuMjFX7XeA2IMXgrBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56aee56aa6ce9869bd23d0fadf36eff90b0c8c531d343e73894eee389ba87a50","last_reissued_at":"2026-05-17T23:44:24.300529Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:24.300529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.00626","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":"2026-05-17T23:44:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UmravSXAw1IuB0Bs7zjKB8qZepZI4vTy49gEvsZIAk/VFaFY71/J9uxt9B86iVwp7J7I1MB8Pnrxl+IRjMQSCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:59:38.308896Z"},"content_sha256":"3748c595a2a5309a71b7b665caa3f21ce3cbc2e3d43d8bed648a55ae6bec5d83","schema_version":"1.0","event_id":"sha256:3748c595a2a5309a71b7b665caa3f21ce3cbc2e3d43d8bed648a55ae6bec5d83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:K2XOK2VGZ2MGTPJD2D5N6NXP7E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The module of Valabrega-Valla of the Jacobian ideal of points in projective plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Abbas Nasrollah Nejad, Zahra Shahidi","submitted_at":"2019-06-03T08:22:39Z","abstract_excerpt":"The module of Valabrega-Valla of the Jacobian ideal of a reduced projective variety $V$ is the torsion of the Aluffi algebra. One considers the problem of its vanishing in the case of where $V$ is a reduced set of points in the projective plane. It is shown that the module is nonzero for several cases of a special configuration class therein -- called $(s-r)$-{fold collinear configuration}. A complete classification of types is given for $5$ and $6$ points in regard to this problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.00626","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":"2026-05-17T23:44:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ttG3b0dC13Oyds8pasniC/pKKrB75QMWxseRD+nQplsa0SW8s6GcOPEBoCOvhJigwWjwk+b/49YuUWzSPzAaAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:59:38.309232Z"},"content_sha256":"33db2a894df4f6001bae9f19962a39882611888eb91607d0db854fe7dde4c241","schema_version":"1.0","event_id":"sha256:33db2a894df4f6001bae9f19962a39882611888eb91607d0db854fe7dde4c241"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K2XOK2VGZ2MGTPJD2D5N6NXP7E/bundle.json","state_url":"https://pith.science/pith/K2XOK2VGZ2MGTPJD2D5N6NXP7E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K2XOK2VGZ2MGTPJD2D5N6NXP7E/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":"2026-06-25T17:59:38Z","links":{"resolver":"https://pith.science/pith/K2XOK2VGZ2MGTPJD2D5N6NXP7E","bundle":"https://pith.science/pith/K2XOK2VGZ2MGTPJD2D5N6NXP7E/bundle.json","state":"https://pith.science/pith/K2XOK2VGZ2MGTPJD2D5N6NXP7E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K2XOK2VGZ2MGTPJD2D5N6NXP7E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:K2XOK2VGZ2MGTPJD2D5N6NXP7E","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":"21e5c1f2e6267c5f1190070c3fb715feb65434704b7d82a37cd42ac7c249a514","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-06-03T08:22:39Z","title_canon_sha256":"434a737dc3dd790b7979e3a741874e7bb5852405c625c8343d39f876e44ef3ca"},"schema_version":"1.0","source":{"id":"1906.00626","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.00626","created_at":"2026-05-17T23:44:24Z"},{"alias_kind":"arxiv_version","alias_value":"1906.00626v1","created_at":"2026-05-17T23:44:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.00626","created_at":"2026-05-17T23:44:24Z"},{"alias_kind":"pith_short_12","alias_value":"K2XOK2VGZ2MG","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"K2XOK2VGZ2MGTPJD","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"K2XOK2VG","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:33db2a894df4f6001bae9f19962a39882611888eb91607d0db854fe7dde4c241","target":"graph","created_at":"2026-05-17T23:44:24Z","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":"The module of Valabrega-Valla of the Jacobian ideal of a reduced projective variety $V$ is the torsion of the Aluffi algebra. One considers the problem of its vanishing in the case of where $V$ is a reduced set of points in the projective plane. It is shown that the module is nonzero for several cases of a special configuration class therein -- called $(s-r)$-{fold collinear configuration}. A complete classification of types is given for $5$ and $6$ points in regard to this problem.","authors_text":"Abbas Nasrollah Nejad, Zahra Shahidi","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-06-03T08:22:39Z","title":"The module of Valabrega-Valla of the Jacobian ideal of points in projective plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.00626","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":"sha256:3748c595a2a5309a71b7b665caa3f21ce3cbc2e3d43d8bed648a55ae6bec5d83","target":"record","created_at":"2026-05-17T23:44:24Z","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":"21e5c1f2e6267c5f1190070c3fb715feb65434704b7d82a37cd42ac7c249a514","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-06-03T08:22:39Z","title_canon_sha256":"434a737dc3dd790b7979e3a741874e7bb5852405c625c8343d39f876e44ef3ca"},"schema_version":"1.0","source":{"id":"1906.00626","kind":"arxiv","version":1}},"canonical_sha256":"56aee56aa6ce9869bd23d0fadf36eff90b0c8c531d343e73894eee389ba87a50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56aee56aa6ce9869bd23d0fadf36eff90b0c8c531d343e73894eee389ba87a50","first_computed_at":"2026-05-17T23:44:24.300529Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:24.300529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qFWGos9nwFAZEhG8MeSgxozudS//FYTKNoPvxGwk8nUYOs1uyzzQ7yE0OHBqCfloCmiBTuMjFX7XeA2IMXgrBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:24.301083Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.00626","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3748c595a2a5309a71b7b665caa3f21ce3cbc2e3d43d8bed648a55ae6bec5d83","sha256:33db2a894df4f6001bae9f19962a39882611888eb91607d0db854fe7dde4c241"],"state_sha256":"6389afde9d2459a3a9d0b334b6b30a9f99a2f4de3e425dfd0cc9be3c4ea10545"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xy6/8+2GQxrm9n/Bh7E1xzc+Meb2+w41Wg+lnKKe1/QvyZaaqV/bdDLWbpphmSssHpe18dY2z75EGYKBDPFFCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T17:59:38.311261Z","bundle_sha256":"d6f740676a778170d43cd18ad46dc61d27df768db3ed15b6338ca8e246435fda"}}