{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4OM6X7SGSLRCV372GCPAURW6V7","short_pith_number":"pith:4OM6X7SG","canonical_record":{"source":{"id":"1501.06982","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-01-28T03:40:57Z","cross_cats_sorted":[],"title_canon_sha256":"ecf9c5b8142c6d56be1b77c9c30df3f129a600cddc23abc82942aac2c1167f81","abstract_canon_sha256":"dffd61b4f5f3f2f6117e148e4f7c1c6c49e26ed634b20ef765409b7bcfe7b2b4"},"schema_version":"1.0"},"canonical_sha256":"e399ebfe4692e22aeffa309e0a46deafc42826db730023aa334a9717c2fb8bc7","source":{"kind":"arxiv","id":"1501.06982","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06982","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06982v2","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06982","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"4OM6X7SGSLRC","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4OM6X7SGSLRCV372","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4OM6X7SG","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4OM6X7SGSLRCV372GCPAURW6V7","target":"record","payload":{"canonical_record":{"source":{"id":"1501.06982","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-01-28T03:40:57Z","cross_cats_sorted":[],"title_canon_sha256":"ecf9c5b8142c6d56be1b77c9c30df3f129a600cddc23abc82942aac2c1167f81","abstract_canon_sha256":"dffd61b4f5f3f2f6117e148e4f7c1c6c49e26ed634b20ef765409b7bcfe7b2b4"},"schema_version":"1.0"},"canonical_sha256":"e399ebfe4692e22aeffa309e0a46deafc42826db730023aa334a9717c2fb8bc7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:20.321693Z","signature_b64":"7tJEvOWdue0MTo0MNbK2lrKPNEbwENZkcB0SszUWJvbJLmmA+c3TXIyLYEGezxWKv3qeT1U4MzJnUScBjgkSDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e399ebfe4692e22aeffa309e0a46deafc42826db730023aa334a9717c2fb8bc7","last_reissued_at":"2026-05-18T02:16:20.321037Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:20.321037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.06982","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:16:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/aKmkZxSm/0L06gjMI2IxUq4cIBIYBrcU3UF7DcPAqdWmV3xi1qz6hyg1XyUJagssHnjnRFVq2iq8O3YP6ZcBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T06:37:20.617912Z"},"content_sha256":"0b0cfa1cdbe68e8cfa96d24bcdfd0a3e6a41a6205743a3dcbcc0d77660278158","schema_version":"1.0","event_id":"sha256:0b0cfa1cdbe68e8cfa96d24bcdfd0a3e6a41a6205743a3dcbcc0d77660278158"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4OM6X7SGSLRCV372GCPAURW6V7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The quadratic complete intersections with the action of the symmetric group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Akihito Wachi, Junzo Watanabe, Tadahito Harima","submitted_at":"2015-01-28T03:40:57Z","abstract_excerpt":"We prove that any quadratic complete intersection with certain action of the symmetric group has the strong Lefschetz property over a field of characteristic zero. As a consequence of it we construct a new class of homogeneous complete intersections with generators of higher degrees which have the strong Lefschetz property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06982","kind":"arxiv","version":2},"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":"2026-05-18T02:16:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HYl1LLLW3ls1q2SwpWGduPOlquLvrD1dhFuvpcBfZ/rA4c2IYIeYxfwf4wVMd5HYbD/xhEcW3a9BG8GzPynsDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T06:37:20.618253Z"},"content_sha256":"5dff93c6200b628b9029bf317120de0679c0d670f3b7bf71edfeffea06c8a170","schema_version":"1.0","event_id":"sha256:5dff93c6200b628b9029bf317120de0679c0d670f3b7bf71edfeffea06c8a170"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4OM6X7SGSLRCV372GCPAURW6V7/bundle.json","state_url":"https://pith.science/pith/4OM6X7SGSLRCV372GCPAURW6V7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4OM6X7SGSLRCV372GCPAURW6V7/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":"2026-07-02T06:37:20Z","links":{"resolver":"https://pith.science/pith/4OM6X7SGSLRCV372GCPAURW6V7","bundle":"https://pith.science/pith/4OM6X7SGSLRCV372GCPAURW6V7/bundle.json","state":"https://pith.science/pith/4OM6X7SGSLRCV372GCPAURW6V7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4OM6X7SGSLRCV372GCPAURW6V7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4OM6X7SGSLRCV372GCPAURW6V7","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":"dffd61b4f5f3f2f6117e148e4f7c1c6c49e26ed634b20ef765409b7bcfe7b2b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-01-28T03:40:57Z","title_canon_sha256":"ecf9c5b8142c6d56be1b77c9c30df3f129a600cddc23abc82942aac2c1167f81"},"schema_version":"1.0","source":{"id":"1501.06982","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06982","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06982v2","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06982","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"4OM6X7SGSLRC","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4OM6X7SGSLRCV372","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4OM6X7SG","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:5dff93c6200b628b9029bf317120de0679c0d670f3b7bf71edfeffea06c8a170","target":"graph","created_at":"2026-05-18T02:16:20Z","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 prove that any quadratic complete intersection with certain action of the symmetric group has the strong Lefschetz property over a field of characteristic zero. As a consequence of it we construct a new class of homogeneous complete intersections with generators of higher degrees which have the strong Lefschetz property.","authors_text":"Akihito Wachi, Junzo Watanabe, Tadahito Harima","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-01-28T03:40:57Z","title":"The quadratic complete intersections with the action of the symmetric group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06982","kind":"arxiv","version":2},"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":"sha256:0b0cfa1cdbe68e8cfa96d24bcdfd0a3e6a41a6205743a3dcbcc0d77660278158","target":"record","created_at":"2026-05-18T02:16:20Z","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":"dffd61b4f5f3f2f6117e148e4f7c1c6c49e26ed634b20ef765409b7bcfe7b2b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-01-28T03:40:57Z","title_canon_sha256":"ecf9c5b8142c6d56be1b77c9c30df3f129a600cddc23abc82942aac2c1167f81"},"schema_version":"1.0","source":{"id":"1501.06982","kind":"arxiv","version":2}},"canonical_sha256":"e399ebfe4692e22aeffa309e0a46deafc42826db730023aa334a9717c2fb8bc7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e399ebfe4692e22aeffa309e0a46deafc42826db730023aa334a9717c2fb8bc7","first_computed_at":"2026-05-18T02:16:20.321037Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:20.321037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7tJEvOWdue0MTo0MNbK2lrKPNEbwENZkcB0SszUWJvbJLmmA+c3TXIyLYEGezxWKv3qeT1U4MzJnUScBjgkSDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:20.321693Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06982","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b0cfa1cdbe68e8cfa96d24bcdfd0a3e6a41a6205743a3dcbcc0d77660278158","sha256:5dff93c6200b628b9029bf317120de0679c0d670f3b7bf71edfeffea06c8a170"],"state_sha256":"4a269e9d34112f187b8f0055b5faad89885819f8355fa4f47666027e247ed011"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JrcZ84QiwjXZYwHGedcuuaTCaabVOum9ktulgJJ81Weg/t9gsFld3cSC1zgjVPTAigoWSTmKC+Momwt0lsBLAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T06:37:20.620551Z","bundle_sha256":"21c4d4fb32eb4b192710862e3a2eea4f73c198b24879ec5ad9fe27542a2fcbf9"}}