{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:6PG4GCAFYRCYS4GC7QBGCYL6IO","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":"f464890f2aac5040608a12d8fff819d127244e5f31f2da243d7c5d7328974b78","cross_cats_sorted":["math.AC"],"license":"","primary_cat":"math.RT","submitted_at":"2007-03-01T00:00:02Z","title_canon_sha256":"5632d52c8c6559dfa52551c6beb1dc451ab52e2caeef258834a231eb08a53e61"},"schema_version":"1.0","source":{"id":"math/0703003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0703003","created_at":"2026-05-18T02:55:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0703003v1","created_at":"2026-05-18T02:55:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0703003","created_at":"2026-05-18T02:55:26Z"},{"alias_kind":"pith_short_12","alias_value":"6PG4GCAFYRCY","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"6PG4GCAFYRCYS4GC","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"6PG4GCAF","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:172795c960fb3aaee5d5d098455a7fd26b764d32ef0098d52f31aeee1bf4fa20","target":"graph","created_at":"2026-05-18T02:55:26Z","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 the coinvariant ring of the irreducible Coxeter group of type H4 has the strong Lefschetz property.","authors_text":"Akihito Wachi, Yasuhide Numata","cross_cats":["math.AC"],"headline":"","license":"","primary_cat":"math.RT","submitted_at":"2007-03-01T00:00:02Z","title":"The strong Lefschetz property of the coinvariant ring of the Coxeter group of type H4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703003","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":"sha256:5349240321a3f5614193965c4a06b04e6a33266c8095659dd6411461f6810587","target":"record","created_at":"2026-05-18T02:55:26Z","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":"f464890f2aac5040608a12d8fff819d127244e5f31f2da243d7c5d7328974b78","cross_cats_sorted":["math.AC"],"license":"","primary_cat":"math.RT","submitted_at":"2007-03-01T00:00:02Z","title_canon_sha256":"5632d52c8c6559dfa52551c6beb1dc451ab52e2caeef258834a231eb08a53e61"},"schema_version":"1.0","source":{"id":"math/0703003","kind":"arxiv","version":1}},"canonical_sha256":"f3cdc30805c4458970c2fc0261617e4397f66b340221d324222de6052b2d4e35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3cdc30805c4458970c2fc0261617e4397f66b340221d324222de6052b2d4e35","first_computed_at":"2026-05-18T02:55:26.303016Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:26.303016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XPU2SY+eXd/ZNvMWbhlyctoU75+lIQaRsFQCRXgcwaErxpvh2WfwGCsDYyJFBO0B8gesfcaJA6wDFaFyW26GCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:26.303588Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0703003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5349240321a3f5614193965c4a06b04e6a33266c8095659dd6411461f6810587","sha256:172795c960fb3aaee5d5d098455a7fd26b764d32ef0098d52f31aeee1bf4fa20"],"state_sha256":"d4911c14757d1bae7f9b15565f4b793aed9a07a5c460ca87387fb18752f0e609"}