{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:FDRVDNHNHY6PGGADSA4XU7HL4Y","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":"a490d19d661ec9e6013aa23d87270b9c646432a9b19e5ec66fcef200cd5708c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-09-28T17:14:08Z","title_canon_sha256":"7afe7390f553c4a0c7ebe4ba4ab66afa3356135153d626224f060973758451c0"},"schema_version":"1.0","source":{"id":"0909.5147","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.5147","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"arxiv_version","alias_value":"0909.5147v2","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.5147","created_at":"2026-05-18T00:36:14Z"},{"alias_kind":"pith_short_12","alias_value":"FDRVDNHNHY6P","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"FDRVDNHNHY6PGGAD","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"FDRVDNHN","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:fe3815654c9ccf5e52d30047c67ebf701995ca927e501d409de8bc039b1ff45d","target":"graph","created_at":"2026-05-18T00:36:14Z","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 Lewis-Zagier correspondence, which attaches period functions to Maa\\ss\\ wave forms, is extended to wave forms of higher order, which are higher invariants of the Fuchsian group in question. The key ingredient is an identification of Higher order invariants with ordinary invariants of unipotent twists. This makes it possible to apply standard methods of automorphic forms to higher order forms.","authors_text":"Anton Deitmar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-09-28T17:14:08Z","title":"Lewis-Zagier correspondence for higher order forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.5147","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":"sha256:8acc58932c0426812a27d72deac3d16a8f68937bb855cd6aae368068c51e76b6","target":"record","created_at":"2026-05-18T00:36:14Z","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":"a490d19d661ec9e6013aa23d87270b9c646432a9b19e5ec66fcef200cd5708c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-09-28T17:14:08Z","title_canon_sha256":"7afe7390f553c4a0c7ebe4ba4ab66afa3356135153d626224f060973758451c0"},"schema_version":"1.0","source":{"id":"0909.5147","kind":"arxiv","version":2}},"canonical_sha256":"28e351b4ed3e3cf3180390397a7cebe62c25b00baa6448578a75dbc9a93d6eca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28e351b4ed3e3cf3180390397a7cebe62c25b00baa6448578a75dbc9a93d6eca","first_computed_at":"2026-05-18T00:36:14.833287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:14.833287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f4al8dYVw96nsdp1lvtcOaaELq6EEU6tg3OhTbaVGR/UHb6XDAwqQwq6oGYMHjSJQiYOXtO2PEnuqi9xgXEWCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:14.833858Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.5147","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8acc58932c0426812a27d72deac3d16a8f68937bb855cd6aae368068c51e76b6","sha256:fe3815654c9ccf5e52d30047c67ebf701995ca927e501d409de8bc039b1ff45d"],"state_sha256":"a71349b51408037652052fb4986f88bd3227a0134d0bc43004432963dc3d87d2"}