{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:NMLILBLHPNICAWEDM3ATI6RVD6","short_pith_number":"pith:NMLILBLH","canonical_record":{"source":{"id":"0909.0714","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2009-09-03T16:58:50Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b8f775e96ee4462b4f487a621a0b7ca345f0ea8c057a9891f6e50c947885d83d","abstract_canon_sha256":"2532bdc71e3c7eff0e03c1550645ceca99dfc5207afd19110212eef1de5906e3"},"schema_version":"1.0"},"canonical_sha256":"6b168585677b5020588366c1347a351fab00b73be48a64d881be766b87eaa272","source":{"kind":"arxiv","id":"0909.0714","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.0714","created_at":"2026-05-18T02:12:00Z"},{"alias_kind":"arxiv_version","alias_value":"0909.0714v2","created_at":"2026-05-18T02:12:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.0714","created_at":"2026-05-18T02:12:00Z"},{"alias_kind":"pith_short_12","alias_value":"NMLILBLHPNIC","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"NMLILBLHPNICAWED","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"NMLILBLH","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:NMLILBLHPNICAWEDM3ATI6RVD6","target":"record","payload":{"canonical_record":{"source":{"id":"0909.0714","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2009-09-03T16:58:50Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b8f775e96ee4462b4f487a621a0b7ca345f0ea8c057a9891f6e50c947885d83d","abstract_canon_sha256":"2532bdc71e3c7eff0e03c1550645ceca99dfc5207afd19110212eef1de5906e3"},"schema_version":"1.0"},"canonical_sha256":"6b168585677b5020588366c1347a351fab00b73be48a64d881be766b87eaa272","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:12:00.158359Z","signature_b64":"ZFqvvEaBLnIQrs6+ejiqmVDJ6R70xCGsow4jcnaHuEcwvC7adotnbeojdHp79abwmjtXgLTjazITCSUBQwQ3Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b168585677b5020588366c1347a351fab00b73be48a64d881be766b87eaa272","last_reissued_at":"2026-05-18T02:12:00.157254Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:12:00.157254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.0714","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":"2026-05-18T02:12:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7aZ+Zb/EF6uT8MlUBwX/iHexa4vuoH762Swmf7IlAoC6zObcAV7yAQwEBj8jdqjuBbkN1Bx6NX0YLSNCaUVBAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:46:06.220385Z"},"content_sha256":"732aa8be1d225205c5915079db346c382f5ab313a01d487cd53898efdea6f0f1","schema_version":"1.0","event_id":"sha256:732aa8be1d225205c5915079db346c382f5ab313a01d487cd53898efdea6f0f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:NMLILBLHPNICAWEDM3ATI6RVD6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher order modular forms and mixed Hodge theory","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Ramesh Sreekantan","submitted_at":"2009-09-03T16:58:50Z","abstract_excerpt":"In this paper we introduce a certain space of higher order modular forms of weight 0 and show that it has a Hodge structure coming from the geometry of the fundamental group of a modular curve. This generalizes the usual structure on classical weight 2 forms coming from the cohomology of the modular curve. Further we construct some higher order Poincare series to get higher order higher weight forms and using them we define a space of higher weight, higher order forms which has a mixed Hodge structure as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0714","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":"2026-05-18T02:12:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OWCz0Ivm1zIsWkyVxOOFip2YvEjCOUXLH7QFrkPIWwzpvNw4vwqfoy/Mx/QWBfG///ZURjhppsp/yCNIXeBfBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:46:06.220725Z"},"content_sha256":"a832ff8428751ccf7e85d9dc5b92b021d1dffb5bba16cc35b8d3257ff7f909ee","schema_version":"1.0","event_id":"sha256:a832ff8428751ccf7e85d9dc5b92b021d1dffb5bba16cc35b8d3257ff7f909ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NMLILBLHPNICAWEDM3ATI6RVD6/bundle.json","state_url":"https://pith.science/pith/NMLILBLHPNICAWEDM3ATI6RVD6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NMLILBLHPNICAWEDM3ATI6RVD6/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":"2026-06-26T14:46:06Z","links":{"resolver":"https://pith.science/pith/NMLILBLHPNICAWEDM3ATI6RVD6","bundle":"https://pith.science/pith/NMLILBLHPNICAWEDM3ATI6RVD6/bundle.json","state":"https://pith.science/pith/NMLILBLHPNICAWEDM3ATI6RVD6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NMLILBLHPNICAWEDM3ATI6RVD6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:NMLILBLHPNICAWEDM3ATI6RVD6","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":"2532bdc71e3c7eff0e03c1550645ceca99dfc5207afd19110212eef1de5906e3","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2009-09-03T16:58:50Z","title_canon_sha256":"b8f775e96ee4462b4f487a621a0b7ca345f0ea8c057a9891f6e50c947885d83d"},"schema_version":"1.0","source":{"id":"0909.0714","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.0714","created_at":"2026-05-18T02:12:00Z"},{"alias_kind":"arxiv_version","alias_value":"0909.0714v2","created_at":"2026-05-18T02:12:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.0714","created_at":"2026-05-18T02:12:00Z"},{"alias_kind":"pith_short_12","alias_value":"NMLILBLHPNIC","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"NMLILBLHPNICAWED","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"NMLILBLH","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:a832ff8428751ccf7e85d9dc5b92b021d1dffb5bba16cc35b8d3257ff7f909ee","target":"graph","created_at":"2026-05-18T02:12:00Z","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":"In this paper we introduce a certain space of higher order modular forms of weight 0 and show that it has a Hodge structure coming from the geometry of the fundamental group of a modular curve. This generalizes the usual structure on classical weight 2 forms coming from the cohomology of the modular curve. Further we construct some higher order Poincare series to get higher order higher weight forms and using them we define a space of higher weight, higher order forms which has a mixed Hodge structure as well.","authors_text":"Ramesh Sreekantan","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2009-09-03T16:58:50Z","title":"Higher order modular forms and mixed Hodge theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0714","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":"sha256:732aa8be1d225205c5915079db346c382f5ab313a01d487cd53898efdea6f0f1","target":"record","created_at":"2026-05-18T02:12:00Z","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":"2532bdc71e3c7eff0e03c1550645ceca99dfc5207afd19110212eef1de5906e3","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2009-09-03T16:58:50Z","title_canon_sha256":"b8f775e96ee4462b4f487a621a0b7ca345f0ea8c057a9891f6e50c947885d83d"},"schema_version":"1.0","source":{"id":"0909.0714","kind":"arxiv","version":2}},"canonical_sha256":"6b168585677b5020588366c1347a351fab00b73be48a64d881be766b87eaa272","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b168585677b5020588366c1347a351fab00b73be48a64d881be766b87eaa272","first_computed_at":"2026-05-18T02:12:00.157254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:12:00.157254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZFqvvEaBLnIQrs6+ejiqmVDJ6R70xCGsow4jcnaHuEcwvC7adotnbeojdHp79abwmjtXgLTjazITCSUBQwQ3Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:12:00.158359Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.0714","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:732aa8be1d225205c5915079db346c382f5ab313a01d487cd53898efdea6f0f1","sha256:a832ff8428751ccf7e85d9dc5b92b021d1dffb5bba16cc35b8d3257ff7f909ee"],"state_sha256":"8f2f3d8e042bdbe74cc6e9d154bf1ba1f9909ef5af2720848722568f2ea22825"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wSL3azRLWm02skCVLJxaRVts/wyieKVlOpYyioLqk27awJ2Pw1IDI6HaFhefo/91DLyK5QFTf4pNxQJRrwNyCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T14:46:06.222815Z","bundle_sha256":"06fac7efeb17020c7158ae7c8ca4a4c3097fbb923e215008ee8633851d958191"}}