{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:TCKKABD4WCO4V7KF6VZLKTHJ3V","short_pith_number":"pith:TCKKABD4","canonical_record":{"source":{"id":"1310.1633","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-06T21:20:01Z","cross_cats_sorted":[],"title_canon_sha256":"9717230a3aa9af2059a5ceef68ae8d0d70d3b518be0e4cad778012defa36bf3d","abstract_canon_sha256":"a2bc5d9543d2303113e2f1dad7e6d4049e5c44026fc29e3e6d9801aa720136dc"},"schema_version":"1.0"},"canonical_sha256":"9894a0047cb09dcafd45f572b54ce9dd7477e6aed61231d02085b74934367e3f","source":{"kind":"arxiv","id":"1310.1633","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1633","created_at":"2026-05-18T02:41:42Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1633v4","created_at":"2026-05-18T02:41:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1633","created_at":"2026-05-18T02:41:42Z"},{"alias_kind":"pith_short_12","alias_value":"TCKKABD4WCO4","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"TCKKABD4WCO4V7KF","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"TCKKABD4","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:TCKKABD4WCO4V7KF6VZLKTHJ3V","target":"record","payload":{"canonical_record":{"source":{"id":"1310.1633","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-06T21:20:01Z","cross_cats_sorted":[],"title_canon_sha256":"9717230a3aa9af2059a5ceef68ae8d0d70d3b518be0e4cad778012defa36bf3d","abstract_canon_sha256":"a2bc5d9543d2303113e2f1dad7e6d4049e5c44026fc29e3e6d9801aa720136dc"},"schema_version":"1.0"},"canonical_sha256":"9894a0047cb09dcafd45f572b54ce9dd7477e6aed61231d02085b74934367e3f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:42.132529Z","signature_b64":"s/kFAlxPeGq76PKAE0clIEGgTL9v1tPe0AABmaBrVD6QMK+MEynp/ssd7qSooMCPJdAZRoIpEuURMGZZ1nOtBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9894a0047cb09dcafd45f572b54ce9dd7477e6aed61231d02085b74934367e3f","last_reissued_at":"2026-05-18T02:41:42.131788Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:42.131788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.1633","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DOOwCoaWZ057JC809nz3Pe6WPbA/ZPdViw5oi3Xcu1Olr6/XskO5Bc54zJN7UGo5PMjd+LGw+UY4GawanZreCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:37:22.180566Z"},"content_sha256":"ae047c9a2746f6635b455cace982bb0d34a584d6cddf7a13ad39a15db4b53028","schema_version":"1.0","event_id":"sha256:ae047c9a2746f6635b455cace982bb0d34a584d6cddf7a13ad39a15db4b53028"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:TCKKABD4WCO4V7KF6VZLKTHJ3V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On hyperderivatives of single-cuspidal Drinfeld modular forms with A-expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aleksandar Petrov","submitted_at":"2013-10-06T21:20:01Z","abstract_excerpt":"We show that the Drinfeld modular forms with $A$-expansion that have been constructed by the author are precisely the hyperderivatives of the subfamily of single-cuspidal Drinfeld modular forms with $A$-expansions that remain modular after hyperdifferentiation. In addition, we show that Drinfeld-Poincar\\'{e} series display a similar behavior with respect to hyperdifferentiation, giving indirect evidence that the Drinfeld modular forms with $A$-expansions are Drinfeld-Poincar\\'{e} series. The Drinfeld-Poincar\\'{e} series that we consider generalize previous examples of such series by Gekeler, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1633","kind":"arxiv","version":4},"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":"2026-05-18T02:41:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UFyB0yAr2KlLHOWXVzDJhb9AvwG3EgrWFmpoJHrIoCpWHiI+g6xZ87uqvWk9b9CgWS1qSBMbxZnIKQrE6Vg2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:37:22.180909Z"},"content_sha256":"8089bb98c563fbc868ef6daedbcd567cb135d188fc006a3496d9d240116eba6c","schema_version":"1.0","event_id":"sha256:8089bb98c563fbc868ef6daedbcd567cb135d188fc006a3496d9d240116eba6c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TCKKABD4WCO4V7KF6VZLKTHJ3V/bundle.json","state_url":"https://pith.science/pith/TCKKABD4WCO4V7KF6VZLKTHJ3V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TCKKABD4WCO4V7KF6VZLKTHJ3V/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":"2026-06-24T05:37:22Z","links":{"resolver":"https://pith.science/pith/TCKKABD4WCO4V7KF6VZLKTHJ3V","bundle":"https://pith.science/pith/TCKKABD4WCO4V7KF6VZLKTHJ3V/bundle.json","state":"https://pith.science/pith/TCKKABD4WCO4V7KF6VZLKTHJ3V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TCKKABD4WCO4V7KF6VZLKTHJ3V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TCKKABD4WCO4V7KF6VZLKTHJ3V","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":"a2bc5d9543d2303113e2f1dad7e6d4049e5c44026fc29e3e6d9801aa720136dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-06T21:20:01Z","title_canon_sha256":"9717230a3aa9af2059a5ceef68ae8d0d70d3b518be0e4cad778012defa36bf3d"},"schema_version":"1.0","source":{"id":"1310.1633","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1633","created_at":"2026-05-18T02:41:42Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1633v4","created_at":"2026-05-18T02:41:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1633","created_at":"2026-05-18T02:41:42Z"},{"alias_kind":"pith_short_12","alias_value":"TCKKABD4WCO4","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"TCKKABD4WCO4V7KF","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"TCKKABD4","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:8089bb98c563fbc868ef6daedbcd567cb135d188fc006a3496d9d240116eba6c","target":"graph","created_at":"2026-05-18T02:41:42Z","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 show that the Drinfeld modular forms with $A$-expansion that have been constructed by the author are precisely the hyperderivatives of the subfamily of single-cuspidal Drinfeld modular forms with $A$-expansions that remain modular after hyperdifferentiation. In addition, we show that Drinfeld-Poincar\\'{e} series display a similar behavior with respect to hyperdifferentiation, giving indirect evidence that the Drinfeld modular forms with $A$-expansions are Drinfeld-Poincar\\'{e} series. The Drinfeld-Poincar\\'{e} series that we consider generalize previous examples of such series by Gekeler, a","authors_text":"Aleksandar Petrov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-06T21:20:01Z","title":"On hyperderivatives of single-cuspidal Drinfeld modular forms with A-expansions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1633","kind":"arxiv","version":4},"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:ae047c9a2746f6635b455cace982bb0d34a584d6cddf7a13ad39a15db4b53028","target":"record","created_at":"2026-05-18T02:41:42Z","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":"a2bc5d9543d2303113e2f1dad7e6d4049e5c44026fc29e3e6d9801aa720136dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-06T21:20:01Z","title_canon_sha256":"9717230a3aa9af2059a5ceef68ae8d0d70d3b518be0e4cad778012defa36bf3d"},"schema_version":"1.0","source":{"id":"1310.1633","kind":"arxiv","version":4}},"canonical_sha256":"9894a0047cb09dcafd45f572b54ce9dd7477e6aed61231d02085b74934367e3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9894a0047cb09dcafd45f572b54ce9dd7477e6aed61231d02085b74934367e3f","first_computed_at":"2026-05-18T02:41:42.131788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:42.131788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s/kFAlxPeGq76PKAE0clIEGgTL9v1tPe0AABmaBrVD6QMK+MEynp/ssd7qSooMCPJdAZRoIpEuURMGZZ1nOtBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:42.132529Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1633","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae047c9a2746f6635b455cace982bb0d34a584d6cddf7a13ad39a15db4b53028","sha256:8089bb98c563fbc868ef6daedbcd567cb135d188fc006a3496d9d240116eba6c"],"state_sha256":"5c50cd3e962447340f68e787c0a6e0e8a30bfc1e9927f78d460a7a7479394418"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DgIkFNcP+1grPYeWWX1GfYdIH0ZKO83st1/jxaI95kfruMl3vQ1h+a3YqEfhVd23q0WAphKWJUBJiVhvHB0DCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:37:22.182814Z","bundle_sha256":"f8032b470b1776c65538b4c67320d43306671e0fa7b926d9eddceb764f3c7148"}}