{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:EFBUP5AKMFG34SPTWEGZMLGTRI","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":"dfc118705cf553686069499ff67e55364e1c8b59edf59e8da2de1ebfd098dbef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-06-08T07:35:21Z","title_canon_sha256":"8fa8dedd30665ad96aa2f8732056d3b2816cf2635297019657f62a8ec192f03b"},"schema_version":"1.0","source":{"id":"1006.1469","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1469","created_at":"2026-05-18T04:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1469v3","created_at":"2026-05-18T04:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1469","created_at":"2026-05-18T04:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"EFBUP5AKMFG3","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EFBUP5AKMFG34SPT","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EFBUP5AK","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:85682888235f60e44bfe9a8da09c6bc7f652670c6f9ef9548976a7d5a4728a39","target":"graph","created_at":"2026-05-18T04:42:43Z","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 find some modularity criterion for a product of Klein forms of the congruence subgroup $\\Gamma_1(N)$ and, as its application, construct a basis of the space of modular forms for $\\Gamma_1(13)$ of weight $2$. In the process we face with an interesting property about the coefficients of certain theta function from a quadratic form and prove it conditionally by applying Hecke operators.","authors_text":"Dong Hwa Shin, Ick Sun Eum, Ja Kyung Koo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-06-08T07:35:21Z","title":"A modularity criterion for Klein forms, with an application to modular forms of level $13$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1469","kind":"arxiv","version":3},"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":"sha256:59b5cb2a3691945cffefe646b63a42054f4a322654ade0d102b884c3dd03d716","target":"record","created_at":"2026-05-18T04:42:43Z","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":"dfc118705cf553686069499ff67e55364e1c8b59edf59e8da2de1ebfd098dbef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-06-08T07:35:21Z","title_canon_sha256":"8fa8dedd30665ad96aa2f8732056d3b2816cf2635297019657f62a8ec192f03b"},"schema_version":"1.0","source":{"id":"1006.1469","kind":"arxiv","version":3}},"canonical_sha256":"214347f40a614dbe49f3b10d962cd38a181763e3a2948280362bad2941ac858a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"214347f40a614dbe49f3b10d962cd38a181763e3a2948280362bad2941ac858a","first_computed_at":"2026-05-18T04:42:43.184303Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:43.184303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SUZoJpc4LrNjG68yiatQh3DyUU456gafSd6w/pRCkDj9fohlCt+TTG+ai0haT9BDW927op5IJlj/NyK5QicECg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:43.184741Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.1469","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59b5cb2a3691945cffefe646b63a42054f4a322654ade0d102b884c3dd03d716","sha256:85682888235f60e44bfe9a8da09c6bc7f652670c6f9ef9548976a7d5a4728a39"],"state_sha256":"1ea38d268d8eb88b4d2906bd728da20c287b438eaa138d6993c1710611740e92"}