{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XGD6NOHSCWR6AM7XJPJ26LFRE3","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":"0c6d8e6485bdc570332ac256a187372003e4ee6c23c3637ff578b6b5d47a1475","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-22T07:57:45Z","title_canon_sha256":"cdb4f5ac5b697bec57ba8590ba85c3be9f6dd3bf7e4aadd26df76537d84ebb13"},"schema_version":"1.0","source":{"id":"1203.4902","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4902","created_at":"2026-05-18T03:59:28Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4902v1","created_at":"2026-05-18T03:59:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4902","created_at":"2026-05-18T03:59:28Z"},{"alias_kind":"pith_short_12","alias_value":"XGD6NOHSCWR6","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XGD6NOHSCWR6AM7X","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XGD6NOHS","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:78d1b7f04255d2c1f2065fd5b17a0c3e0ed3cbb8348554c049e92696fe782fe7","target":"graph","created_at":"2026-05-18T03:59:28Z","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":"Shimura reciprocity law allows us to verify that a modular function is a class invariant. Here we present a new method based on Shimura reciprocity that allows us not only to verify but to find new class invariants from a modular function of level $N$.","authors_text":"Aristides Kontogeorgis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-22T07:57:45Z","title":"Constructing Class invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4902","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":"sha256:54a927441bf1acc8c2b399f01a70156b9d08e0897f229289085fbf5b49416000","target":"record","created_at":"2026-05-18T03:59:28Z","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":"0c6d8e6485bdc570332ac256a187372003e4ee6c23c3637ff578b6b5d47a1475","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-22T07:57:45Z","title_canon_sha256":"cdb4f5ac5b697bec57ba8590ba85c3be9f6dd3bf7e4aadd26df76537d84ebb13"},"schema_version":"1.0","source":{"id":"1203.4902","kind":"arxiv","version":1}},"canonical_sha256":"b987e6b8f215a3e033f74bd3af2cb126fabe4e07503b1d5486c5c207902da0c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b987e6b8f215a3e033f74bd3af2cb126fabe4e07503b1d5486c5c207902da0c0","first_computed_at":"2026-05-18T03:59:28.426029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:28.426029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I2RnmnE/KUbbdxrsC3IguWqGZylb/MWDYnh31zn6njMW+A0wjp/IuXTnqzyoQCzdv4rtN3HrWouZHk6RDWz0AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:28.426979Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.4902","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54a927441bf1acc8c2b399f01a70156b9d08e0897f229289085fbf5b49416000","sha256:78d1b7f04255d2c1f2065fd5b17a0c3e0ed3cbb8348554c049e92696fe782fe7"],"state_sha256":"0f262988a031de38bb7c38d929b47c1e5e5c232891289cf57720555608bc5298"}