{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:BUGDEOZHHOA72PW3YDAKQ4KNWQ","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":"ae7b33d29e22e44b0548ad544d39330b341b8623c12bef067063b2a605c8a23b","cross_cats_sorted":["math.CO","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2019-07-25T16:05:48Z","title_canon_sha256":"1e624a7ca4b4b4a52a6dba8f626e2826fec6c6d2a7fa2a56eaa43633978c99fa"},"schema_version":"1.0","source":{"id":"1907.11159","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.11159","created_at":"2026-05-17T23:39:23Z"},{"alias_kind":"arxiv_version","alias_value":"1907.11159v2","created_at":"2026-05-17T23:39:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.11159","created_at":"2026-05-17T23:39:23Z"},{"alias_kind":"pith_short_12","alias_value":"BUGDEOZHHOA7","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"BUGDEOZHHOA72PW3","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"BUGDEOZH","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:a76ec453e1f4bbcd8b55d2aa40593b927a15c1da207ba93c438258f8b10a6d8b","target":"graph","created_at":"2026-05-17T23:39:23Z","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 Rascal Triangle was introduced by three middle school students in 2010, and in this paper we describe number triangles that are generalizations of the Rascal Triangle and show that these Generalized Rascal Triangles are characterized by arithmetic sequences on all diagonals as well as a Rascal-like multiplication and addition rules.","authors_text":"Philip K. Hotchkiss","cross_cats":["math.CO","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2019-07-25T16:05:48Z","title":"Generalized Rascal Triangles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11159","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":"sha256:476aa56bd65eb3035e10ccac739f1386051f72c49916108b46a81dd39724d06d","target":"record","created_at":"2026-05-17T23:39:23Z","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":"ae7b33d29e22e44b0548ad544d39330b341b8623c12bef067063b2a605c8a23b","cross_cats_sorted":["math.CO","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2019-07-25T16:05:48Z","title_canon_sha256":"1e624a7ca4b4b4a52a6dba8f626e2826fec6c6d2a7fa2a56eaa43633978c99fa"},"schema_version":"1.0","source":{"id":"1907.11159","kind":"arxiv","version":2}},"canonical_sha256":"0d0c323b273b81fd3edbc0c0a8714db400328dcfe21347a27ba7ed29b9b6426e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d0c323b273b81fd3edbc0c0a8714db400328dcfe21347a27ba7ed29b9b6426e","first_computed_at":"2026-05-17T23:39:23.446987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:23.446987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9wOpldkJcdzUfVM2COaa6X8tCMpiyM4lDSHW0d/bGoRI0cxbGUXp3wHavlTtAqfx0vvA+Uwr3T6zLsyvPqt6BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:23.447672Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.11159","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:476aa56bd65eb3035e10ccac739f1386051f72c49916108b46a81dd39724d06d","sha256:a76ec453e1f4bbcd8b55d2aa40593b927a15c1da207ba93c438258f8b10a6d8b"],"state_sha256":"eff4d972a14c8d4bd3e56d69a0f7a334d1869703f25ef73a5554b0eff5636fc9"}