{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7N54WCECGAE47ZG7SN6OIZUODM","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":"eae02a8e030364873880b02f75a6409fff9f701dfcd873ed8d3c8015683141b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-18T09:32:06Z","title_canon_sha256":"885f51f3d519ccd2e33ffae625b235a020fe9490e22aeaf81a3b8e52d9553335"},"schema_version":"1.0","source":{"id":"1906.07461","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.07461","created_at":"2026-05-17T23:43:07Z"},{"alias_kind":"arxiv_version","alias_value":"1906.07461v1","created_at":"2026-05-17T23:43:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.07461","created_at":"2026-05-17T23:43:07Z"},{"alias_kind":"pith_short_12","alias_value":"7N54WCECGAE4","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"7N54WCECGAE47ZG7","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"7N54WCEC","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:5052a597c0284e2236189a6d745b042bd8dcc2de9fe952fe3ad44f383df09994","target":"graph","created_at":"2026-05-17T23:43:07Z","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":"An associative magic square is a magic square such that the sum of any 2 cells at symmetric positions with respect to the center is constant. The total number of associative magic squares of order 7 is enormous, and thus, it is not realistic to obtain the number by simple backtracking. As a recent result, Artem Ripatti reported the number of semi-magic squares of order 6 (the magic squares of 6x6 without diagonal sum conditions) in 2018. In this research, with reference to Ripatti's method of enumerating semi-magic squares, we have calculated the total number of associative magic squares of or","authors_text":"Go Kato, Shin-ichi Minato","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-18T09:32:06Z","title":"Enumeration of associative magic squares of order 7"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07461","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":"sha256:793fccea1e9b30b5b327de1035330359bb387e721d26c89e81dbf2f2ffca9408","target":"record","created_at":"2026-05-17T23:43:07Z","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":"eae02a8e030364873880b02f75a6409fff9f701dfcd873ed8d3c8015683141b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-18T09:32:06Z","title_canon_sha256":"885f51f3d519ccd2e33ffae625b235a020fe9490e22aeaf81a3b8e52d9553335"},"schema_version":"1.0","source":{"id":"1906.07461","kind":"arxiv","version":1}},"canonical_sha256":"fb7bcb08823009cfe4df937ce4668e1b1b068d0f667ca97ffee9c27960ff5b83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb7bcb08823009cfe4df937ce4668e1b1b068d0f667ca97ffee9c27960ff5b83","first_computed_at":"2026-05-17T23:43:07.840373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:07.840373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a227LRfhvaBZ6fIb3ERdlBV0+M06fPsiu9HdKgmJQCj2IylsE0wpNSLggFZ88NgeezRNt0be3Be/66MtpGkoDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:07.840999Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.07461","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:793fccea1e9b30b5b327de1035330359bb387e721d26c89e81dbf2f2ffca9408","sha256:5052a597c0284e2236189a6d745b042bd8dcc2de9fe952fe3ad44f383df09994"],"state_sha256":"4fd15300ff28a23d7335e8bc775f106460825c382645d1b6f7ca2d08cfc40a5e"}