{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:NXVTZA5IN5HBHH3JB46E6HUDHS","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":"e63e711dbc87a4c729caf84c15a14ed2b84cba7faf471feee377233aecd43158","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-12-01T12:10:48Z","title_canon_sha256":"bd1512e44e84ce853d9d45dab129d882cedd6d2ed5e7bd4371a0ef462f5bc9b5"},"schema_version":"1.0","source":{"id":"2112.00444","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.00444","created_at":"2026-07-05T03:47:02Z"},{"alias_kind":"arxiv_version","alias_value":"2112.00444v2","created_at":"2026-07-05T03:47:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.00444","created_at":"2026-07-05T03:47:02Z"},{"alias_kind":"pith_short_12","alias_value":"NXVTZA5IN5HB","created_at":"2026-07-05T03:47:02Z"},{"alias_kind":"pith_short_16","alias_value":"NXVTZA5IN5HBHH3J","created_at":"2026-07-05T03:47:02Z"},{"alias_kind":"pith_short_8","alias_value":"NXVTZA5I","created_at":"2026-07-05T03:47:02Z"}],"graph_snapshots":[{"event_id":"sha256:b0a9ebb8dbead2c61f2640bc5ca72842178eb62025cb03de501e39245e535392","target":"graph","created_at":"2026-07-05T03:47:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2112.00444/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider integers whose squares have just three decimal digits. Examples are e.g. given by $2108436491907081488939581538^2 = 4445504440405440505004450045555054500055550554550445444$ and $10100000000010401000000000101^2 = 102010000000210100200000110221001000002101002000000010201$. The aim of this paper is to summarize the current knowledge on squares with three digits, scattered around webpages and newsgroup postings, and to add a few new insights. While we will mostly focus on the base $B=10$, several results are presented for general values of $B$. The used mathematical tools are completel","authors_text":"Anne Zahn, Michael Gei{\\ss}er, Sascha Kurz, Theresa K\\\"orner","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-12-01T12:10:48Z","title":"Squares with three digits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.00444","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:a2eb9cf635904191c8d650b23c1a0276b68dbf78d0e5db33ee2b351612bcc81c","target":"record","created_at":"2026-07-05T03:47:02Z","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":"e63e711dbc87a4c729caf84c15a14ed2b84cba7faf471feee377233aecd43158","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-12-01T12:10:48Z","title_canon_sha256":"bd1512e44e84ce853d9d45dab129d882cedd6d2ed5e7bd4371a0ef462f5bc9b5"},"schema_version":"1.0","source":{"id":"2112.00444","kind":"arxiv","version":2}},"canonical_sha256":"6deb3c83a86f4e139f690f3c4f1e833cad47ab98612a8171b86f58b655f806cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6deb3c83a86f4e139f690f3c4f1e833cad47ab98612a8171b86f58b655f806cb","first_computed_at":"2026-07-05T03:47:02.663744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:47:02.663744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b/SoWCmmMvF64jZ/n2onJXlIWGHk3zHXbqGrp0djmpluKRJCioBUDJlDS7EZZeRDCrAArHSeni/H0G4jecmnDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:47:02.664241Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.00444","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2eb9cf635904191c8d650b23c1a0276b68dbf78d0e5db33ee2b351612bcc81c","sha256:b0a9ebb8dbead2c61f2640bc5ca72842178eb62025cb03de501e39245e535392"],"state_sha256":"912f18fbd96797133bb9961f32bad0b0afe5ecbafe91b34cba6d78351383078b"}