{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:D4F527YVM5KSGP37EFTMJ65NXU","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":"68326e5b2031a6b98356c9d890d3b03b35dd637764a3d767b20d93372ba26e8a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-14T14:25:54Z","title_canon_sha256":"9a3f6b967e49d91f22adaffd796be3f1ab9a3d4ef589be2c0629f04447ef0d57"},"schema_version":"1.0","source":{"id":"1301.2986","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2986","created_at":"2026-05-18T03:36:03Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2986v2","created_at":"2026-05-18T03:36:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2986","created_at":"2026-05-18T03:36:03Z"},{"alias_kind":"pith_short_12","alias_value":"D4F527YVM5KS","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D4F527YVM5KSGP37","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D4F527YV","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:455faccebb73e62bd843a12214b3fa1e28f93d24d2a55412316254a4a23d8977","target":"graph","created_at":"2026-05-18T03:36:03Z","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":"Recently, Straub gave an interesting $q$-analogue of a binomial congruence of Ljunggren. In this note we give an inductive proof of his result.","authors_text":"Bo Ning","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-14T14:25:54Z","title":"An inductive proof of Straub's q-analogue of Ljunggren's congruence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2986","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:f53c72c545b02018ab0d7719601be949d6a3c7437ddf49fcbd48355389c9ee38","target":"record","created_at":"2026-05-18T03:36:03Z","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":"68326e5b2031a6b98356c9d890d3b03b35dd637764a3d767b20d93372ba26e8a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-14T14:25:54Z","title_canon_sha256":"9a3f6b967e49d91f22adaffd796be3f1ab9a3d4ef589be2c0629f04447ef0d57"},"schema_version":"1.0","source":{"id":"1301.2986","kind":"arxiv","version":2}},"canonical_sha256":"1f0bdd7f156755233f7f2166c4fbadbd153bb821ee6d043225db8d62439647fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f0bdd7f156755233f7f2166c4fbadbd153bb821ee6d043225db8d62439647fe","first_computed_at":"2026-05-18T03:36:03.802382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:03.802382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"68lPsr4+X1npmq/tV6WSXTyOzpa4i9Ai+bl0skKVY+H0hsX1vyjseu6FML33xQ6zwJWRftplvk5uykpEid5uDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:03.803197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2986","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f53c72c545b02018ab0d7719601be949d6a3c7437ddf49fcbd48355389c9ee38","sha256:455faccebb73e62bd843a12214b3fa1e28f93d24d2a55412316254a4a23d8977"],"state_sha256":"18573c5c584ec0e4fc93791428c66b7b3e2948481a1a35d5c082ad6bf185fa6b"}