{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:23DCWM4NILT72ZQ5LMZLAXKHOR","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":"a55913f2c6db94e8d1c8d14f29bd9dc41610b2ee6d6dc9d7ac87d04b667f5763","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-29T03:48:33Z","title_canon_sha256":"8c7492874bc101b948b47e26ff401b33262a42569c8f4de3b78ac3b62dcce048"},"schema_version":"1.0","source":{"id":"1812.11279","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.11279","created_at":"2026-05-17T23:57:12Z"},{"alias_kind":"arxiv_version","alias_value":"1812.11279v1","created_at":"2026-05-17T23:57:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11279","created_at":"2026-05-17T23:57:12Z"},{"alias_kind":"pith_short_12","alias_value":"23DCWM4NILT7","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"23DCWM4NILT72ZQ5","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"23DCWM4N","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:d45f261fb54729b892541e8601d93de2f7592676062b3d245ada27760f02e8c4","target":"graph","created_at":"2026-05-17T23:57:12Z","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":"In this article we obtain a general polynomial identity in $k$ variables, where $k\\geq 2$ is an arbitrary positive integer. We use this identity to give a closed-form expression for the entries of the powers of a $k \\times k$ matrix. Finally, we use these results to derive various combinatorial identities.","authors_text":"B. Sury, James Mc Laughlin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-29T03:48:33Z","title":"Powers of a matrix and combinatorial identities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11279","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:f5e6761b529a4c48f35bdf6e45d67e142dc94af602417467007c90f1d9f835d6","target":"record","created_at":"2026-05-17T23:57:12Z","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":"a55913f2c6db94e8d1c8d14f29bd9dc41610b2ee6d6dc9d7ac87d04b667f5763","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-12-29T03:48:33Z","title_canon_sha256":"8c7492874bc101b948b47e26ff401b33262a42569c8f4de3b78ac3b62dcce048"},"schema_version":"1.0","source":{"id":"1812.11279","kind":"arxiv","version":1}},"canonical_sha256":"d6c62b338d42e7fd661d5b32b05d47747bb0d11835e84fa5290d3909860c4f17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6c62b338d42e7fd661d5b32b05d47747bb0d11835e84fa5290d3909860c4f17","first_computed_at":"2026-05-17T23:57:12.352347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:12.352347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D3VFoXOn+WKBtlRziosqmuozWQQvO2ClWRP3ZpaWFaAfA95IxRAlRm7Q9taMcgKkKheJOqctj+SEFrWg7QqFBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:12.352775Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.11279","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5e6761b529a4c48f35bdf6e45d67e142dc94af602417467007c90f1d9f835d6","sha256:d45f261fb54729b892541e8601d93de2f7592676062b3d245ada27760f02e8c4"],"state_sha256":"ab57bd7ccbb64eb372770ecc0abb1fd800b4d09ed893eb25fb604161d09bae43"}