{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LL43MEX5A25YB3YBHR5LIKDVIX","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":"c0804b447098705fca87c853a2f1261bf3a2da580a06b3f27adc4730c290577c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-06T13:58:00Z","title_canon_sha256":"6ed1fb2e6c126476f13cc49a383b3a75cb6f4b4b8228ec4f7412b60a1372e362"},"schema_version":"1.0","source":{"id":"1312.1867","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1867","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1867v2","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1867","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"pith_short_12","alias_value":"LL43MEX5A25Y","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LL43MEX5A25YB3YB","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LL43MEX5","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:cf5d7c0c60a5e3a7048a38e0781cb5a2b3e99260ea2441b4b7bdfecc210e7b92","target":"graph","created_at":"2026-05-18T02:45:49Z","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 paper, we introduce a new family of generalized colored Motzkin paths, where horizontal steps are colored by means of $F_{k,l}$ colors, where $F_{k,l}$ is the $l$th $k$-Fibonacci number. We study the enumeration of this family according to the length. For this, we use infinite weighted automata.","authors_text":"Jos\\'e L. Ram\\'irez, Rodrigo De Castro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-06T13:58:00Z","title":"Enumeration of $k$-Fibonacci Paths using Infinite Weighted Automata"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1867","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:c1dd3c2c5c9c84d3a68e898e7fda81555f796b71a544ab7a38f6dc74831e1645","target":"record","created_at":"2026-05-18T02:45:49Z","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":"c0804b447098705fca87c853a2f1261bf3a2da580a06b3f27adc4730c290577c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-06T13:58:00Z","title_canon_sha256":"6ed1fb2e6c126476f13cc49a383b3a75cb6f4b4b8228ec4f7412b60a1372e362"},"schema_version":"1.0","source":{"id":"1312.1867","kind":"arxiv","version":2}},"canonical_sha256":"5af9b612fd06bb80ef013c7ab4287545d4958f66f3870a6cf78dedf41f1a2463","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5af9b612fd06bb80ef013c7ab4287545d4958f66f3870a6cf78dedf41f1a2463","first_computed_at":"2026-05-18T02:45:49.641901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:49.641901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+zsKqxVaZ7cMId9sstmJjAd8aGP54qcXvgqKGD2kyEiG9KlxEWf+QIGVj6Qivyqpp69U+vrahoyO+A2AanXLAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:49.642446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1867","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1dd3c2c5c9c84d3a68e898e7fda81555f796b71a544ab7a38f6dc74831e1645","sha256:cf5d7c0c60a5e3a7048a38e0781cb5a2b3e99260ea2441b4b7bdfecc210e7b92"],"state_sha256":"97a564951d90d5bf886ee9282abb81ceee96079f582f82eae7f7269d0fbb4594"}