{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5NE7R5AATYWHBONTCBUNPHKAXO","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":"e32e6cb21cd71eaa17e75f9628f7a19e6237342daa53242076adf199cb6a6c6c","cross_cats_sorted":["cs.LO","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-06-13T10:33:05Z","title_canon_sha256":"7b906e076e339577ae362c337719d8fdfae6a3b79258b465249778de18d8cea9"},"schema_version":"1.0","source":{"id":"1906.05590","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.05590","created_at":"2026-05-17T23:43:24Z"},{"alias_kind":"arxiv_version","alias_value":"1906.05590v1","created_at":"2026-05-17T23:43:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.05590","created_at":"2026-05-17T23:43:24Z"},{"alias_kind":"pith_short_12","alias_value":"5NE7R5AATYWH","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5NE7R5AATYWHBONT","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5NE7R5AA","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:faf195c3a37364c7a1c6df71d2208f22a7b1e307b4cad70c9f8bb182864115ca","target":"graph","created_at":"2026-05-17T23:43:24Z","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":"The set of discrete lattice paths from (0, 0) to (n, n) with North and East steps (i.e. words w $\\in$ { x, y } * such that |w| x = |w| y = n) has a canonical monoid structure inherited from the bijection with the set of join-continuous maps from the chain { 0, 1,. .. , n } to itself. We explicitly describe this monoid structure and, relying on a general characterization of idempotent join-continuous maps from a complete lattice to itself, we characterize idempotent paths as upper zigzag paths. We argue that these paths are counted by the odd Fibonacci numbers. Our method yields a geometric/com","authors_text":"Luigi Santocanale (LIS)","cross_cats":["cs.LO","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-06-13T10:33:05Z","title":"On discrete idempotent paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05590","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":"sha256:0489ea5dad435b4c3f62d5ddcfa8897a0fac74c9c738c5b71751c926e2e3f0c2","target":"record","created_at":"2026-05-17T23:43:24Z","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":"e32e6cb21cd71eaa17e75f9628f7a19e6237342daa53242076adf199cb6a6c6c","cross_cats_sorted":["cs.LO","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-06-13T10:33:05Z","title_canon_sha256":"7b906e076e339577ae362c337719d8fdfae6a3b79258b465249778de18d8cea9"},"schema_version":"1.0","source":{"id":"1906.05590","kind":"arxiv","version":1}},"canonical_sha256":"eb49f8f4009e2c70b9b31068d79d40bb970b43ee8bb4996fd1a4d409585830da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb49f8f4009e2c70b9b31068d79d40bb970b43ee8bb4996fd1a4d409585830da","first_computed_at":"2026-05-17T23:43:24.856871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:24.856871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WYAWPSacfDDyvgqWpSdOqB2G3+8mgt4lHlh3OplJIozRQlBbCkV57q8JGB/MbT5XYxQPyzOrpyBIQzV3oBHVAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:24.857357Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.05590","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0489ea5dad435b4c3f62d5ddcfa8897a0fac74c9c738c5b71751c926e2e3f0c2","sha256:faf195c3a37364c7a1c6df71d2208f22a7b1e307b4cad70c9f8bb182864115ca"],"state_sha256":"1407d1e4671062456bd29da34f07013942d4f3565c4be6e82523ff1ff2780460"}