{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:KTFZACWJK5BVZYDEGVL5SO5OLD","short_pith_number":"pith:KTFZACWJ","schema_version":"1.0","canonical_sha256":"54cb900ac957435ce0643557d93bae58e1a019850e7b0896203af93942ce14d8","source":{"kind":"arxiv","id":"1305.2206","version":2},"attestation_state":"computed","paper":{"title":"Symmetries of statistics on lattice paths between two boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Martin Rubey, Sergi Elizalde","submitted_at":"2013-05-09T20:13:43Z","abstract_excerpt":"We prove that on the set of lattice paths with steps N=(0,1) and E=(1,0) that lie between two fixed boundaries T and B (which are themselves lattice paths), the statistics `number of E steps shared with B' and `number of E steps shared with T' have a symmetric joint distribution. To do so, we give an involution that switches these statistics, preserves additional parameters, and generalizes to paths that contain steps S=(0,-1) at prescribed x-coordinates. We also show that a similar equidistribution result for path statistics follows from the fact that the Tutte polynomial of a matroid is inde"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1305.2206","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-09T20:13:43Z","cross_cats_sorted":[],"title_canon_sha256":"900a01510e98add48fc50dbdc9e74463ae4269402da60b1f3e78eb92a5af1f36","abstract_canon_sha256":"03e5a4668918194cdca61ed6f0e12147d20368be6f3a51c821aa91ea335493fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:03.209892Z","signature_b64":"fMYIzMFXKbf9B3qOivNhOeEp5SBZdVueONtwMbUR5TNviKB6bz8p3oq7Ai4iUqOsvAE9JtKF58yWhjseSerYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54cb900ac957435ce0643557d93bae58e1a019850e7b0896203af93942ce14d8","last_reissued_at":"2026-05-18T01:26:03.209473Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:03.209473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetries of statistics on lattice paths between two boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Martin Rubey, Sergi Elizalde","submitted_at":"2013-05-09T20:13:43Z","abstract_excerpt":"We prove that on the set of lattice paths with steps N=(0,1) and E=(1,0) that lie between two fixed boundaries T and B (which are themselves lattice paths), the statistics `number of E steps shared with B' and `number of E steps shared with T' have a symmetric joint distribution. To do so, we give an involution that switches these statistics, preserves additional parameters, and generalizes to paths that contain steps S=(0,-1) at prescribed x-coordinates. We also show that a similar equidistribution result for path statistics follows from the fact that the Tutte polynomial of a matroid is inde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2206","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1305.2206","created_at":"2026-05-18T01:26:03.209535+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.2206v2","created_at":"2026-05-18T01:26:03.209535+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2206","created_at":"2026-05-18T01:26:03.209535+00:00"},{"alias_kind":"pith_short_12","alias_value":"KTFZACWJK5BV","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"KTFZACWJK5BVZYDE","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"KTFZACWJ","created_at":"2026-05-18T12:27:51.066281+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KTFZACWJK5BVZYDEGVL5SO5OLD","json":"https://pith.science/pith/KTFZACWJK5BVZYDEGVL5SO5OLD.json","graph_json":"https://pith.science/api/pith-number/KTFZACWJK5BVZYDEGVL5SO5OLD/graph.json","events_json":"https://pith.science/api/pith-number/KTFZACWJK5BVZYDEGVL5SO5OLD/events.json","paper":"https://pith.science/paper/KTFZACWJ"},"agent_actions":{"view_html":"https://pith.science/pith/KTFZACWJK5BVZYDEGVL5SO5OLD","download_json":"https://pith.science/pith/KTFZACWJK5BVZYDEGVL5SO5OLD.json","view_paper":"https://pith.science/paper/KTFZACWJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.2206&json=true","fetch_graph":"https://pith.science/api/pith-number/KTFZACWJK5BVZYDEGVL5SO5OLD/graph.json","fetch_events":"https://pith.science/api/pith-number/KTFZACWJK5BVZYDEGVL5SO5OLD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KTFZACWJK5BVZYDEGVL5SO5OLD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KTFZACWJK5BVZYDEGVL5SO5OLD/action/storage_attestation","attest_author":"https://pith.science/pith/KTFZACWJK5BVZYDEGVL5SO5OLD/action/author_attestation","sign_citation":"https://pith.science/pith/KTFZACWJK5BVZYDEGVL5SO5OLD/action/citation_signature","submit_replication":"https://pith.science/pith/KTFZACWJK5BVZYDEGVL5SO5OLD/action/replication_record"}},"created_at":"2026-05-18T01:26:03.209535+00:00","updated_at":"2026-05-18T01:26:03.209535+00:00"}