{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:OLRK5R6H6TFRZSTWYREA7CWJNQ","short_pith_number":"pith:OLRK5R6H","schema_version":"1.0","canonical_sha256":"72e2aec7c7f4cb1cca76c4480f8ac96c333aab6440fa5ae7296360c1bae12930","source":{"kind":"arxiv","id":"2112.05776","version":1},"attestation_state":"computed","paper":{"title":"Enumeration of three-quadrant walks via invariants: some diagonally symmetric models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Mireille Bousquet-M\\'elou","submitted_at":"2021-12-10T19:02:40Z","abstract_excerpt":"In the past 20 years, the enumeration of plane lattice walks confined to a convex cone -- normalized into the first quadrant -- has received a lot of attention, stimulated the development of several original approaches, and led to a rich collection of results. Most of them deal with the nature of the associated generating function: for which models is it algebraic, D-finite, D-algebraic? By model, what we mean is a finite collection of allowed steps.\n  More recently, similar questions have been raised for non-convex cones, typically the three-quadrant cone $C = \\{ (i,j) : i \\geq 0 \\text{ or } "},"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":"2112.05776","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-12-10T19:02:40Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"f7dd1a53132f132fc3a1dd4e9dcfd99ff507f96101c3c6ea4abd5c8cd98e3c8b","abstract_canon_sha256":"374dc4a4324f82f9ee8729e26387ba779cbcf1644c6413c1434cbc28f3d76637"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:46:51.788593Z","signature_b64":"TjnT+tdLLKUjRyNubWp50keDaaCmjFoCh/7viaDXvnM1ctsdiK/6LAictB00xoFNwcXRUnCtSLCj1A+SzSBpAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72e2aec7c7f4cb1cca76c4480f8ac96c333aab6440fa5ae7296360c1bae12930","last_reissued_at":"2026-07-05T10:46:51.788117Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:46:51.788117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Enumeration of three-quadrant walks via invariants: some diagonally symmetric models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Mireille Bousquet-M\\'elou","submitted_at":"2021-12-10T19:02:40Z","abstract_excerpt":"In the past 20 years, the enumeration of plane lattice walks confined to a convex cone -- normalized into the first quadrant -- has received a lot of attention, stimulated the development of several original approaches, and led to a rich collection of results. Most of them deal with the nature of the associated generating function: for which models is it algebraic, D-finite, D-algebraic? By model, what we mean is a finite collection of allowed steps.\n  More recently, similar questions have been raised for non-convex cones, typically the three-quadrant cone $C = \\{ (i,j) : i \\geq 0 \\text{ or } "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.05776","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.05776/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2112.05776","created_at":"2026-07-05T10:46:51.788171+00:00"},{"alias_kind":"arxiv_version","alias_value":"2112.05776v1","created_at":"2026-07-05T10:46:51.788171+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.05776","created_at":"2026-07-05T10:46:51.788171+00:00"},{"alias_kind":"pith_short_12","alias_value":"OLRK5R6H6TFR","created_at":"2026-07-05T10:46:51.788171+00:00"},{"alias_kind":"pith_short_16","alias_value":"OLRK5R6H6TFRZSTW","created_at":"2026-07-05T10:46:51.788171+00:00"},{"alias_kind":"pith_short_8","alias_value":"OLRK5R6H","created_at":"2026-07-05T10:46:51.788171+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/OLRK5R6H6TFRZSTWYREA7CWJNQ","json":"https://pith.science/pith/OLRK5R6H6TFRZSTWYREA7CWJNQ.json","graph_json":"https://pith.science/api/pith-number/OLRK5R6H6TFRZSTWYREA7CWJNQ/graph.json","events_json":"https://pith.science/api/pith-number/OLRK5R6H6TFRZSTWYREA7CWJNQ/events.json","paper":"https://pith.science/paper/OLRK5R6H"},"agent_actions":{"view_html":"https://pith.science/pith/OLRK5R6H6TFRZSTWYREA7CWJNQ","download_json":"https://pith.science/pith/OLRK5R6H6TFRZSTWYREA7CWJNQ.json","view_paper":"https://pith.science/paper/OLRK5R6H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2112.05776&json=true","fetch_graph":"https://pith.science/api/pith-number/OLRK5R6H6TFRZSTWYREA7CWJNQ/graph.json","fetch_events":"https://pith.science/api/pith-number/OLRK5R6H6TFRZSTWYREA7CWJNQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OLRK5R6H6TFRZSTWYREA7CWJNQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OLRK5R6H6TFRZSTWYREA7CWJNQ/action/storage_attestation","attest_author":"https://pith.science/pith/OLRK5R6H6TFRZSTWYREA7CWJNQ/action/author_attestation","sign_citation":"https://pith.science/pith/OLRK5R6H6TFRZSTWYREA7CWJNQ/action/citation_signature","submit_replication":"https://pith.science/pith/OLRK5R6H6TFRZSTWYREA7CWJNQ/action/replication_record"}},"created_at":"2026-07-05T10:46:51.788171+00:00","updated_at":"2026-07-05T10:46:51.788171+00:00"}