{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:P7YJ7PCEA77PYYRV5UJBK45QBK","short_pith_number":"pith:P7YJ7PCE","canonical_record":{"source":{"id":"0902.2329","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-02-13T15:37:27Z","cross_cats_sorted":[],"title_canon_sha256":"b789f996f9fc0eacd56c84b3ae8c7e3839036042270ec3effd3f91715b6e17c9","abstract_canon_sha256":"87b1da4ced07b77403dbb82b68f56a7c64649c2fb7b886eb6e83f73b44f78270"},"schema_version":"1.0"},"canonical_sha256":"7ff09fbc4407fefc6235ed121573b00aaac72a7f616b53dd7ce9f1adc73eacb9","source":{"kind":"arxiv","id":"0902.2329","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.2329","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"arxiv_version","alias_value":"0902.2329v1","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.2329","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"pith_short_12","alias_value":"P7YJ7PCEA77P","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"P7YJ7PCEA77PYYRV","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"P7YJ7PCE","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:P7YJ7PCEA77PYYRV5UJBK45QBK","target":"record","payload":{"canonical_record":{"source":{"id":"0902.2329","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-02-13T15:37:27Z","cross_cats_sorted":[],"title_canon_sha256":"b789f996f9fc0eacd56c84b3ae8c7e3839036042270ec3effd3f91715b6e17c9","abstract_canon_sha256":"87b1da4ced07b77403dbb82b68f56a7c64649c2fb7b886eb6e83f73b44f78270"},"schema_version":"1.0"},"canonical_sha256":"7ff09fbc4407fefc6235ed121573b00aaac72a7f616b53dd7ce9f1adc73eacb9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:04.337494Z","signature_b64":"jH7jlLNQv6GlDgOpLw3DP5lLp8rAWbpgK2kROsEbRyATLx1tmFQNPX4qXPmlHRdDLhcXNRpbZbMuwsXLWQthDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ff09fbc4407fefc6235ed121573b00aaac72a7f616b53dd7ce9f1adc73eacb9","last_reissued_at":"2026-05-18T04:24:04.336877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:04.336877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.2329","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:24:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B7mtYb2kBK1d6fr9tnSHb4ItqYqeIRFU1CjrPnPH9P7IGnvA6VRhawxGk6CIxLnOGsJuZ+tO29MzQpPy6jDKBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:00:02.756981Z"},"content_sha256":"12dea78381aef7f916cf56efbba5fe40b1168db81ecf320f0869d89953dde4ed","schema_version":"1.0","event_id":"sha256:12dea78381aef7f916cf56efbba5fe40b1168db81ecf320f0869d89953dde4ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:P7YJ7PCEA77PYYRV5UJBK45QBK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards a human proof of Gessel's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arvind Ayyer","submitted_at":"2009-02-13T15:37:27Z","abstract_excerpt":"We interpret walks in the first quadrant with steps {(1,1),(1,0),(-1,0), (-1,-1)} as a generalization of Dyck words with two sets of letters. Using this language, we give a formal expression for the number of walks in the steps above beginning and ending at the origin. We give an explicit formula for a restricted class of such words using a correspondance between such words and Dyck paths. This explicit formula is exactly the same as that for the degree of the polynomial satisfied by the square of the area of cyclic n-gons conjectured by Dave Robbins although the connection is a mystery. Final"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2329","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:24:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zJSMKRjBvEDNXoDyShaixeZ9IfNsug8FNsJRAOP8BUUCgq1hb0l3+u19Fkeu106Y84Be5eXhRLvI13nOPeSvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:00:02.757340Z"},"content_sha256":"f2fbf5a68365d7b913a078169b99277f5d689b0e49abe360d7bc49e4f7960895","schema_version":"1.0","event_id":"sha256:f2fbf5a68365d7b913a078169b99277f5d689b0e49abe360d7bc49e4f7960895"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P7YJ7PCEA77PYYRV5UJBK45QBK/bundle.json","state_url":"https://pith.science/pith/P7YJ7PCEA77PYYRV5UJBK45QBK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P7YJ7PCEA77PYYRV5UJBK45QBK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T19:00:02Z","links":{"resolver":"https://pith.science/pith/P7YJ7PCEA77PYYRV5UJBK45QBK","bundle":"https://pith.science/pith/P7YJ7PCEA77PYYRV5UJBK45QBK/bundle.json","state":"https://pith.science/pith/P7YJ7PCEA77PYYRV5UJBK45QBK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P7YJ7PCEA77PYYRV5UJBK45QBK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:P7YJ7PCEA77PYYRV5UJBK45QBK","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":"87b1da4ced07b77403dbb82b68f56a7c64649c2fb7b886eb6e83f73b44f78270","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-02-13T15:37:27Z","title_canon_sha256":"b789f996f9fc0eacd56c84b3ae8c7e3839036042270ec3effd3f91715b6e17c9"},"schema_version":"1.0","source":{"id":"0902.2329","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.2329","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"arxiv_version","alias_value":"0902.2329v1","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.2329","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"pith_short_12","alias_value":"P7YJ7PCEA77P","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"P7YJ7PCEA77PYYRV","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"P7YJ7PCE","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:f2fbf5a68365d7b913a078169b99277f5d689b0e49abe360d7bc49e4f7960895","target":"graph","created_at":"2026-05-18T04:24:04Z","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":"We interpret walks in the first quadrant with steps {(1,1),(1,0),(-1,0), (-1,-1)} as a generalization of Dyck words with two sets of letters. Using this language, we give a formal expression for the number of walks in the steps above beginning and ending at the origin. We give an explicit formula for a restricted class of such words using a correspondance between such words and Dyck paths. This explicit formula is exactly the same as that for the degree of the polynomial satisfied by the square of the area of cyclic n-gons conjectured by Dave Robbins although the connection is a mystery. Final","authors_text":"Arvind Ayyer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-02-13T15:37:27Z","title":"Towards a human proof of Gessel's conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2329","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":"sha256:12dea78381aef7f916cf56efbba5fe40b1168db81ecf320f0869d89953dde4ed","target":"record","created_at":"2026-05-18T04:24:04Z","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":"87b1da4ced07b77403dbb82b68f56a7c64649c2fb7b886eb6e83f73b44f78270","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-02-13T15:37:27Z","title_canon_sha256":"b789f996f9fc0eacd56c84b3ae8c7e3839036042270ec3effd3f91715b6e17c9"},"schema_version":"1.0","source":{"id":"0902.2329","kind":"arxiv","version":1}},"canonical_sha256":"7ff09fbc4407fefc6235ed121573b00aaac72a7f616b53dd7ce9f1adc73eacb9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ff09fbc4407fefc6235ed121573b00aaac72a7f616b53dd7ce9f1adc73eacb9","first_computed_at":"2026-05-18T04:24:04.336877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:04.336877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jH7jlLNQv6GlDgOpLw3DP5lLp8rAWbpgK2kROsEbRyATLx1tmFQNPX4qXPmlHRdDLhcXNRpbZbMuwsXLWQthDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:04.337494Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.2329","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12dea78381aef7f916cf56efbba5fe40b1168db81ecf320f0869d89953dde4ed","sha256:f2fbf5a68365d7b913a078169b99277f5d689b0e49abe360d7bc49e4f7960895"],"state_sha256":"d902772ab44bc80e4961777c582b2ed6b7a908a2c385a118e4a43ef3f6a7b2cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Vm1s+ekuyQI9KWW2eYYRIbfaT0AIpr5lAAdS5bN5saJUzMuw3jQKg2DodqJBerei7yw1M3jZBMi9oyVhiWjAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:00:02.759266Z","bundle_sha256":"b8c75413ce0b3b8ee48c13a76733c13173d184f9b19cae5ced1717de9dc7c391"}}