{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:W2SUUJXOSMPLEVN5M5NWS4BBIL","short_pith_number":"pith:W2SUUJXO","canonical_record":{"source":{"id":"1303.2724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-11T23:53:11Z","cross_cats_sorted":[],"title_canon_sha256":"c5502dd020185b8d6dd0184b49e370566867713cc5ff6fe1e6cb444dd1c942e0","abstract_canon_sha256":"e33c607620e100750e647910f68f8ca41cb4d3fc7353ce31d3f07a99096f99b8"},"schema_version":"1.0"},"canonical_sha256":"b6a54a26ee931eb255bd675b69702142f50e0b9cc400affb0f80303120e9ba55","source":{"kind":"arxiv","id":"1303.2724","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.2724","created_at":"2026-05-18T03:31:08Z"},{"alias_kind":"arxiv_version","alias_value":"1303.2724v1","created_at":"2026-05-18T03:31:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.2724","created_at":"2026-05-18T03:31:08Z"},{"alias_kind":"pith_short_12","alias_value":"W2SUUJXOSMPL","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W2SUUJXOSMPLEVN5","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W2SUUJXO","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:W2SUUJXOSMPLEVN5M5NWS4BBIL","target":"record","payload":{"canonical_record":{"source":{"id":"1303.2724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-11T23:53:11Z","cross_cats_sorted":[],"title_canon_sha256":"c5502dd020185b8d6dd0184b49e370566867713cc5ff6fe1e6cb444dd1c942e0","abstract_canon_sha256":"e33c607620e100750e647910f68f8ca41cb4d3fc7353ce31d3f07a99096f99b8"},"schema_version":"1.0"},"canonical_sha256":"b6a54a26ee931eb255bd675b69702142f50e0b9cc400affb0f80303120e9ba55","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:08.274862Z","signature_b64":"wgXx8VtT2zGHIJeZmX0aN/2oy5DxzkoE/cJtAOYnyk98giit2/xJAA4xlF67g0duG4Q4EcU2enZlxv+Juj84DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6a54a26ee931eb255bd675b69702142f50e0b9cc400affb0f80303120e9ba55","last_reissued_at":"2026-05-18T03:31:08.273921Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:08.273921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.2724","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":"2026-05-18T03:31:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aCyem++ta9oFGSp/OQZOnczkIPLkJCH3FMQj78ezOzabLAeKGBWEyj0kp2RJe2koW0vgkyuf0+I1YWlnGsGWDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:22:20.758694Z"},"content_sha256":"a83f62d59caa6ecd68c417949bd991302dc550e4cabc9ad63c36d2e0b89c516c","schema_version":"1.0","event_id":"sha256:a83f62d59caa6ecd68c417949bd991302dc550e4cabc9ad63c36d2e0b89c516c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:W2SUUJXOSMPLEVN5M5NWS4BBIL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Dyck paths of bounded height","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Axel Bacher","submitted_at":"2013-03-11T23:53:11Z","abstract_excerpt":"Generalized Dyck paths (or discrete excursions) are one-dimensional paths that take their steps in a given finite set S, start and end at height 0, and remain at a non-negative height. Bousquet-M\\'elou showed that the generating function E_k of excursions of height at most k is of the form F_k/F_{k+1}, where the F_k are polynomials satisfying a linear recurrence relation. We give a combinatorial interpretation of the polynomials F_k and of their recurrence relation using a transfer matrix method. We then extend our method to enumerate discrete meanders (or paths that start at 0 and remain at a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2724","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":"2026-05-18T03:31:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cCBVm/h+XV0M1fkAKzklg/by+fXWsyFQcq3fCE0y0l7sHJmnzj0Z7qaylaQGvPy576GRgJvRTEDS3wJWGaqrAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:22:20.759045Z"},"content_sha256":"439941d31cb58d1bc525a3549e41585ff4f7a3a674688ab3ad33668682adcf1a","schema_version":"1.0","event_id":"sha256:439941d31cb58d1bc525a3549e41585ff4f7a3a674688ab3ad33668682adcf1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W2SUUJXOSMPLEVN5M5NWS4BBIL/bundle.json","state_url":"https://pith.science/pith/W2SUUJXOSMPLEVN5M5NWS4BBIL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W2SUUJXOSMPLEVN5M5NWS4BBIL/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":"2026-06-09T12:22:20Z","links":{"resolver":"https://pith.science/pith/W2SUUJXOSMPLEVN5M5NWS4BBIL","bundle":"https://pith.science/pith/W2SUUJXOSMPLEVN5M5NWS4BBIL/bundle.json","state":"https://pith.science/pith/W2SUUJXOSMPLEVN5M5NWS4BBIL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W2SUUJXOSMPLEVN5M5NWS4BBIL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:W2SUUJXOSMPLEVN5M5NWS4BBIL","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":"e33c607620e100750e647910f68f8ca41cb4d3fc7353ce31d3f07a99096f99b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-11T23:53:11Z","title_canon_sha256":"c5502dd020185b8d6dd0184b49e370566867713cc5ff6fe1e6cb444dd1c942e0"},"schema_version":"1.0","source":{"id":"1303.2724","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.2724","created_at":"2026-05-18T03:31:08Z"},{"alias_kind":"arxiv_version","alias_value":"1303.2724v1","created_at":"2026-05-18T03:31:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.2724","created_at":"2026-05-18T03:31:08Z"},{"alias_kind":"pith_short_12","alias_value":"W2SUUJXOSMPL","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W2SUUJXOSMPLEVN5","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W2SUUJXO","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:439941d31cb58d1bc525a3549e41585ff4f7a3a674688ab3ad33668682adcf1a","target":"graph","created_at":"2026-05-18T03:31:08Z","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":"Generalized Dyck paths (or discrete excursions) are one-dimensional paths that take their steps in a given finite set S, start and end at height 0, and remain at a non-negative height. Bousquet-M\\'elou showed that the generating function E_k of excursions of height at most k is of the form F_k/F_{k+1}, where the F_k are polynomials satisfying a linear recurrence relation. We give a combinatorial interpretation of the polynomials F_k and of their recurrence relation using a transfer matrix method. We then extend our method to enumerate discrete meanders (or paths that start at 0 and remain at a","authors_text":"Axel Bacher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-11T23:53:11Z","title":"Generalized Dyck paths of bounded height"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2724","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:a83f62d59caa6ecd68c417949bd991302dc550e4cabc9ad63c36d2e0b89c516c","target":"record","created_at":"2026-05-18T03:31:08Z","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":"e33c607620e100750e647910f68f8ca41cb4d3fc7353ce31d3f07a99096f99b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-11T23:53:11Z","title_canon_sha256":"c5502dd020185b8d6dd0184b49e370566867713cc5ff6fe1e6cb444dd1c942e0"},"schema_version":"1.0","source":{"id":"1303.2724","kind":"arxiv","version":1}},"canonical_sha256":"b6a54a26ee931eb255bd675b69702142f50e0b9cc400affb0f80303120e9ba55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6a54a26ee931eb255bd675b69702142f50e0b9cc400affb0f80303120e9ba55","first_computed_at":"2026-05-18T03:31:08.273921Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:08.273921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wgXx8VtT2zGHIJeZmX0aN/2oy5DxzkoE/cJtAOYnyk98giit2/xJAA4xlF67g0duG4Q4EcU2enZlxv+Juj84DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:08.274862Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.2724","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a83f62d59caa6ecd68c417949bd991302dc550e4cabc9ad63c36d2e0b89c516c","sha256:439941d31cb58d1bc525a3549e41585ff4f7a3a674688ab3ad33668682adcf1a"],"state_sha256":"5c565723ed51e22fe43e3e5ade3c904c65045692ffa6deb2cb93999c5d4aa7ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E1o4b8lYvX8EGvC7sf5k46ufDFxR5pXq2nEgsjzBwiwu/BJ2ZKlRsDcDZFw00XnFjO+BC8lQ9vuQpHGkJpUxCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T12:22:20.761013Z","bundle_sha256":"372aa3c7f86eaa58b96736f5eab50b049dda8818e75ade45ed69b9f8ae1f7773"}}