{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BWGNWBIZ5EUIGBPY4SJBQMGA4J","short_pith_number":"pith:BWGNWBIZ","canonical_record":{"source":{"id":"1803.10920","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-29T04:35:10Z","cross_cats_sorted":[],"title_canon_sha256":"7f9eb9c61a6d79c9c4013a2e63fee7cc962151edc685c08854257312efa5fbb6","abstract_canon_sha256":"61e2befa2da7b68ba33fac39473722be075373a17166e12f0d589370aa77f85a"},"schema_version":"1.0"},"canonical_sha256":"0d8cdb0519e9288305f8e4921830c0e261b63b09eb2802c5d9679887cf729c76","source":{"kind":"arxiv","id":"1803.10920","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10920","created_at":"2026-05-18T00:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10920v3","created_at":"2026-05-18T00:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10920","created_at":"2026-05-18T00:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"BWGNWBIZ5EUI","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BWGNWBIZ5EUIGBPY","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BWGNWBIZ","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BWGNWBIZ5EUIGBPY4SJBQMGA4J","target":"record","payload":{"canonical_record":{"source":{"id":"1803.10920","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-29T04:35:10Z","cross_cats_sorted":[],"title_canon_sha256":"7f9eb9c61a6d79c9c4013a2e63fee7cc962151edc685c08854257312efa5fbb6","abstract_canon_sha256":"61e2befa2da7b68ba33fac39473722be075373a17166e12f0d589370aa77f85a"},"schema_version":"1.0"},"canonical_sha256":"0d8cdb0519e9288305f8e4921830c0e261b63b09eb2802c5d9679887cf729c76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:25.082746Z","signature_b64":"rh/ZeFSMt8GqcQhOIqsEJcbdsHdCxgCW/PUVbyLROnXtwORDJCUV7KGC2Z3GZqcZzBf2MiX/plzHTXHMUyzwBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d8cdb0519e9288305f8e4921830c0e261b63b09eb2802c5d9679887cf729c76","last_reissued_at":"2026-05-18T00:18:25.082121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:25.082121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.10920","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uMPcO0AercLR44OCA1L79Jcq/T59LBUAf8yJOvm0IIaYaFtqBDlRf6AKp7sQlCyJKnHD9w8tNy5BI+MOMk0GBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:05:20.522856Z"},"content_sha256":"a1eb4fa6b2f5860e13cd6d65f4829f365627e7af93c9b6692616d2fefef0ec9a","schema_version":"1.0","event_id":"sha256:a1eb4fa6b2f5860e13cd6d65f4829f365627e7af93c9b6692616d2fefef0ec9a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BWGNWBIZ5EUIGBPY4SJBQMGA4J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lattice Walk Enumeration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bryan Ek","submitted_at":"2018-03-29T04:35:10Z","abstract_excerpt":"Trying to enumerate all of the walks in a 2D lattice is a fun combinatorial problem and there are numerous applications, from polymers to sports. Computers provide a wonderful tool for analyzing these walks; we provide a Maple package for automatically describing generating functions of walks restricted to any step set in a 2D lattice. We always obtain a closed system of relations for generating functions of walks that are bounded, semi-bounded, or unbounded. For bounded walks, this leads to explicit rational solutions! For semi-bounded or unbounded walks, we may get lucky and obtain algebraic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10920","kind":"arxiv","version":3},"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":"2026-05-18T00:18:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xcMlWjlDB1SfD1v0hHVEls4vOhmLTJZhdutR7PS0cKlDbGpTa+5pVby25JYzi8bK0vZSiM2U5iSJ8Wh8fM1ODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:05:20.523704Z"},"content_sha256":"dc41a725ed8e7ac861550f41021164029602aa79eeee524b0237b77b914bdd93","schema_version":"1.0","event_id":"sha256:dc41a725ed8e7ac861550f41021164029602aa79eeee524b0237b77b914bdd93"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BWGNWBIZ5EUIGBPY4SJBQMGA4J/bundle.json","state_url":"https://pith.science/pith/BWGNWBIZ5EUIGBPY4SJBQMGA4J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BWGNWBIZ5EUIGBPY4SJBQMGA4J/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":"2026-06-09T12:05:20Z","links":{"resolver":"https://pith.science/pith/BWGNWBIZ5EUIGBPY4SJBQMGA4J","bundle":"https://pith.science/pith/BWGNWBIZ5EUIGBPY4SJBQMGA4J/bundle.json","state":"https://pith.science/pith/BWGNWBIZ5EUIGBPY4SJBQMGA4J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BWGNWBIZ5EUIGBPY4SJBQMGA4J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BWGNWBIZ5EUIGBPY4SJBQMGA4J","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":"61e2befa2da7b68ba33fac39473722be075373a17166e12f0d589370aa77f85a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-29T04:35:10Z","title_canon_sha256":"7f9eb9c61a6d79c9c4013a2e63fee7cc962151edc685c08854257312efa5fbb6"},"schema_version":"1.0","source":{"id":"1803.10920","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10920","created_at":"2026-05-18T00:18:25Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10920v3","created_at":"2026-05-18T00:18:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10920","created_at":"2026-05-18T00:18:25Z"},{"alias_kind":"pith_short_12","alias_value":"BWGNWBIZ5EUI","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BWGNWBIZ5EUIGBPY","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BWGNWBIZ","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:dc41a725ed8e7ac861550f41021164029602aa79eeee524b0237b77b914bdd93","target":"graph","created_at":"2026-05-18T00:18:25Z","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":"Trying to enumerate all of the walks in a 2D lattice is a fun combinatorial problem and there are numerous applications, from polymers to sports. Computers provide a wonderful tool for analyzing these walks; we provide a Maple package for automatically describing generating functions of walks restricted to any step set in a 2D lattice. We always obtain a closed system of relations for generating functions of walks that are bounded, semi-bounded, or unbounded. For bounded walks, this leads to explicit rational solutions! For semi-bounded or unbounded walks, we may get lucky and obtain algebraic","authors_text":"Bryan Ek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-29T04:35:10Z","title":"Lattice Walk Enumeration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10920","kind":"arxiv","version":3},"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:a1eb4fa6b2f5860e13cd6d65f4829f365627e7af93c9b6692616d2fefef0ec9a","target":"record","created_at":"2026-05-18T00:18:25Z","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":"61e2befa2da7b68ba33fac39473722be075373a17166e12f0d589370aa77f85a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-29T04:35:10Z","title_canon_sha256":"7f9eb9c61a6d79c9c4013a2e63fee7cc962151edc685c08854257312efa5fbb6"},"schema_version":"1.0","source":{"id":"1803.10920","kind":"arxiv","version":3}},"canonical_sha256":"0d8cdb0519e9288305f8e4921830c0e261b63b09eb2802c5d9679887cf729c76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d8cdb0519e9288305f8e4921830c0e261b63b09eb2802c5d9679887cf729c76","first_computed_at":"2026-05-18T00:18:25.082121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:25.082121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rh/ZeFSMt8GqcQhOIqsEJcbdsHdCxgCW/PUVbyLROnXtwORDJCUV7KGC2Z3GZqcZzBf2MiX/plzHTXHMUyzwBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:25.082746Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.10920","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1eb4fa6b2f5860e13cd6d65f4829f365627e7af93c9b6692616d2fefef0ec9a","sha256:dc41a725ed8e7ac861550f41021164029602aa79eeee524b0237b77b914bdd93"],"state_sha256":"230e8912dda8332d875d43dba8e89b1d59c7f2bc00eb891e38b30671926afb72"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yG9m/fuKXSTz+S1BtsT5060OQ/XYjwEiqgmnjeySzSYpnjeSz2KhjL4Rn/l/TMlCtL8lbyT+gmDd53+gb/5AAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T12:05:20.528119Z","bundle_sha256":"faaac8affef5aecb7b9cb0fc848d15bedeb1384b8bd3e00e4171b75cfe7e15c9"}}