{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5MFLLEJC2ZJI4PTH32XM44YLXL","short_pith_number":"pith:5MFLLEJC","canonical_record":{"source":{"id":"1804.08725","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-23T20:30:09Z","cross_cats_sorted":[],"title_canon_sha256":"4bd9e6f8bb0f82ea6d8e58c1e6c36dbe9010c979f6522f8ed7c299cdd7b9fca9","abstract_canon_sha256":"e2531b9497da394997a505891f929e17641a50d55bbaef8ec43a6512ed15e4e2"},"schema_version":"1.0"},"canonical_sha256":"eb0ab59122d6528e3e67deaece730bbad880a582ba9fd3afd458abc78483302a","source":{"kind":"arxiv","id":"1804.08725","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.08725","created_at":"2026-05-17T23:48:40Z"},{"alias_kind":"arxiv_version","alias_value":"1804.08725v2","created_at":"2026-05-17T23:48:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08725","created_at":"2026-05-17T23:48:40Z"},{"alias_kind":"pith_short_12","alias_value":"5MFLLEJC2ZJI","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5MFLLEJC2ZJI4PTH","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5MFLLEJC","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5MFLLEJC2ZJI4PTH32XM44YLXL","target":"record","payload":{"canonical_record":{"source":{"id":"1804.08725","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-23T20:30:09Z","cross_cats_sorted":[],"title_canon_sha256":"4bd9e6f8bb0f82ea6d8e58c1e6c36dbe9010c979f6522f8ed7c299cdd7b9fca9","abstract_canon_sha256":"e2531b9497da394997a505891f929e17641a50d55bbaef8ec43a6512ed15e4e2"},"schema_version":"1.0"},"canonical_sha256":"eb0ab59122d6528e3e67deaece730bbad880a582ba9fd3afd458abc78483302a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:40.561593Z","signature_b64":"UOQeCjTLGE/0E2n0+C4jWeIiA+pHQkr63+/iqeMDpoevLEdI7o0R7FIFUmRURxKQCVGRNOkyRoocjx5gC09XCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb0ab59122d6528e3e67deaece730bbad880a582ba9fd3afd458abc78483302a","last_reissued_at":"2026-05-17T23:48:40.560978Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:40.560978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.08725","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EKXp/f66QNAfPQpiXU/BaYKuAi/flZrtuXD7kPadSL8V2XI5R1OJZDR98svyCepk0/oP1gVrlDNd5QZukgXABg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:41:38.520649Z"},"content_sha256":"8027a0beefc2f7422b27e12d8ac90f8f4300f6bbcae590d757a091f96cdd2fa0","schema_version":"1.0","event_id":"sha256:8027a0beefc2f7422b27e12d8ac90f8f4300f6bbcae590d757a091f96cdd2fa0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5MFLLEJC2ZJI4PTH32XM44YLXL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vertically constrained Motzkin-like paths inspired by bobbin lace","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Frank Ruskey, Stephen Melczer, Veronika Irvine","submitted_at":"2018-04-23T20:30:09Z","abstract_excerpt":"Inspired by a new mathematical model for bobbin lace, this paper considers finite lattice paths formed from the set of step vectors $\\mathfrak{A}=$$\\{\\rightarrow,$ $\\nearrow,$ $\\searrow,$ $\\uparrow,$ $\\downarrow\\}$ with the restriction that vertical steps $(\\uparrow, \\downarrow)$ cannot be consecutive. The set $\\mathfrak{A}$ is the union of the well known Motzkin step vectors $\\mathfrak{M}=$$\\{\\rightarrow,$ $\\nearrow,$ $\\searrow\\}$ with the vertical steps $\\{\\uparrow, \\downarrow\\}$. An explicit bijection $\\phi$ between the exhaustive set of vertically constrained paths formed from $\\mathfrak{A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08725","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m9RzM83jahlXynH7nS7lCiFUIDHI8kMreTpK+OolIkefoof7XMQ4iz3F74d65Qozh/frsyIOLbKwbSGDsGNOCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:41:38.521344Z"},"content_sha256":"5aee1795605f72f98a6a51f47692e113f953671c8e3d293c600a8c7aa4c84d23","schema_version":"1.0","event_id":"sha256:5aee1795605f72f98a6a51f47692e113f953671c8e3d293c600a8c7aa4c84d23"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5MFLLEJC2ZJI4PTH32XM44YLXL/bundle.json","state_url":"https://pith.science/pith/5MFLLEJC2ZJI4PTH32XM44YLXL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5MFLLEJC2ZJI4PTH32XM44YLXL/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":"2026-05-26T15:41:38Z","links":{"resolver":"https://pith.science/pith/5MFLLEJC2ZJI4PTH32XM44YLXL","bundle":"https://pith.science/pith/5MFLLEJC2ZJI4PTH32XM44YLXL/bundle.json","state":"https://pith.science/pith/5MFLLEJC2ZJI4PTH32XM44YLXL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5MFLLEJC2ZJI4PTH32XM44YLXL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5MFLLEJC2ZJI4PTH32XM44YLXL","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":"e2531b9497da394997a505891f929e17641a50d55bbaef8ec43a6512ed15e4e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-23T20:30:09Z","title_canon_sha256":"4bd9e6f8bb0f82ea6d8e58c1e6c36dbe9010c979f6522f8ed7c299cdd7b9fca9"},"schema_version":"1.0","source":{"id":"1804.08725","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.08725","created_at":"2026-05-17T23:48:40Z"},{"alias_kind":"arxiv_version","alias_value":"1804.08725v2","created_at":"2026-05-17T23:48:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08725","created_at":"2026-05-17T23:48:40Z"},{"alias_kind":"pith_short_12","alias_value":"5MFLLEJC2ZJI","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5MFLLEJC2ZJI4PTH","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5MFLLEJC","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:5aee1795605f72f98a6a51f47692e113f953671c8e3d293c600a8c7aa4c84d23","target":"graph","created_at":"2026-05-17T23:48:40Z","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":"Inspired by a new mathematical model for bobbin lace, this paper considers finite lattice paths formed from the set of step vectors $\\mathfrak{A}=$$\\{\\rightarrow,$ $\\nearrow,$ $\\searrow,$ $\\uparrow,$ $\\downarrow\\}$ with the restriction that vertical steps $(\\uparrow, \\downarrow)$ cannot be consecutive. The set $\\mathfrak{A}$ is the union of the well known Motzkin step vectors $\\mathfrak{M}=$$\\{\\rightarrow,$ $\\nearrow,$ $\\searrow\\}$ with the vertical steps $\\{\\uparrow, \\downarrow\\}$. An explicit bijection $\\phi$ between the exhaustive set of vertically constrained paths formed from $\\mathfrak{A","authors_text":"Frank Ruskey, Stephen Melczer, Veronika Irvine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-23T20:30:09Z","title":"Vertically constrained Motzkin-like paths inspired by bobbin lace"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08725","kind":"arxiv","version":2},"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":"sha256:8027a0beefc2f7422b27e12d8ac90f8f4300f6bbcae590d757a091f96cdd2fa0","target":"record","created_at":"2026-05-17T23:48:40Z","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":"e2531b9497da394997a505891f929e17641a50d55bbaef8ec43a6512ed15e4e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-23T20:30:09Z","title_canon_sha256":"4bd9e6f8bb0f82ea6d8e58c1e6c36dbe9010c979f6522f8ed7c299cdd7b9fca9"},"schema_version":"1.0","source":{"id":"1804.08725","kind":"arxiv","version":2}},"canonical_sha256":"eb0ab59122d6528e3e67deaece730bbad880a582ba9fd3afd458abc78483302a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb0ab59122d6528e3e67deaece730bbad880a582ba9fd3afd458abc78483302a","first_computed_at":"2026-05-17T23:48:40.560978Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:40.560978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UOQeCjTLGE/0E2n0+C4jWeIiA+pHQkr63+/iqeMDpoevLEdI7o0R7FIFUmRURxKQCVGRNOkyRoocjx5gC09XCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:40.561593Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.08725","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8027a0beefc2f7422b27e12d8ac90f8f4300f6bbcae590d757a091f96cdd2fa0","sha256:5aee1795605f72f98a6a51f47692e113f953671c8e3d293c600a8c7aa4c84d23"],"state_sha256":"e0310ff3b23b1316b0f489f0e2fa90d3204f1bd930dc344ae47fc002c75fbac6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yApJYaSKDTEwkk6KwjKxPuMKgdFkE+CmnEaoiJc4SJa0ILnoDEOPYq/bEqyG6dpAsN1iimctqdvzJA6IEjKtCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T15:41:38.524743Z","bundle_sha256":"6731d0c1eba7f41bc198c371df8df807e378ebdf80d77dc9386e7e0922f03c9d"}}