{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SI2Z6FDM7TTZ2JTCOMMXT74G7B","short_pith_number":"pith:SI2Z6FDM","canonical_record":{"source":{"id":"1705.05984","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-17T02:17:07Z","cross_cats_sorted":[],"title_canon_sha256":"1ccb7e2614e19ebf9c4bd2ed54748191b1b80f45ff1f1b071348e94b2f3acb50","abstract_canon_sha256":"48db532fd61c5a3d21b30e159941934c0996dc1af9ce12d769b8c262da7ebb55"},"schema_version":"1.0"},"canonical_sha256":"92359f146cfce79d2662731979ff86f87771522ff00b3315c9429aac8856c05c","source":{"kind":"arxiv","id":"1705.05984","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05984","created_at":"2026-05-18T00:44:19Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05984v1","created_at":"2026-05-18T00:44:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05984","created_at":"2026-05-18T00:44:19Z"},{"alias_kind":"pith_short_12","alias_value":"SI2Z6FDM7TTZ","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SI2Z6FDM7TTZ2JTC","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SI2Z6FDM","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SI2Z6FDM7TTZ2JTCOMMXT74G7B","target":"record","payload":{"canonical_record":{"source":{"id":"1705.05984","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-17T02:17:07Z","cross_cats_sorted":[],"title_canon_sha256":"1ccb7e2614e19ebf9c4bd2ed54748191b1b80f45ff1f1b071348e94b2f3acb50","abstract_canon_sha256":"48db532fd61c5a3d21b30e159941934c0996dc1af9ce12d769b8c262da7ebb55"},"schema_version":"1.0"},"canonical_sha256":"92359f146cfce79d2662731979ff86f87771522ff00b3315c9429aac8856c05c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:19.292967Z","signature_b64":"7eq0KmxPGbYnZdaJwwlCJrCsdooG6PqYeD8BaoJvatw52b7zw8pU90zX5AZAcNh3d4Mp6x3f9iDR4hU8rbvoAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92359f146cfce79d2662731979ff86f87771522ff00b3315c9429aac8856c05c","last_reissued_at":"2026-05-18T00:44:19.292523Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:19.292523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.05984","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":"2026-05-18T00:44:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pNfkYvtk8jWcJPULqqQ2doUhCbqq0mL+fR/DCpLx7XqitdLw2H4t6WZGhG2YyA9U97ZmWVNSZh2x2iN7DlbYAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:15:15.026666Z"},"content_sha256":"a2cfe1fe9eaf3a945f24458621a712c9f3144dff1bc862ddcedba3a384585a83","schema_version":"1.0","event_id":"sha256:a2cfe1fe9eaf3a945f24458621a712c9f3144dff1bc862ddcedba3a384585a83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SI2Z6FDM7TTZ2JTCOMMXT74G7B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A bijection between bargraphs and Dyck paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Emeric Deutsch, Sergi Elizalde","submitted_at":"2017-05-17T02:17:07Z","abstract_excerpt":"Bargraphs are a special class of convex polyominoes. They can be identified with lattice paths with unit steps north, east, and south that start at the origin, end on the $x$-axis, and stay strictly above the $x$-axis everywhere except at the endpoints. Bargraphs, which are used to represent histograms and to model polymers in statistical physics, have been enumerated in the literature by semiperimeter and by several other statistics, using different methods such as the wasp-waist decomposition of Bousquet-M\\'elou and Rechnitzer, and a bijection with certain Motzkin paths.\n  In this paper we d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05984","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":"2026-05-18T00:44:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zdXLSvgRtPRpP5hNCwea/wcTZnybjGz8qW0rxHkkELTb6ZFmnFsgQ2xF5XLgSt0XMH7evQle6sGQcKrDWHBIAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:15:15.027014Z"},"content_sha256":"16dbc4306433defce31a4542aeca47fe06aa6544e49f72f648a39091d26521ab","schema_version":"1.0","event_id":"sha256:16dbc4306433defce31a4542aeca47fe06aa6544e49f72f648a39091d26521ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SI2Z6FDM7TTZ2JTCOMMXT74G7B/bundle.json","state_url":"https://pith.science/pith/SI2Z6FDM7TTZ2JTCOMMXT74G7B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SI2Z6FDM7TTZ2JTCOMMXT74G7B/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":"2026-05-31T03:15:15Z","links":{"resolver":"https://pith.science/pith/SI2Z6FDM7TTZ2JTCOMMXT74G7B","bundle":"https://pith.science/pith/SI2Z6FDM7TTZ2JTCOMMXT74G7B/bundle.json","state":"https://pith.science/pith/SI2Z6FDM7TTZ2JTCOMMXT74G7B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SI2Z6FDM7TTZ2JTCOMMXT74G7B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SI2Z6FDM7TTZ2JTCOMMXT74G7B","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":"48db532fd61c5a3d21b30e159941934c0996dc1af9ce12d769b8c262da7ebb55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-17T02:17:07Z","title_canon_sha256":"1ccb7e2614e19ebf9c4bd2ed54748191b1b80f45ff1f1b071348e94b2f3acb50"},"schema_version":"1.0","source":{"id":"1705.05984","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05984","created_at":"2026-05-18T00:44:19Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05984v1","created_at":"2026-05-18T00:44:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05984","created_at":"2026-05-18T00:44:19Z"},{"alias_kind":"pith_short_12","alias_value":"SI2Z6FDM7TTZ","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SI2Z6FDM7TTZ2JTC","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SI2Z6FDM","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:16dbc4306433defce31a4542aeca47fe06aa6544e49f72f648a39091d26521ab","target":"graph","created_at":"2026-05-18T00:44:19Z","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":"Bargraphs are a special class of convex polyominoes. They can be identified with lattice paths with unit steps north, east, and south that start at the origin, end on the $x$-axis, and stay strictly above the $x$-axis everywhere except at the endpoints. Bargraphs, which are used to represent histograms and to model polymers in statistical physics, have been enumerated in the literature by semiperimeter and by several other statistics, using different methods such as the wasp-waist decomposition of Bousquet-M\\'elou and Rechnitzer, and a bijection with certain Motzkin paths.\n  In this paper we d","authors_text":"Emeric Deutsch, Sergi Elizalde","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-17T02:17:07Z","title":"A bijection between bargraphs and Dyck paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05984","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:a2cfe1fe9eaf3a945f24458621a712c9f3144dff1bc862ddcedba3a384585a83","target":"record","created_at":"2026-05-18T00:44:19Z","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":"48db532fd61c5a3d21b30e159941934c0996dc1af9ce12d769b8c262da7ebb55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-17T02:17:07Z","title_canon_sha256":"1ccb7e2614e19ebf9c4bd2ed54748191b1b80f45ff1f1b071348e94b2f3acb50"},"schema_version":"1.0","source":{"id":"1705.05984","kind":"arxiv","version":1}},"canonical_sha256":"92359f146cfce79d2662731979ff86f87771522ff00b3315c9429aac8856c05c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92359f146cfce79d2662731979ff86f87771522ff00b3315c9429aac8856c05c","first_computed_at":"2026-05-18T00:44:19.292523Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:19.292523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7eq0KmxPGbYnZdaJwwlCJrCsdooG6PqYeD8BaoJvatw52b7zw8pU90zX5AZAcNh3d4Mp6x3f9iDR4hU8rbvoAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:19.292967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.05984","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2cfe1fe9eaf3a945f24458621a712c9f3144dff1bc862ddcedba3a384585a83","sha256:16dbc4306433defce31a4542aeca47fe06aa6544e49f72f648a39091d26521ab"],"state_sha256":"4dba54354d8d59aceb41225b077aa6c9d6e726d789889e42ec6f02f390bfdf8f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TJFQ++kL/HKIm9ONAReInbgqMRIajmACswcd8M6fbCbUEr5MeAVCRajzJ0DsBa4v7C6IBBx3Y5lIiI3syOldCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:15:15.029103Z","bundle_sha256":"340dfe9716b25c27a163ec7e3545ea853a86ee83ee8b3b6f55a2ddf05d6b5430"}}