{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:DITGTXEIQKUNBH7HXKETMGNQ3Q","short_pith_number":"pith:DITGTXEI","canonical_record":{"source":{"id":"2103.15827","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-03-29T18:00:00Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.CO","math.MP"],"title_canon_sha256":"7ed77f90176fbb038c8cd44fdf6c921b933a32a3d4336f52cc30c07b21859404","abstract_canon_sha256":"f1c546d1be9e83763ec1e57baa08915e12fb281f3d676a4dd899bfd087721844"},"schema_version":"1.0"},"canonical_sha256":"1a2669dc8882a8d09fe7ba893619b0dc171863a72cb6e8bf9f7b8b470f1f1764","source":{"kind":"arxiv","id":"2103.15827","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.15827","created_at":"2026-07-05T03:55:26Z"},{"alias_kind":"arxiv_version","alias_value":"2103.15827v2","created_at":"2026-07-05T03:55:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.15827","created_at":"2026-07-05T03:55:26Z"},{"alias_kind":"pith_short_12","alias_value":"DITGTXEIQKUN","created_at":"2026-07-05T03:55:26Z"},{"alias_kind":"pith_short_16","alias_value":"DITGTXEIQKUNBH7H","created_at":"2026-07-05T03:55:26Z"},{"alias_kind":"pith_short_8","alias_value":"DITGTXEI","created_at":"2026-07-05T03:55:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:DITGTXEIQKUNBH7HXKETMGNQ3Q","target":"record","payload":{"canonical_record":{"source":{"id":"2103.15827","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-03-29T18:00:00Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.CO","math.MP"],"title_canon_sha256":"7ed77f90176fbb038c8cd44fdf6c921b933a32a3d4336f52cc30c07b21859404","abstract_canon_sha256":"f1c546d1be9e83763ec1e57baa08915e12fb281f3d676a4dd899bfd087721844"},"schema_version":"1.0"},"canonical_sha256":"1a2669dc8882a8d09fe7ba893619b0dc171863a72cb6e8bf9f7b8b470f1f1764","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:55:26.608828Z","signature_b64":"4KZm86fzOnWhFxs6GfPFUnaXJLcGE2G6aa3FnX8PV25tSPcE4CpNyVvvzAKTx1Zd428m7Za/b8eyw2feUJloCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a2669dc8882a8d09fe7ba893619b0dc171863a72cb6e8bf9f7b8b470f1f1764","last_reissued_at":"2026-07-05T03:55:26.608301Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:55:26.608301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2103.15827","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":"2026-07-05T03:55:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IMeiwnqbxpKpGMx5355H8rpyVCjD/y8e7eaa7eylA17rcakVhzkSN0vF3UMDH6MzeHmZzjbsQB6QmrFnaq1YAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T09:39:59.756122Z"},"content_sha256":"fba5849f5e52daf1c9e953597b0376c55bb120934e08b590a704eec4492b6ba4","schema_version":"1.0","event_id":"sha256:fba5849f5e52daf1c9e953597b0376c55bb120934e08b590a704eec4492b6ba4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:DITGTXEIQKUNBH7HXKETMGNQ3Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hamiltonian and exclusion statistics approach to discrete forward-moving paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Alexios P. Polychronakos, St\\'ephane OUVRY","submitted_at":"2021-03-29T18:00:00Z","abstract_excerpt":"We use a Hamiltonian (transition matrix) description of height-restricted Dyck paths on the plane in which generating functions for the paths arise as matrix elements of the propagator to evaluate the length and area generating function for paths with arbitrary starting and ending points, expressing it as a rational combination of determinants. Exploiting a connection between random walks and quantum exclusion statistics that we previously established, we express this generating function in terms of grand partition functions for exclusion particles in a finite harmonic spectrum and present an "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.15827","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.15827/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:55:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D+Q6Y2LSTJ/6SJEjI9tBgb+Z99Nb85DZPt+FT90PpTyFSSuFQhwjNwgZ+VN0vTxKcU/pjDsD7pXwp7ZG7z1ACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T09:39:59.756830Z"},"content_sha256":"20e8262043f64c886c9821c24e936f39e6daac0d8fb717081799ac1595acb34b","schema_version":"1.0","event_id":"sha256:20e8262043f64c886c9821c24e936f39e6daac0d8fb717081799ac1595acb34b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DITGTXEIQKUNBH7HXKETMGNQ3Q/bundle.json","state_url":"https://pith.science/pith/DITGTXEIQKUNBH7HXKETMGNQ3Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DITGTXEIQKUNBH7HXKETMGNQ3Q/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":"2026-08-17T09:39:59Z","links":{"resolver":"https://pith.science/pith/DITGTXEIQKUNBH7HXKETMGNQ3Q","bundle":"https://pith.science/pith/DITGTXEIQKUNBH7HXKETMGNQ3Q/bundle.json","state":"https://pith.science/pith/DITGTXEIQKUNBH7HXKETMGNQ3Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DITGTXEIQKUNBH7HXKETMGNQ3Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:DITGTXEIQKUNBH7HXKETMGNQ3Q","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":"f1c546d1be9e83763ec1e57baa08915e12fb281f3d676a4dd899bfd087721844","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-03-29T18:00:00Z","title_canon_sha256":"7ed77f90176fbb038c8cd44fdf6c921b933a32a3d4336f52cc30c07b21859404"},"schema_version":"1.0","source":{"id":"2103.15827","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.15827","created_at":"2026-07-05T03:55:26Z"},{"alias_kind":"arxiv_version","alias_value":"2103.15827v2","created_at":"2026-07-05T03:55:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.15827","created_at":"2026-07-05T03:55:26Z"},{"alias_kind":"pith_short_12","alias_value":"DITGTXEIQKUN","created_at":"2026-07-05T03:55:26Z"},{"alias_kind":"pith_short_16","alias_value":"DITGTXEIQKUNBH7H","created_at":"2026-07-05T03:55:26Z"},{"alias_kind":"pith_short_8","alias_value":"DITGTXEI","created_at":"2026-07-05T03:55:26Z"}],"graph_snapshots":[{"event_id":"sha256:20e8262043f64c886c9821c24e936f39e6daac0d8fb717081799ac1595acb34b","target":"graph","created_at":"2026-07-05T03:55:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2103.15827/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We use a Hamiltonian (transition matrix) description of height-restricted Dyck paths on the plane in which generating functions for the paths arise as matrix elements of the propagator to evaluate the length and area generating function for paths with arbitrary starting and ending points, expressing it as a rational combination of determinants. Exploiting a connection between random walks and quantum exclusion statistics that we previously established, we express this generating function in terms of grand partition functions for exclusion particles in a finite harmonic spectrum and present an ","authors_text":"Alexios P. Polychronakos, St\\'ephane OUVRY","cross_cats":["cond-mat.stat-mech","hep-th","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-03-29T18:00:00Z","title":"Hamiltonian and exclusion statistics approach to discrete forward-moving paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.15827","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:fba5849f5e52daf1c9e953597b0376c55bb120934e08b590a704eec4492b6ba4","target":"record","created_at":"2026-07-05T03:55:26Z","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":"f1c546d1be9e83763ec1e57baa08915e12fb281f3d676a4dd899bfd087721844","cross_cats_sorted":["cond-mat.stat-mech","hep-th","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2021-03-29T18:00:00Z","title_canon_sha256":"7ed77f90176fbb038c8cd44fdf6c921b933a32a3d4336f52cc30c07b21859404"},"schema_version":"1.0","source":{"id":"2103.15827","kind":"arxiv","version":2}},"canonical_sha256":"1a2669dc8882a8d09fe7ba893619b0dc171863a72cb6e8bf9f7b8b470f1f1764","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a2669dc8882a8d09fe7ba893619b0dc171863a72cb6e8bf9f7b8b470f1f1764","first_computed_at":"2026-07-05T03:55:26.608301Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:55:26.608301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4KZm86fzOnWhFxs6GfPFUnaXJLcGE2G6aa3FnX8PV25tSPcE4CpNyVvvzAKTx1Zd428m7Za/b8eyw2feUJloCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:55:26.608828Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.15827","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fba5849f5e52daf1c9e953597b0376c55bb120934e08b590a704eec4492b6ba4","sha256:20e8262043f64c886c9821c24e936f39e6daac0d8fb717081799ac1595acb34b"],"state_sha256":"acd3c2477ae68f48e52bd0583aa0b6587309d96bad3e52edd6faac56b24cdbff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vw94usEpk5Nl1y5F+gpdtkGWedGgwxrSEP90f1GZVgf7S1lbl1qidjzbKwh7DhXu11O09bsbKclkNN0ODV0RBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T09:39:59.761037Z","bundle_sha256":"2c6480e362a331d91b12f48790e58f15c6ca5989cc1cfe834ddafb8e3447ea8d"}}