{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:OA75APNMWLG72TEY3LD3KKKQLL","short_pith_number":"pith:OA75APNM","canonical_record":{"source":{"id":"1602.04574","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-15T06:58:33Z","cross_cats_sorted":["math.MP","math.QA","nlin.SI"],"title_canon_sha256":"d514cbb462bf8a163cb0d48f39ba50377be4781349c76be160027eb9bb866754","abstract_canon_sha256":"fe5caff2d1e7396313452498a432a238611a3ee0dac292e53f384d60e5baa683"},"schema_version":"1.0"},"canonical_sha256":"703fd03dacb2cdfd4c98dac7b529505acf64b071a32588ef983966a5fba57d22","source":{"kind":"arxiv","id":"1602.04574","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04574","created_at":"2026-05-18T01:02:30Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04574v2","created_at":"2026-05-18T01:02:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04574","created_at":"2026-05-18T01:02:30Z"},{"alias_kind":"pith_short_12","alias_value":"OA75APNMWLG7","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OA75APNMWLG72TEY","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OA75APNM","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:OA75APNMWLG72TEY3LD3KKKQLL","target":"record","payload":{"canonical_record":{"source":{"id":"1602.04574","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-15T06:58:33Z","cross_cats_sorted":["math.MP","math.QA","nlin.SI"],"title_canon_sha256":"d514cbb462bf8a163cb0d48f39ba50377be4781349c76be160027eb9bb866754","abstract_canon_sha256":"fe5caff2d1e7396313452498a432a238611a3ee0dac292e53f384d60e5baa683"},"schema_version":"1.0"},"canonical_sha256":"703fd03dacb2cdfd4c98dac7b529505acf64b071a32588ef983966a5fba57d22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:30.845817Z","signature_b64":"xyIRzrDAK2bFF+kphc1QgFRqhwGcB8H/vppRTwvRfZGr9uUXEuLrtO3nrXDuAX9SQuQgsceLK2LbEcfFWbVCCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"703fd03dacb2cdfd4c98dac7b529505acf64b071a32588ef983966a5fba57d22","last_reissued_at":"2026-05-18T01:02:30.845176Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:30.845176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.04574","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":"2026-05-18T01:02:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NmCN81LraRX8xYAhn9P8r36YsTjr/Sr6iHIemIdS90c1KRO2FOJ7y1Ng81HpcA3ex4TYw1sI2m9RtIsMQuCrAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T19:58:30.268846Z"},"content_sha256":"4c0e9b26f673d45eebf6828abb59d21998a65ffb7160de672fd51299ae7ee41e","schema_version":"1.0","event_id":"sha256:4c0e9b26f673d45eebf6828abb59d21998a65ffb7160de672fd51299ae7ee41e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:OA75APNMWLG72TEY3LD3KKKQLL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multispecies totally asymmetric zero range process: II. Hat relation and tetrahedron equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.QA","nlin.SI"],"primary_cat":"math-ph","authors_text":"Atsuo Kuniba, Masato Okado, Shouya Maruyama","submitted_at":"2016-02-15T06:58:33Z","abstract_excerpt":"We consider a three-dimensional (3D) lattice model associated with the intertwiner of the quantized coordinate ring $A_q(sl_3)$, and introduce a family of layer to layer transfer matrices on $m\\times n$ square lattice. By using the tetrahedron equation we derive their commutativity and bilinear relations mixing various boundary conditions. At $q=0$ and $m=n$, they lead to a new proof of the steady state probability of the $n$-species totally asymmetric zero range process obtained recently by the authors, revealing the 3D integrability in the matrix product construction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04574","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":"2026-05-18T01:02:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vuqZrsFUDzZMLjIE7nsSnE5POkh7+ojDbAIcKbAJcQtM/fbfa7rmVmS4dZoKSaAz1FPIXVg+YdY3+baO7GQqDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T19:58:30.269191Z"},"content_sha256":"7d9f63b900b42bc0bed51b2a0b7f33ecbfb1f46c197c6eff949b6562fd53836b","schema_version":"1.0","event_id":"sha256:7d9f63b900b42bc0bed51b2a0b7f33ecbfb1f46c197c6eff949b6562fd53836b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OA75APNMWLG72TEY3LD3KKKQLL/bundle.json","state_url":"https://pith.science/pith/OA75APNMWLG72TEY3LD3KKKQLL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OA75APNMWLG72TEY3LD3KKKQLL/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":"2026-05-22T19:58:30Z","links":{"resolver":"https://pith.science/pith/OA75APNMWLG72TEY3LD3KKKQLL","bundle":"https://pith.science/pith/OA75APNMWLG72TEY3LD3KKKQLL/bundle.json","state":"https://pith.science/pith/OA75APNMWLG72TEY3LD3KKKQLL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OA75APNMWLG72TEY3LD3KKKQLL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OA75APNMWLG72TEY3LD3KKKQLL","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":"fe5caff2d1e7396313452498a432a238611a3ee0dac292e53f384d60e5baa683","cross_cats_sorted":["math.MP","math.QA","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-15T06:58:33Z","title_canon_sha256":"d514cbb462bf8a163cb0d48f39ba50377be4781349c76be160027eb9bb866754"},"schema_version":"1.0","source":{"id":"1602.04574","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04574","created_at":"2026-05-18T01:02:30Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04574v2","created_at":"2026-05-18T01:02:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04574","created_at":"2026-05-18T01:02:30Z"},{"alias_kind":"pith_short_12","alias_value":"OA75APNMWLG7","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OA75APNMWLG72TEY","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OA75APNM","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:7d9f63b900b42bc0bed51b2a0b7f33ecbfb1f46c197c6eff949b6562fd53836b","target":"graph","created_at":"2026-05-18T01:02:30Z","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":"We consider a three-dimensional (3D) lattice model associated with the intertwiner of the quantized coordinate ring $A_q(sl_3)$, and introduce a family of layer to layer transfer matrices on $m\\times n$ square lattice. By using the tetrahedron equation we derive their commutativity and bilinear relations mixing various boundary conditions. At $q=0$ and $m=n$, they lead to a new proof of the steady state probability of the $n$-species totally asymmetric zero range process obtained recently by the authors, revealing the 3D integrability in the matrix product construction.","authors_text":"Atsuo Kuniba, Masato Okado, Shouya Maruyama","cross_cats":["math.MP","math.QA","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-15T06:58:33Z","title":"Multispecies totally asymmetric zero range process: II. Hat relation and tetrahedron equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04574","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":"sha256:4c0e9b26f673d45eebf6828abb59d21998a65ffb7160de672fd51299ae7ee41e","target":"record","created_at":"2026-05-18T01:02:30Z","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":"fe5caff2d1e7396313452498a432a238611a3ee0dac292e53f384d60e5baa683","cross_cats_sorted":["math.MP","math.QA","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-15T06:58:33Z","title_canon_sha256":"d514cbb462bf8a163cb0d48f39ba50377be4781349c76be160027eb9bb866754"},"schema_version":"1.0","source":{"id":"1602.04574","kind":"arxiv","version":2}},"canonical_sha256":"703fd03dacb2cdfd4c98dac7b529505acf64b071a32588ef983966a5fba57d22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"703fd03dacb2cdfd4c98dac7b529505acf64b071a32588ef983966a5fba57d22","first_computed_at":"2026-05-18T01:02:30.845176Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:30.845176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xyIRzrDAK2bFF+kphc1QgFRqhwGcB8H/vppRTwvRfZGr9uUXEuLrtO3nrXDuAX9SQuQgsceLK2LbEcfFWbVCCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:30.845817Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04574","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c0e9b26f673d45eebf6828abb59d21998a65ffb7160de672fd51299ae7ee41e","sha256:7d9f63b900b42bc0bed51b2a0b7f33ecbfb1f46c197c6eff949b6562fd53836b"],"state_sha256":"bd851732ef82e7751506f53b0884a460ccdf818efcd32e6991427c49ad3678e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oNGIPYA1W6Ok/B4hXw1KXzvf27ddQV0svC2Nr3qJQsR9ft3LsM0eADgN+CCJBUHm6QEPJ9ToyYauIKD3eDBnAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T19:58:30.271147Z","bundle_sha256":"e4146f5d801c8b8e0bed5fef1d75c3359e9b4ce517e57242620624e313d72ba0"}}