{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IAMUMW4URLGIWVZCK3OZZKZ5IV","short_pith_number":"pith:IAMUMW4U","canonical_record":{"source":{"id":"1605.01171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-05-04T07:41:36Z","cross_cats_sorted":[],"title_canon_sha256":"aeeb6a01b482209dce0b8b44f90ea6853ef6737cc24e0d82ac17831b768968e9","abstract_canon_sha256":"bdd121c6352a7478777a65e08f8324e04f326887edc7d206ec195140d3d50b87"},"schema_version":"1.0"},"canonical_sha256":"4019465b948acc8b572256dd9cab3d4574545e55cd4755a39d4f8bd63420dc18","source":{"kind":"arxiv","id":"1605.01171","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01171","created_at":"2026-05-18T01:15:37Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01171v1","created_at":"2026-05-18T01:15:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01171","created_at":"2026-05-18T01:15:37Z"},{"alias_kind":"pith_short_12","alias_value":"IAMUMW4URLGI","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IAMUMW4URLGIWVZC","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IAMUMW4U","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IAMUMW4URLGIWVZCK3OZZKZ5IV","target":"record","payload":{"canonical_record":{"source":{"id":"1605.01171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-05-04T07:41:36Z","cross_cats_sorted":[],"title_canon_sha256":"aeeb6a01b482209dce0b8b44f90ea6853ef6737cc24e0d82ac17831b768968e9","abstract_canon_sha256":"bdd121c6352a7478777a65e08f8324e04f326887edc7d206ec195140d3d50b87"},"schema_version":"1.0"},"canonical_sha256":"4019465b948acc8b572256dd9cab3d4574545e55cd4755a39d4f8bd63420dc18","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:37.609306Z","signature_b64":"nxo8CFEJ08dtfSr1E82VFnHwLq93M1bS+MqjFOM+idYzCl8Ws/JMOYW6mJSsMxMgTRl+qplnmYnuuZL/Q/y1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4019465b948acc8b572256dd9cab3d4574545e55cd4755a39d4f8bd63420dc18","last_reissued_at":"2026-05-18T01:15:37.608628Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:37.608628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.01171","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":"2026-05-18T01:15:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/LmCaiOpL073dJRaGNsLCgf3Jh2XmtQcxlS+sM9ga4P7+pfmJjYEQdaSB3+Q5sQgmRsL+PVGRRJu3TVDLZusCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:40:14.397557Z"},"content_sha256":"10d449f1c75d4df69bc6dcc5aecde22d43db77922886f0a9d8a45bffe623ad42","schema_version":"1.0","event_id":"sha256:10d449f1c75d4df69bc6dcc5aecde22d43db77922886f0a9d8a45bffe623ad42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IAMUMW4URLGIWVZCK3OZZKZ5IV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reflection groups and discrete integrable systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Nalini Joshi, Nobutaka Nakazono, Yang Shi","submitted_at":"2016-05-04T07:41:36Z","abstract_excerpt":"We present a method of constructing discrete integrable systems with crystallographic reflection group (Weyl) symmetries, thus clarifying the relationship between different discrete integrable systems in terms of their symmetry groups. Discrete integrable systems are associated with space-filling polytopes arise from the geometric representation of the Weyl groups in the $n$-dimensional real Euclidean space $\\mathbb{R}^n$. The \"multi-dimensional consistency\" property of the discrete integrable system is shown to be inherited from the combinatorial properties of the polytope; while the dynamics"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01171","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":"2026-05-18T01:15:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zyIFtk7+9NfsM6C7zlL2BgRuTDoDVKZAewMUPp8eMJ8YrRowyRWKKb33cAX6adPx0Pv1w/2X1qoldM+utCmEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:40:14.398089Z"},"content_sha256":"82fef016e1e0fb644aa17ad0240201fa96a301f34bafd8a1db17a0f519872e8c","schema_version":"1.0","event_id":"sha256:82fef016e1e0fb644aa17ad0240201fa96a301f34bafd8a1db17a0f519872e8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IAMUMW4URLGIWVZCK3OZZKZ5IV/bundle.json","state_url":"https://pith.science/pith/IAMUMW4URLGIWVZCK3OZZKZ5IV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IAMUMW4URLGIWVZCK3OZZKZ5IV/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":"2026-06-05T02:40:14Z","links":{"resolver":"https://pith.science/pith/IAMUMW4URLGIWVZCK3OZZKZ5IV","bundle":"https://pith.science/pith/IAMUMW4URLGIWVZCK3OZZKZ5IV/bundle.json","state":"https://pith.science/pith/IAMUMW4URLGIWVZCK3OZZKZ5IV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IAMUMW4URLGIWVZCK3OZZKZ5IV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IAMUMW4URLGIWVZCK3OZZKZ5IV","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":"bdd121c6352a7478777a65e08f8324e04f326887edc7d206ec195140d3d50b87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-05-04T07:41:36Z","title_canon_sha256":"aeeb6a01b482209dce0b8b44f90ea6853ef6737cc24e0d82ac17831b768968e9"},"schema_version":"1.0","source":{"id":"1605.01171","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01171","created_at":"2026-05-18T01:15:37Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01171v1","created_at":"2026-05-18T01:15:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01171","created_at":"2026-05-18T01:15:37Z"},{"alias_kind":"pith_short_12","alias_value":"IAMUMW4URLGI","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IAMUMW4URLGIWVZC","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IAMUMW4U","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:82fef016e1e0fb644aa17ad0240201fa96a301f34bafd8a1db17a0f519872e8c","target":"graph","created_at":"2026-05-18T01:15:37Z","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 present a method of constructing discrete integrable systems with crystallographic reflection group (Weyl) symmetries, thus clarifying the relationship between different discrete integrable systems in terms of their symmetry groups. Discrete integrable systems are associated with space-filling polytopes arise from the geometric representation of the Weyl groups in the $n$-dimensional real Euclidean space $\\mathbb{R}^n$. The \"multi-dimensional consistency\" property of the discrete integrable system is shown to be inherited from the combinatorial properties of the polytope; while the dynamics","authors_text":"Nalini Joshi, Nobutaka Nakazono, Yang Shi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-05-04T07:41:36Z","title":"Reflection groups and discrete integrable systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01171","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":"sha256:10d449f1c75d4df69bc6dcc5aecde22d43db77922886f0a9d8a45bffe623ad42","target":"record","created_at":"2026-05-18T01:15:37Z","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":"bdd121c6352a7478777a65e08f8324e04f326887edc7d206ec195140d3d50b87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2016-05-04T07:41:36Z","title_canon_sha256":"aeeb6a01b482209dce0b8b44f90ea6853ef6737cc24e0d82ac17831b768968e9"},"schema_version":"1.0","source":{"id":"1605.01171","kind":"arxiv","version":1}},"canonical_sha256":"4019465b948acc8b572256dd9cab3d4574545e55cd4755a39d4f8bd63420dc18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4019465b948acc8b572256dd9cab3d4574545e55cd4755a39d4f8bd63420dc18","first_computed_at":"2026-05-18T01:15:37.608628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:37.608628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nxo8CFEJ08dtfSr1E82VFnHwLq93M1bS+MqjFOM+idYzCl8Ws/JMOYW6mJSsMxMgTRl+qplnmYnuuZL/Q/y1Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:37.609306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01171","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10d449f1c75d4df69bc6dcc5aecde22d43db77922886f0a9d8a45bffe623ad42","sha256:82fef016e1e0fb644aa17ad0240201fa96a301f34bafd8a1db17a0f519872e8c"],"state_sha256":"605edd8de3f45743885fa3a4a0329f4a5fc67eec200db64c6bb632589f135e5d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FRK+az/aJN7GFzp9Y9xWp1MsxCbZ3IkfN3rultOq7zBHLS6PrZ7B2BSdhcvYgA8FN1xgiYYbNV7KI5PoUXhYBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T02:40:14.400686Z","bundle_sha256":"bfda7f4d826a962c0838b5234dc0c345705bb448ebca6c49be7fcbd54caf745d"}}