{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:22MPULZ34YRYFX3F3KM362QAWP","short_pith_number":"pith:22MPULZ3","canonical_record":{"source":{"id":"1301.4613","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-01-20T00:23:17Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4ed6344928ede959650c37b26c50c9dda86734250b69551147dc1fe1ad7f216c","abstract_canon_sha256":"467dfca1fea32331df2a396ce8dba714233cbb029438ca5d77992c153b168177"},"schema_version":"1.0"},"canonical_sha256":"d698fa2f3be62382df65da99bf6a00b3de8fef076b98fd04160eb3d1baa9d754","source":{"kind":"arxiv","id":"1301.4613","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4613","created_at":"2026-05-18T03:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4613v2","created_at":"2026-05-18T03:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4613","created_at":"2026-05-18T03:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"22MPULZ34YRY","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"22MPULZ34YRYFX3F","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"22MPULZ3","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:22MPULZ34YRYFX3F3KM362QAWP","target":"record","payload":{"canonical_record":{"source":{"id":"1301.4613","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-01-20T00:23:17Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4ed6344928ede959650c37b26c50c9dda86734250b69551147dc1fe1ad7f216c","abstract_canon_sha256":"467dfca1fea32331df2a396ce8dba714233cbb029438ca5d77992c153b168177"},"schema_version":"1.0"},"canonical_sha256":"d698fa2f3be62382df65da99bf6a00b3de8fef076b98fd04160eb3d1baa9d754","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:06.659987Z","signature_b64":"kErfS5dejSmYCSUwdJ+ku5PkQKz3S5OA0rEgeEvJbUtr9rkhVMFPHUAtjX5UssDl2/mYiZJaYXGp8jnRBknwBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d698fa2f3be62382df65da99bf6a00b3de8fef076b98fd04160eb3d1baa9d754","last_reissued_at":"2026-05-18T03:04:06.659502Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:06.659502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.4613","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":"2026-05-18T03:04:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Ev0++dz8RvMEET7jIs7Z5p2tn2OiQYHR3s6gIsFCkRi4u/ZsE6LPX2u47Ai19hzfggcU+CLYIl0xWLkRx3dDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:52:16.446515Z"},"content_sha256":"f44ba49839bce16bd953686ff3a06e5907fc3ebd4ff64f30564ad5c209980fa4","schema_version":"1.0","event_id":"sha256:f44ba49839bce16bd953686ff3a06e5907fc3ebd4ff64f30564ad5c209980fa4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:22MPULZ34YRYFX3F3KM362QAWP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Idempotent biquadratics, Yang-Baxter maps and birational representations of Coxeter groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"James Atkinson","submitted_at":"2013-01-20T00:23:17Z","abstract_excerpt":"A transformation is obtained which completes the unification of quadrirational Yang-Baxter maps and known integrable multi-quadratic quad equations. By combining theory from these two classes of quad-graph models we find an extension of the known integrability feature, and show how this leads subsequently to a natural extension of the associated lattice geometry. The extended lattice is encoded in a birational representation of a particular sequence of Coxeter groups. In this setting the usual quad-graph is associated with a subgroup of type BC_n, and is part of a larger and more symmetric amb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4613","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":"2026-05-18T03:04:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yMBeqKzyvqFR8TcU4wRXTkuTU7GBcGzXYIZdyl0aegq5yjdVqF5oeSo0TCdPoHPOHtXrHUyj/SAmVF+VmKJODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:52:16.446857Z"},"content_sha256":"c0d4396b2bf6228b9e5946319f2eedbfcf1074d468cf8fe1c8c93853b88e1bfe","schema_version":"1.0","event_id":"sha256:c0d4396b2bf6228b9e5946319f2eedbfcf1074d468cf8fe1c8c93853b88e1bfe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/22MPULZ34YRYFX3F3KM362QAWP/bundle.json","state_url":"https://pith.science/pith/22MPULZ34YRYFX3F3KM362QAWP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/22MPULZ34YRYFX3F3KM362QAWP/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":"2026-06-20T06:52:16Z","links":{"resolver":"https://pith.science/pith/22MPULZ34YRYFX3F3KM362QAWP","bundle":"https://pith.science/pith/22MPULZ34YRYFX3F3KM362QAWP/bundle.json","state":"https://pith.science/pith/22MPULZ34YRYFX3F3KM362QAWP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/22MPULZ34YRYFX3F3KM362QAWP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:22MPULZ34YRYFX3F3KM362QAWP","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":"467dfca1fea32331df2a396ce8dba714233cbb029438ca5d77992c153b168177","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-01-20T00:23:17Z","title_canon_sha256":"4ed6344928ede959650c37b26c50c9dda86734250b69551147dc1fe1ad7f216c"},"schema_version":"1.0","source":{"id":"1301.4613","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4613","created_at":"2026-05-18T03:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4613v2","created_at":"2026-05-18T03:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4613","created_at":"2026-05-18T03:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"22MPULZ34YRY","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"22MPULZ34YRYFX3F","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"22MPULZ3","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:c0d4396b2bf6228b9e5946319f2eedbfcf1074d468cf8fe1c8c93853b88e1bfe","target":"graph","created_at":"2026-05-18T03:04:06Z","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":"A transformation is obtained which completes the unification of quadrirational Yang-Baxter maps and known integrable multi-quadratic quad equations. By combining theory from these two classes of quad-graph models we find an extension of the known integrability feature, and show how this leads subsequently to a natural extension of the associated lattice geometry. The extended lattice is encoded in a birational representation of a particular sequence of Coxeter groups. In this setting the usual quad-graph is associated with a subgroup of type BC_n, and is part of a larger and more symmetric amb","authors_text":"James Atkinson","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-01-20T00:23:17Z","title":"Idempotent biquadratics, Yang-Baxter maps and birational representations of Coxeter groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4613","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:f44ba49839bce16bd953686ff3a06e5907fc3ebd4ff64f30564ad5c209980fa4","target":"record","created_at":"2026-05-18T03:04:06Z","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":"467dfca1fea32331df2a396ce8dba714233cbb029438ca5d77992c153b168177","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-01-20T00:23:17Z","title_canon_sha256":"4ed6344928ede959650c37b26c50c9dda86734250b69551147dc1fe1ad7f216c"},"schema_version":"1.0","source":{"id":"1301.4613","kind":"arxiv","version":2}},"canonical_sha256":"d698fa2f3be62382df65da99bf6a00b3de8fef076b98fd04160eb3d1baa9d754","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d698fa2f3be62382df65da99bf6a00b3de8fef076b98fd04160eb3d1baa9d754","first_computed_at":"2026-05-18T03:04:06.659502Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:06.659502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kErfS5dejSmYCSUwdJ+ku5PkQKz3S5OA0rEgeEvJbUtr9rkhVMFPHUAtjX5UssDl2/mYiZJaYXGp8jnRBknwBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:06.659987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.4613","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f44ba49839bce16bd953686ff3a06e5907fc3ebd4ff64f30564ad5c209980fa4","sha256:c0d4396b2bf6228b9e5946319f2eedbfcf1074d468cf8fe1c8c93853b88e1bfe"],"state_sha256":"9dc4c21ff7d0e3fee3731e03eb9d43a2284f085b94c21f8375d801dc91d2bf37"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cry+EKiWqESuvONX5X4co3Y1jMG9pnktJlv8fpf0XrJ9UONlSwF31S2y0/wh44D6bcvU9+9fqfHlmMmRnehcBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:52:16.448668Z","bundle_sha256":"e6c9a6dab4a599ee6267562abee249915f5ee75420a53ab21f9b91a4b9a5440c"}}