{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:KIW2LYY627JXJ7Z5W5COBQR3VR","short_pith_number":"pith:KIW2LYY6","canonical_record":{"source":{"id":"math/0607379","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2006-07-17T09:17:59Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th"],"title_canon_sha256":"3f95479f1e051cffacb44f776826685d3568ca232848f83b6f135a990b1defb4","abstract_canon_sha256":"f976360984f4c6e5d5c5e4753550e7c8ea5c24b93c1203a518a920b60f228f9f"},"schema_version":"1.0"},"canonical_sha256":"522da5e31ed7d374ff3db744e0c23bac5502b1c2528b56cce68913eba9f63103","source":{"kind":"arxiv","id":"math/0607379","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0607379","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0607379v3","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0607379","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"KIW2LYY627JX","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"KIW2LYY627JXJ7Z5","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"KIW2LYY6","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:KIW2LYY627JXJ7Z5W5COBQR3VR","target":"record","payload":{"canonical_record":{"source":{"id":"math/0607379","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2006-07-17T09:17:59Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th"],"title_canon_sha256":"3f95479f1e051cffacb44f776826685d3568ca232848f83b6f135a990b1defb4","abstract_canon_sha256":"f976360984f4c6e5d5c5e4753550e7c8ea5c24b93c1203a518a920b60f228f9f"},"schema_version":"1.0"},"canonical_sha256":"522da5e31ed7d374ff3db744e0c23bac5502b1c2528b56cce68913eba9f63103","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:23.942685Z","signature_b64":"ZMC7G45BI/oPB45aEm3M8yWz8OU/5KxdqAzaZigYGEifz5wEofj0717DhEqfWeesTX5ZWUSB5RGe0AI8CS3jAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"522da5e31ed7d374ff3db744e0c23bac5502b1c2528b56cce68913eba9f63103","last_reissued_at":"2026-05-18T01:38:23.941995Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:23.941995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0607379","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0TJdj68vqu0JXAMJsRGt4h+wvXe3qVG++RNiq1AxJG4bH69WodMdnhjcnQ37xprfutI8OJZ2APq3hZEz5oKtCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T03:15:58.547600Z"},"content_sha256":"50d715cf962e3249b9e2bafef287201fbba024fe719353bb61860ac53a29a927","schema_version":"1.0","event_id":"sha256:50d715cf962e3249b9e2bafef287201fbba024fe719353bb61860ac53a29a927"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:KIW2LYY627JXJ7Z5W5COBQR3VR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new class ${\\hat o}_N$ of statistical models: Transfer matrix eigenstates, chain Hamiltonians, factorizable $S$-matrix","license":"","headline":"","cross_cats":["cond-mat.stat-mech","hep-th"],"primary_cat":"math.QA","authors_text":"A. Chakrabarti (CPHT, B. Abdesselam (CU. Mascara), Ecole Polytechnique)","submitted_at":"2006-07-17T09:17:59Z","abstract_excerpt":"Statistical models corresponding to a new class of braid matrices ($\\hat{o}_N; N\\geq 3$) presented in a previous paper are studied. Indices labeling states spanning the $N^r$ dimensional base space of $T^{(r)}(\\theta)$, the $r$-th order transfer matrix are so chosen that the operators $W$ (the sum of the state labels) and (CP) (the circular permutation of state labels) commute with $T^{(r)}(\\theta)$. This drastically simplifies the construction of eigenstates, reducing it to solutions of relatively small number of simultaneous linear equations. Roots of unity play a crucial role. Thus for diag"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607379","kind":"arxiv","version":3},"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":"2026-05-18T01:38:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BVyim+xNDIeMXorZa3RMjwT1E+qjT5oEUlGCOd7HUjsQwDxAMkGdXsuFnUsPvu1vY6viDJu/JanYGskZ4OksAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T03:15:58.548261Z"},"content_sha256":"52b2f569b055162108e67a5f7078d2627a0164cb2c105590ca24cba58e52b9e3","schema_version":"1.0","event_id":"sha256:52b2f569b055162108e67a5f7078d2627a0164cb2c105590ca24cba58e52b9e3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KIW2LYY627JXJ7Z5W5COBQR3VR/bundle.json","state_url":"https://pith.science/pith/KIW2LYY627JXJ7Z5W5COBQR3VR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KIW2LYY627JXJ7Z5W5COBQR3VR/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":"2026-06-05T03:15:58Z","links":{"resolver":"https://pith.science/pith/KIW2LYY627JXJ7Z5W5COBQR3VR","bundle":"https://pith.science/pith/KIW2LYY627JXJ7Z5W5COBQR3VR/bundle.json","state":"https://pith.science/pith/KIW2LYY627JXJ7Z5W5COBQR3VR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KIW2LYY627JXJ7Z5W5COBQR3VR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:KIW2LYY627JXJ7Z5W5COBQR3VR","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":"f976360984f4c6e5d5c5e4753550e7c8ea5c24b93c1203a518a920b60f228f9f","cross_cats_sorted":["cond-mat.stat-mech","hep-th"],"license":"","primary_cat":"math.QA","submitted_at":"2006-07-17T09:17:59Z","title_canon_sha256":"3f95479f1e051cffacb44f776826685d3568ca232848f83b6f135a990b1defb4"},"schema_version":"1.0","source":{"id":"math/0607379","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0607379","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0607379v3","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0607379","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"KIW2LYY627JX","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"KIW2LYY627JXJ7Z5","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"KIW2LYY6","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:52b2f569b055162108e67a5f7078d2627a0164cb2c105590ca24cba58e52b9e3","target":"graph","created_at":"2026-05-18T01:38:23Z","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":"Statistical models corresponding to a new class of braid matrices ($\\hat{o}_N; N\\geq 3$) presented in a previous paper are studied. Indices labeling states spanning the $N^r$ dimensional base space of $T^{(r)}(\\theta)$, the $r$-th order transfer matrix are so chosen that the operators $W$ (the sum of the state labels) and (CP) (the circular permutation of state labels) commute with $T^{(r)}(\\theta)$. This drastically simplifies the construction of eigenstates, reducing it to solutions of relatively small number of simultaneous linear equations. Roots of unity play a crucial role. Thus for diag","authors_text":"A. Chakrabarti (CPHT, B. Abdesselam (CU. Mascara), Ecole Polytechnique)","cross_cats":["cond-mat.stat-mech","hep-th"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2006-07-17T09:17:59Z","title":"A new class ${\\hat o}_N$ of statistical models: Transfer matrix eigenstates, chain Hamiltonians, factorizable $S$-matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607379","kind":"arxiv","version":3},"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":"sha256:50d715cf962e3249b9e2bafef287201fbba024fe719353bb61860ac53a29a927","target":"record","created_at":"2026-05-18T01:38:23Z","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":"f976360984f4c6e5d5c5e4753550e7c8ea5c24b93c1203a518a920b60f228f9f","cross_cats_sorted":["cond-mat.stat-mech","hep-th"],"license":"","primary_cat":"math.QA","submitted_at":"2006-07-17T09:17:59Z","title_canon_sha256":"3f95479f1e051cffacb44f776826685d3568ca232848f83b6f135a990b1defb4"},"schema_version":"1.0","source":{"id":"math/0607379","kind":"arxiv","version":3}},"canonical_sha256":"522da5e31ed7d374ff3db744e0c23bac5502b1c2528b56cce68913eba9f63103","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"522da5e31ed7d374ff3db744e0c23bac5502b1c2528b56cce68913eba9f63103","first_computed_at":"2026-05-18T01:38:23.941995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:23.941995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZMC7G45BI/oPB45aEm3M8yWz8OU/5KxdqAzaZigYGEifz5wEofj0717DhEqfWeesTX5ZWUSB5RGe0AI8CS3jAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:23.942685Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0607379","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50d715cf962e3249b9e2bafef287201fbba024fe719353bb61860ac53a29a927","sha256:52b2f569b055162108e67a5f7078d2627a0164cb2c105590ca24cba58e52b9e3"],"state_sha256":"1a2490b9e8fef41c32babb57c51a5595a73d7dfc047389178111a0a086e1ae8b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UhEhJIn1Kyv1db1fEnkaXWZml7HZlsPz/EDbNPFNodoD6IC+FQkBIHXZZZbUpNUaBwjKJuaVHhAWBJZfSmrPBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T03:15:58.551786Z","bundle_sha256":"9377efe20485fec2a01febe3993e8683c7c3e68ca5ac74d0ecc95a130cb02c2d"}}