{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QBYVGA34LHO4VDIBVMBN7UY24H","short_pith_number":"pith:QBYVGA34","canonical_record":{"source":{"id":"1508.02236","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-10T13:23:39Z","cross_cats_sorted":["math.CO","math.MP","math.RT"],"title_canon_sha256":"1f734669ddc664ded2c44decde369daa5a9db5060e5619da81b594553d566c85","abstract_canon_sha256":"3c5b7f92ce6857f7acc5868bebd38e5855c58d090b2d703de25da75a89a2cee4"},"schema_version":"1.0"},"canonical_sha256":"807153037c59ddca8d01ab02dfd31ae1c903d7a97024a13746fd81c6ab440761","source":{"kind":"arxiv","id":"1508.02236","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02236","created_at":"2026-05-18T01:12:30Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02236v2","created_at":"2026-05-18T01:12:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02236","created_at":"2026-05-18T01:12:30Z"},{"alias_kind":"pith_short_12","alias_value":"QBYVGA34LHO4","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QBYVGA34LHO4VDIB","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QBYVGA34","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QBYVGA34LHO4VDIBVMBN7UY24H","target":"record","payload":{"canonical_record":{"source":{"id":"1508.02236","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-10T13:23:39Z","cross_cats_sorted":["math.CO","math.MP","math.RT"],"title_canon_sha256":"1f734669ddc664ded2c44decde369daa5a9db5060e5619da81b594553d566c85","abstract_canon_sha256":"3c5b7f92ce6857f7acc5868bebd38e5855c58d090b2d703de25da75a89a2cee4"},"schema_version":"1.0"},"canonical_sha256":"807153037c59ddca8d01ab02dfd31ae1c903d7a97024a13746fd81c6ab440761","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:30.717450Z","signature_b64":"Tv78dGeVKTEvIePFmDeLYSkXz/ivXU7G39gYa1hK47KfV0hjO/WNAHmx3GLdL4+5TZph/9Hh8VpOplGGe7UQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"807153037c59ddca8d01ab02dfd31ae1c903d7a97024a13746fd81c6ab440761","last_reissued_at":"2026-05-18T01:12:30.717123Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:30.717123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.02236","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":"2026-05-18T01:12:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8a5si0/R1TM4Qr5UntPthop3oz0NCE6JUW9ijOZa74MSehixG4YaMQL9dRaU5LoPzOp4H4df/n6EzVjQ9WATCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:05:56.865474Z"},"content_sha256":"d63b1a5887dab7236cbc070bba63968cde07ba1edc5711450ed62b28d103e9fa","schema_version":"1.0","event_id":"sha256:d63b1a5887dab7236cbc070bba63968cde07ba1edc5711450ed62b28d103e9fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QBYVGA34LHO4VDIBVMBN7UY24H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Refined Cauchy/Littlewood identities and six-vertex model partition functions: III. Deformed bosons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP","math.RT"],"primary_cat":"math-ph","authors_text":"Michael Wheeler, Paul Zinn-Justin","submitted_at":"2015-08-10T13:23:39Z","abstract_excerpt":"We study Hall-Littlewood polynomials using an integrable lattice model of $t$-deformed bosons. Working with row-to-row transfer matrices, we review the construction of Hall-Littlewood polynomials (of the $A_n$ root system) within the framework of this model. Introducing appropriate double-row transfer matrices, we extend this formalism to Hall-Littlewood polynomials based on the $BC_n$ root system, and obtain a new combinatorial formula for them. We then apply our methods to prove a series of refined Cauchy and Littlewood identities involving Hall-Littlewood polynomials. The last two of these "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02236","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":"2026-05-18T01:12:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8IrnRrXT/lrREjZ1tXJrX/1y/cQV/0aNYIT5Kxi1m/D7Vg6RevLla+o2HZvNgQFOlBqK0oiHF1+QxxwruJBWBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:05:56.865822Z"},"content_sha256":"c30a9941d59600ea83ee1b067b7133580c0c5653acf367adc2cf2ffadbaa3a70","schema_version":"1.0","event_id":"sha256:c30a9941d59600ea83ee1b067b7133580c0c5653acf367adc2cf2ffadbaa3a70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QBYVGA34LHO4VDIBVMBN7UY24H/bundle.json","state_url":"https://pith.science/pith/QBYVGA34LHO4VDIBVMBN7UY24H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QBYVGA34LHO4VDIBVMBN7UY24H/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":"2026-06-23T17:05:56Z","links":{"resolver":"https://pith.science/pith/QBYVGA34LHO4VDIBVMBN7UY24H","bundle":"https://pith.science/pith/QBYVGA34LHO4VDIBVMBN7UY24H/bundle.json","state":"https://pith.science/pith/QBYVGA34LHO4VDIBVMBN7UY24H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QBYVGA34LHO4VDIBVMBN7UY24H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QBYVGA34LHO4VDIBVMBN7UY24H","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":"3c5b7f92ce6857f7acc5868bebd38e5855c58d090b2d703de25da75a89a2cee4","cross_cats_sorted":["math.CO","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-10T13:23:39Z","title_canon_sha256":"1f734669ddc664ded2c44decde369daa5a9db5060e5619da81b594553d566c85"},"schema_version":"1.0","source":{"id":"1508.02236","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02236","created_at":"2026-05-18T01:12:30Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02236v2","created_at":"2026-05-18T01:12:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02236","created_at":"2026-05-18T01:12:30Z"},{"alias_kind":"pith_short_12","alias_value":"QBYVGA34LHO4","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QBYVGA34LHO4VDIB","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QBYVGA34","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:c30a9941d59600ea83ee1b067b7133580c0c5653acf367adc2cf2ffadbaa3a70","target":"graph","created_at":"2026-05-18T01:12:30Z","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 study Hall-Littlewood polynomials using an integrable lattice model of $t$-deformed bosons. Working with row-to-row transfer matrices, we review the construction of Hall-Littlewood polynomials (of the $A_n$ root system) within the framework of this model. Introducing appropriate double-row transfer matrices, we extend this formalism to Hall-Littlewood polynomials based on the $BC_n$ root system, and obtain a new combinatorial formula for them. We then apply our methods to prove a series of refined Cauchy and Littlewood identities involving Hall-Littlewood polynomials. The last two of these ","authors_text":"Michael Wheeler, Paul Zinn-Justin","cross_cats":["math.CO","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-10T13:23:39Z","title":"Refined Cauchy/Littlewood identities and six-vertex model partition functions: III. Deformed bosons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02236","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:d63b1a5887dab7236cbc070bba63968cde07ba1edc5711450ed62b28d103e9fa","target":"record","created_at":"2026-05-18T01:12:30Z","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":"3c5b7f92ce6857f7acc5868bebd38e5855c58d090b2d703de25da75a89a2cee4","cross_cats_sorted":["math.CO","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-08-10T13:23:39Z","title_canon_sha256":"1f734669ddc664ded2c44decde369daa5a9db5060e5619da81b594553d566c85"},"schema_version":"1.0","source":{"id":"1508.02236","kind":"arxiv","version":2}},"canonical_sha256":"807153037c59ddca8d01ab02dfd31ae1c903d7a97024a13746fd81c6ab440761","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"807153037c59ddca8d01ab02dfd31ae1c903d7a97024a13746fd81c6ab440761","first_computed_at":"2026-05-18T01:12:30.717123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:30.717123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tv78dGeVKTEvIePFmDeLYSkXz/ivXU7G39gYa1hK47KfV0hjO/WNAHmx3GLdL4+5TZph/9Hh8VpOplGGe7UQCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:30.717450Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.02236","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d63b1a5887dab7236cbc070bba63968cde07ba1edc5711450ed62b28d103e9fa","sha256:c30a9941d59600ea83ee1b067b7133580c0c5653acf367adc2cf2ffadbaa3a70"],"state_sha256":"5e1023ebed4c7bb323063087faaa83f42ce6f2ab0c3ef8e3157c60475bc392a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ni8zLYU7Yt5VPHYzOB4HcDQFnGjK5jHZAhTkLHa8rTH2pzOV+VsfeoYhxjxRtzWFxN5doknH04I0Bq4bg4X2Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T17:05:56.867750Z","bundle_sha256":"e06413b8371a62ffb7f61667b0a2ef35417be43ee5f2c430faee6d13516788e5"}}