{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:PFQO6765NVFV7YWN2WFHFHAS4W","short_pith_number":"pith:PFQO6765","canonical_record":{"source":{"id":"1907.01157","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-07-02T04:19:43Z","cross_cats_sorted":[],"title_canon_sha256":"1c360f342b79694602c02e4a5513c33143f00ba652a1b83f3c808ae33a0d9526","abstract_canon_sha256":"36ea3387d98f33cf01c04eb45ebd48dd1f22926227091852eaf0699fbe7eb742"},"schema_version":"1.0"},"canonical_sha256":"7960ef7fdd6d4b5fe2cdd58a729c12e5ab522e1deba8cd21cf391159e9a74af4","source":{"kind":"arxiv","id":"1907.01157","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.01157","created_at":"2026-07-04T23:51:45Z"},{"alias_kind":"arxiv_version","alias_value":"1907.01157v2","created_at":"2026-07-04T23:51:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01157","created_at":"2026-07-04T23:51:45Z"},{"alias_kind":"pith_short_12","alias_value":"PFQO6765NVFV","created_at":"2026-07-04T23:51:45Z"},{"alias_kind":"pith_short_16","alias_value":"PFQO6765NVFV7YWN","created_at":"2026-07-04T23:51:45Z"},{"alias_kind":"pith_short_8","alias_value":"PFQO6765","created_at":"2026-07-04T23:51:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:PFQO6765NVFV7YWN2WFHFHAS4W","target":"record","payload":{"canonical_record":{"source":{"id":"1907.01157","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-07-02T04:19:43Z","cross_cats_sorted":[],"title_canon_sha256":"1c360f342b79694602c02e4a5513c33143f00ba652a1b83f3c808ae33a0d9526","abstract_canon_sha256":"36ea3387d98f33cf01c04eb45ebd48dd1f22926227091852eaf0699fbe7eb742"},"schema_version":"1.0"},"canonical_sha256":"7960ef7fdd6d4b5fe2cdd58a729c12e5ab522e1deba8cd21cf391159e9a74af4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:51:45.550071Z","signature_b64":"CbKvNNQrdM5Y60t27AnpedbnT8TYVwv4yPg2pg4ODB2mEK5JIHx/rNsFjCF1vtmBeOV3z5vgxqCVplfNlBlvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7960ef7fdd6d4b5fe2cdd58a729c12e5ab522e1deba8cd21cf391159e9a74af4","last_reissued_at":"2026-07-04T23:51:45.549653Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:51:45.549653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.01157","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":"2026-07-04T23:51:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X3b6TlPRoLtZB24o2tUBHS+mnsmDbeDgX8pqim8KBBgu8DOcL0TbolYnGLvQI+8rpfrq7/v37J829xtFGeEJCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T20:15:56.428796Z"},"content_sha256":"ace530935c3d8700ff6e3b9f6f71106b2895019410d4a59cc9f27bf0adb9c20d","schema_version":"1.0","event_id":"sha256:ace530935c3d8700ff6e3b9f6f71106b2895019410d4a59cc9f27bf0adb9c20d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:PFQO6765NVFV7YWN2WFHFHAS4W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some $q$-exponential formulas involving the double lowering operator $\\psi$ for a tridiagonal pair","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Sarah Bockting-Conrad","submitted_at":"2019-07-02T04:19:43Z","abstract_excerpt":"Let $\\mathbb{K}$ denote an algebraically closed field and let $V$ denote a vector space over $\\mathbb{K}$ with finite positive dimension. Let $A,A^*$ denote a tridiagonal pair on $V$. We assume that $A,A^*$ belongs to a family of tridiagonal pairs said to have $q$-Racah type. Let $\\{U_i\\}_{i=0}^d$ and $\\{U_i^\\Downarrow\\}_{i=0}^{d}$ denote the first and second split decompositions of $V$. In an earlier paper we introduced a double lowering operator $\\psi:V\\to V$ with the notable feature that both $\\psi U_i\\subseteq U_{i-1}$ and $\\psi U_i^\\Downarrow\\subseteq U_{i-1}^\\Downarrow$ for $0\\leq i\\leq "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01157","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1907.01157/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T23:51:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"92vCoNAMPSuJb43MMhHCEiN+vsu9sBCVsLigqNNPI1k9UIpIHaitoRZMQM0j8CieE2/8uRVzD5zuTxidZ8R7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T20:15:56.429323Z"},"content_sha256":"4310d365849d7c028bfe4d59fd6908971817e3ffae5a4926d23a796e618c8bca","schema_version":"1.0","event_id":"sha256:4310d365849d7c028bfe4d59fd6908971817e3ffae5a4926d23a796e618c8bca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PFQO6765NVFV7YWN2WFHFHAS4W/bundle.json","state_url":"https://pith.science/pith/PFQO6765NVFV7YWN2WFHFHAS4W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PFQO6765NVFV7YWN2WFHFHAS4W/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":"2026-08-17T20:15:56Z","links":{"resolver":"https://pith.science/pith/PFQO6765NVFV7YWN2WFHFHAS4W","bundle":"https://pith.science/pith/PFQO6765NVFV7YWN2WFHFHAS4W/bundle.json","state":"https://pith.science/pith/PFQO6765NVFV7YWN2WFHFHAS4W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PFQO6765NVFV7YWN2WFHFHAS4W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PFQO6765NVFV7YWN2WFHFHAS4W","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":"36ea3387d98f33cf01c04eb45ebd48dd1f22926227091852eaf0699fbe7eb742","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-07-02T04:19:43Z","title_canon_sha256":"1c360f342b79694602c02e4a5513c33143f00ba652a1b83f3c808ae33a0d9526"},"schema_version":"1.0","source":{"id":"1907.01157","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.01157","created_at":"2026-07-04T23:51:45Z"},{"alias_kind":"arxiv_version","alias_value":"1907.01157v2","created_at":"2026-07-04T23:51:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01157","created_at":"2026-07-04T23:51:45Z"},{"alias_kind":"pith_short_12","alias_value":"PFQO6765NVFV","created_at":"2026-07-04T23:51:45Z"},{"alias_kind":"pith_short_16","alias_value":"PFQO6765NVFV7YWN","created_at":"2026-07-04T23:51:45Z"},{"alias_kind":"pith_short_8","alias_value":"PFQO6765","created_at":"2026-07-04T23:51:45Z"}],"graph_snapshots":[{"event_id":"sha256:4310d365849d7c028bfe4d59fd6908971817e3ffae5a4926d23a796e618c8bca","target":"graph","created_at":"2026-07-04T23:51:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1907.01157/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathbb{K}$ denote an algebraically closed field and let $V$ denote a vector space over $\\mathbb{K}$ with finite positive dimension. Let $A,A^*$ denote a tridiagonal pair on $V$. We assume that $A,A^*$ belongs to a family of tridiagonal pairs said to have $q$-Racah type. Let $\\{U_i\\}_{i=0}^d$ and $\\{U_i^\\Downarrow\\}_{i=0}^{d}$ denote the first and second split decompositions of $V$. In an earlier paper we introduced a double lowering operator $\\psi:V\\to V$ with the notable feature that both $\\psi U_i\\subseteq U_{i-1}$ and $\\psi U_i^\\Downarrow\\subseteq U_{i-1}^\\Downarrow$ for $0\\leq i\\leq ","authors_text":"Sarah Bockting-Conrad","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-07-02T04:19:43Z","title":"Some $q$-exponential formulas involving the double lowering operator $\\psi$ for a tridiagonal pair"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01157","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:ace530935c3d8700ff6e3b9f6f71106b2895019410d4a59cc9f27bf0adb9c20d","target":"record","created_at":"2026-07-04T23:51:45Z","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":"36ea3387d98f33cf01c04eb45ebd48dd1f22926227091852eaf0699fbe7eb742","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-07-02T04:19:43Z","title_canon_sha256":"1c360f342b79694602c02e4a5513c33143f00ba652a1b83f3c808ae33a0d9526"},"schema_version":"1.0","source":{"id":"1907.01157","kind":"arxiv","version":2}},"canonical_sha256":"7960ef7fdd6d4b5fe2cdd58a729c12e5ab522e1deba8cd21cf391159e9a74af4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7960ef7fdd6d4b5fe2cdd58a729c12e5ab522e1deba8cd21cf391159e9a74af4","first_computed_at":"2026-07-04T23:51:45.549653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:51:45.549653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CbKvNNQrdM5Y60t27AnpedbnT8TYVwv4yPg2pg4ODB2mEK5JIHx/rNsFjCF1vtmBeOV3z5vgxqCVplfNlBlvCA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:51:45.550071Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.01157","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ace530935c3d8700ff6e3b9f6f71106b2895019410d4a59cc9f27bf0adb9c20d","sha256:4310d365849d7c028bfe4d59fd6908971817e3ffae5a4926d23a796e618c8bca"],"state_sha256":"05a03977abbef0a4e163abd916616784e9076dce6f96d4b2c3fb79dd65aa5209"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r6nYqxod7NMdPoIdFkdBm3pYsdmOKVS3+SsZHs75cbNhuIIi8lbFseMPlnhJTjswsrCZ4VWc6NGhHgFtjZ9hCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T20:15:56.434982Z","bundle_sha256":"8d00895bc06ecfec9d1b77e218c026a649db0af2ed91eee21ba40ddf61984f73"}}