{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:TYT7ESHZJPD5DKZ7Z6SEOOYOZY","short_pith_number":"pith:TYT7ESHZ","canonical_record":{"source":{"id":"1906.11136","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-06-26T14:47:09Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"64e12800adf346075ea9f74c6382d6fc620bc9570cf975d237c1585caf6c7539","abstract_canon_sha256":"14264a677a47cdebc25fb01afd2908a8d79feb1eeecb0fb9cbcffde4045517b8"},"schema_version":"1.0"},"canonical_sha256":"9e27f248f94bc7d1ab3fcfa4473b0ece1ddaf879473d9bbab7445e8f8fb7ae2d","source":{"kind":"arxiv","id":"1906.11136","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.11136","created_at":"2026-05-17T23:42:09Z"},{"alias_kind":"arxiv_version","alias_value":"1906.11136v1","created_at":"2026-05-17T23:42:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.11136","created_at":"2026-05-17T23:42:09Z"},{"alias_kind":"pith_short_12","alias_value":"TYT7ESHZJPD5","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TYT7ESHZJPD5DKZ7","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TYT7ESHZ","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:TYT7ESHZJPD5DKZ7Z6SEOOYOZY","target":"record","payload":{"canonical_record":{"source":{"id":"1906.11136","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-06-26T14:47:09Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"64e12800adf346075ea9f74c6382d6fc620bc9570cf975d237c1585caf6c7539","abstract_canon_sha256":"14264a677a47cdebc25fb01afd2908a8d79feb1eeecb0fb9cbcffde4045517b8"},"schema_version":"1.0"},"canonical_sha256":"9e27f248f94bc7d1ab3fcfa4473b0ece1ddaf879473d9bbab7445e8f8fb7ae2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:09.733105Z","signature_b64":"w/z40y8eWnOUBPbB0HVsz3El7F4uu/Vv0zCV0QS65mIBD6pd9bWHOc1SHtLQ9FIfyyPr+JPKe52XjvmM/Y/PAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e27f248f94bc7d1ab3fcfa4473b0ece1ddaf879473d9bbab7445e8f8fb7ae2d","last_reissued_at":"2026-05-17T23:42:09.732402Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:09.732402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.11136","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":"2026-05-17T23:42:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hiIgRuZ8xqmfN6Jd2k4cgmaKxVxrEFXE4H46vHLArESX5dIoEJFgHNrLKvqGSXp6pPVyhYvyd9EHYGLh24IsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T00:19:04.408012Z"},"content_sha256":"8d0650f52aff38a8eb47980c44c68058891d86bc9e777f5b6d23fab693a56f26","schema_version":"1.0","event_id":"sha256:8d0650f52aff38a8eb47980c44c68058891d86bc9e777f5b6d23fab693a56f26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:TYT7ESHZJPD5DKZ7Z6SEOOYOZY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large Deviation theorems for Dirichlet determinants of analytic quasi-periodic Jacobi operators with Brjuno-R\\\"ussmann frequency","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.DS","authors_text":"Kai Tao, Wenmeng Geng","submitted_at":"2019-06-26T14:47:09Z","abstract_excerpt":"In this paper, we first study the strong Birkhoff Ergodic Theorem for subharmonic functions with the Brjuno-R\\\"ussmann shift on the Torus. Then, we apply it to prove the large deviation theorems for the finite scale Dirichlet determinants of quasi-periodic analytic Jacobi operators with this frequency. It shows that the Brjuno-R\\\"ussmann function, which reflects the irrationality of the frequency, plays the key role in these theorems via the smallest deviation. At last, as an application, we obtain a distribution of the eigenvalues of the Jacobi operators with Dirichlet boundary conditions, wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11136","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":"2026-05-17T23:42:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gp7ubMxtdB8R1iruGgij54LtYfBJi0P+b26m4Ipnv0Wv3E0RJHLVz6NElqsZpRqgPdZsD+5vzIgES4LmntSSAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T00:19:04.408734Z"},"content_sha256":"b09d47574fb79268891b4f4e7339d5f194b86c3800005a79da100852f86c25ba","schema_version":"1.0","event_id":"sha256:b09d47574fb79268891b4f4e7339d5f194b86c3800005a79da100852f86c25ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TYT7ESHZJPD5DKZ7Z6SEOOYOZY/bundle.json","state_url":"https://pith.science/pith/TYT7ESHZJPD5DKZ7Z6SEOOYOZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TYT7ESHZJPD5DKZ7Z6SEOOYOZY/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":"2026-06-06T00:19:04Z","links":{"resolver":"https://pith.science/pith/TYT7ESHZJPD5DKZ7Z6SEOOYOZY","bundle":"https://pith.science/pith/TYT7ESHZJPD5DKZ7Z6SEOOYOZY/bundle.json","state":"https://pith.science/pith/TYT7ESHZJPD5DKZ7Z6SEOOYOZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TYT7ESHZJPD5DKZ7Z6SEOOYOZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TYT7ESHZJPD5DKZ7Z6SEOOYOZY","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":"14264a677a47cdebc25fb01afd2908a8d79feb1eeecb0fb9cbcffde4045517b8","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-06-26T14:47:09Z","title_canon_sha256":"64e12800adf346075ea9f74c6382d6fc620bc9570cf975d237c1585caf6c7539"},"schema_version":"1.0","source":{"id":"1906.11136","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.11136","created_at":"2026-05-17T23:42:09Z"},{"alias_kind":"arxiv_version","alias_value":"1906.11136v1","created_at":"2026-05-17T23:42:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.11136","created_at":"2026-05-17T23:42:09Z"},{"alias_kind":"pith_short_12","alias_value":"TYT7ESHZJPD5","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TYT7ESHZJPD5DKZ7","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TYT7ESHZ","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:b09d47574fb79268891b4f4e7339d5f194b86c3800005a79da100852f86c25ba","target":"graph","created_at":"2026-05-17T23:42:09Z","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":"In this paper, we first study the strong Birkhoff Ergodic Theorem for subharmonic functions with the Brjuno-R\\\"ussmann shift on the Torus. Then, we apply it to prove the large deviation theorems for the finite scale Dirichlet determinants of quasi-periodic analytic Jacobi operators with this frequency. It shows that the Brjuno-R\\\"ussmann function, which reflects the irrationality of the frequency, plays the key role in these theorems via the smallest deviation. At last, as an application, we obtain a distribution of the eigenvalues of the Jacobi operators with Dirichlet boundary conditions, wh","authors_text":"Kai Tao, Wenmeng Geng","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-06-26T14:47:09Z","title":"Large Deviation theorems for Dirichlet determinants of analytic quasi-periodic Jacobi operators with Brjuno-R\\\"ussmann frequency"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11136","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":"sha256:8d0650f52aff38a8eb47980c44c68058891d86bc9e777f5b6d23fab693a56f26","target":"record","created_at":"2026-05-17T23:42:09Z","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":"14264a677a47cdebc25fb01afd2908a8d79feb1eeecb0fb9cbcffde4045517b8","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-06-26T14:47:09Z","title_canon_sha256":"64e12800adf346075ea9f74c6382d6fc620bc9570cf975d237c1585caf6c7539"},"schema_version":"1.0","source":{"id":"1906.11136","kind":"arxiv","version":1}},"canonical_sha256":"9e27f248f94bc7d1ab3fcfa4473b0ece1ddaf879473d9bbab7445e8f8fb7ae2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e27f248f94bc7d1ab3fcfa4473b0ece1ddaf879473d9bbab7445e8f8fb7ae2d","first_computed_at":"2026-05-17T23:42:09.732402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:09.732402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w/z40y8eWnOUBPbB0HVsz3El7F4uu/Vv0zCV0QS65mIBD6pd9bWHOc1SHtLQ9FIfyyPr+JPKe52XjvmM/Y/PAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:09.733105Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.11136","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d0650f52aff38a8eb47980c44c68058891d86bc9e777f5b6d23fab693a56f26","sha256:b09d47574fb79268891b4f4e7339d5f194b86c3800005a79da100852f86c25ba"],"state_sha256":"f437bc581df18835881046eb9a145ddeea0d7d9c4f5cc88fd697656929f4e631"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y+yMKt/MB0s4rpbylx2T0skDnE37dOfFZ/FFbzD004zJDsaU0YpbahAD0gwwivl6IS08kl0fBDflcGcnTYTQBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T00:19:04.412684Z","bundle_sha256":"07cdf2cb051dbcffaba3d7f08afc1d7126231a43f54d784a403718d656839df0"}}