{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZN6VJEVFS4MOIDCDNB2J4T4Q6S","short_pith_number":"pith:ZN6VJEVF","canonical_record":{"source":{"id":"1811.02647","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-06T21:03:42Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c6160a4ce3844644a99abf975bd1a753b34fd8926c349e32c4676fafbeaabab0","abstract_canon_sha256":"8134dedc0ad5377cd5e877fff28e85b4adbbc35ca956209a0c990844b394ba12"},"schema_version":"1.0"},"canonical_sha256":"cb7d5492a59718e40c4368749e4f90f480a57f0ea356ba18d898337f66cc8668","source":{"kind":"arxiv","id":"1811.02647","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.02647","created_at":"2026-05-18T00:01:21Z"},{"alias_kind":"arxiv_version","alias_value":"1811.02647v1","created_at":"2026-05-18T00:01:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.02647","created_at":"2026-05-18T00:01:21Z"},{"alias_kind":"pith_short_12","alias_value":"ZN6VJEVFS4MO","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZN6VJEVFS4MOIDCD","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZN6VJEVF","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZN6VJEVFS4MOIDCDNB2J4T4Q6S","target":"record","payload":{"canonical_record":{"source":{"id":"1811.02647","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-06T21:03:42Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c6160a4ce3844644a99abf975bd1a753b34fd8926c349e32c4676fafbeaabab0","abstract_canon_sha256":"8134dedc0ad5377cd5e877fff28e85b4adbbc35ca956209a0c990844b394ba12"},"schema_version":"1.0"},"canonical_sha256":"cb7d5492a59718e40c4368749e4f90f480a57f0ea356ba18d898337f66cc8668","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:21.169012Z","signature_b64":"SPNRWOlc+HOW4zIGL1zqiIYYbkeFYB2I+NWiV1I/IPlUAtc5iXJka2shjTaaK41X0HS4YPwXXQtQN2yYSRAqBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb7d5492a59718e40c4368749e4f90f480a57f0ea356ba18d898337f66cc8668","last_reissued_at":"2026-05-18T00:01:21.168569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:21.168569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.02647","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":"2026-05-18T00:01:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5YmTV7bwIzH4Aay3eW1q6gz1BOyRA7F8LyYToFOpcNIWq0IEfUMmF8bIf/3b2l9nYR1aiysjF3CMOOn/JW5SAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:15:18.059605Z"},"content_sha256":"32d9a8ead32178bb1c19acbd81acd62d727050c56ed195ec40a4376fbeeea693","schema_version":"1.0","event_id":"sha256:32d9a8ead32178bb1c19acbd81acd62d727050c56ed195ec40a4376fbeeea693"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZN6VJEVFS4MOIDCDNB2J4T4Q6S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A random cocycle with non H\\\"older Lyapunov exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Manuel Santos, Pedro Duarte, Silvius Klein","submitted_at":"2018-11-06T21:03:42Z","abstract_excerpt":"We provide an example of a Schr\\\"odinger cocycle over a mixing Markov shift for which the integrated density of states has a very weak modulus of continuity, close to the log-H\\\"older lower bound established by W. Craig and B. Simon. This model is based upon a classical example due to Y. Kifer of a random Bernoulli cocycle with zero Lyapunov exponents which is not strongly irreducible. It follows that the Lyapunov exponent of a Bernoulli cocycle near this Kifer example cannot be H\\\"older or weak-H\\\"older continuous, thus providing a limitation on the modulus of continuity of the Lyapunov expon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02647","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":"2026-05-18T00:01:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MdJKwVD5zz0Wr+G7zish8JVla7XczKkufODZ1sSOUJ+/DEX5Q88jDZklqm2V32n9v0HxROixsWuQr5963Re+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:15:18.059950Z"},"content_sha256":"9a23fcd0e14f137d00b10127a90dad5af003f8f6adab7055ba2ac81e9c5d09af","schema_version":"1.0","event_id":"sha256:9a23fcd0e14f137d00b10127a90dad5af003f8f6adab7055ba2ac81e9c5d09af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZN6VJEVFS4MOIDCDNB2J4T4Q6S/bundle.json","state_url":"https://pith.science/pith/ZN6VJEVFS4MOIDCDNB2J4T4Q6S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZN6VJEVFS4MOIDCDNB2J4T4Q6S/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":"2026-06-27T13:15:18Z","links":{"resolver":"https://pith.science/pith/ZN6VJEVFS4MOIDCDNB2J4T4Q6S","bundle":"https://pith.science/pith/ZN6VJEVFS4MOIDCDNB2J4T4Q6S/bundle.json","state":"https://pith.science/pith/ZN6VJEVFS4MOIDCDNB2J4T4Q6S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZN6VJEVFS4MOIDCDNB2J4T4Q6S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZN6VJEVFS4MOIDCDNB2J4T4Q6S","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":"8134dedc0ad5377cd5e877fff28e85b4adbbc35ca956209a0c990844b394ba12","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-06T21:03:42Z","title_canon_sha256":"c6160a4ce3844644a99abf975bd1a753b34fd8926c349e32c4676fafbeaabab0"},"schema_version":"1.0","source":{"id":"1811.02647","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.02647","created_at":"2026-05-18T00:01:21Z"},{"alias_kind":"arxiv_version","alias_value":"1811.02647v1","created_at":"2026-05-18T00:01:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.02647","created_at":"2026-05-18T00:01:21Z"},{"alias_kind":"pith_short_12","alias_value":"ZN6VJEVFS4MO","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZN6VJEVFS4MOIDCD","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZN6VJEVF","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:9a23fcd0e14f137d00b10127a90dad5af003f8f6adab7055ba2ac81e9c5d09af","target":"graph","created_at":"2026-05-18T00:01:21Z","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 provide an example of a Schr\\\"odinger cocycle over a mixing Markov shift for which the integrated density of states has a very weak modulus of continuity, close to the log-H\\\"older lower bound established by W. Craig and B. Simon. This model is based upon a classical example due to Y. Kifer of a random Bernoulli cocycle with zero Lyapunov exponents which is not strongly irreducible. It follows that the Lyapunov exponent of a Bernoulli cocycle near this Kifer example cannot be H\\\"older or weak-H\\\"older continuous, thus providing a limitation on the modulus of continuity of the Lyapunov expon","authors_text":"Manuel Santos, Pedro Duarte, Silvius Klein","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-06T21:03:42Z","title":"A random cocycle with non H\\\"older Lyapunov exponent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02647","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":"sha256:32d9a8ead32178bb1c19acbd81acd62d727050c56ed195ec40a4376fbeeea693","target":"record","created_at":"2026-05-18T00:01:21Z","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":"8134dedc0ad5377cd5e877fff28e85b4adbbc35ca956209a0c990844b394ba12","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-11-06T21:03:42Z","title_canon_sha256":"c6160a4ce3844644a99abf975bd1a753b34fd8926c349e32c4676fafbeaabab0"},"schema_version":"1.0","source":{"id":"1811.02647","kind":"arxiv","version":1}},"canonical_sha256":"cb7d5492a59718e40c4368749e4f90f480a57f0ea356ba18d898337f66cc8668","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb7d5492a59718e40c4368749e4f90f480a57f0ea356ba18d898337f66cc8668","first_computed_at":"2026-05-18T00:01:21.168569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:21.168569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SPNRWOlc+HOW4zIGL1zqiIYYbkeFYB2I+NWiV1I/IPlUAtc5iXJka2shjTaaK41X0HS4YPwXXQtQN2yYSRAqBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:21.169012Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.02647","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32d9a8ead32178bb1c19acbd81acd62d727050c56ed195ec40a4376fbeeea693","sha256:9a23fcd0e14f137d00b10127a90dad5af003f8f6adab7055ba2ac81e9c5d09af"],"state_sha256":"55cc2747270d7e6b3de14da95b910824673c8827e157e6de9797222441d6cba1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BM44ZxBSs1FtTQrbmCYTe/7yI9R2gyXVVHRO9qATtQLVFT2i1gkwnRv/GyVlf6rtgk/EgWluT0goWEbGypj3Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T13:15:18.061831Z","bundle_sha256":"2fa5d5f61c2d4cc65784ef51ac802d1218acb59f5d1bb3027eb2228af69c57af"}}