{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4WQAVEMYLSKXNF6ED2TROG6R6D","short_pith_number":"pith:4WQAVEMY","canonical_record":{"source":{"id":"1108.3746","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-18T13:04:09Z","cross_cats_sorted":[],"title_canon_sha256":"e936bf37fc7a4762d459f5fad55a85ea9e25bbaed92a832cd277e7f55af448fd","abstract_canon_sha256":"157dfd0a3ab32faf27d20e52a1489769dfc9593677b376d5d8199f0a70db4b16"},"schema_version":"1.0"},"canonical_sha256":"e5a00a91985c957697c41ea7171bd1f0f530e740cfa27a5a252b2961bdb7cde4","source":{"kind":"arxiv","id":"1108.3746","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3746","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3746v4","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3746","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"pith_short_12","alias_value":"4WQAVEMYLSKX","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4WQAVEMYLSKXNF6E","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4WQAVEMY","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4WQAVEMYLSKXNF6ED2TROG6R6D","target":"record","payload":{"canonical_record":{"source":{"id":"1108.3746","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-18T13:04:09Z","cross_cats_sorted":[],"title_canon_sha256":"e936bf37fc7a4762d459f5fad55a85ea9e25bbaed92a832cd277e7f55af448fd","abstract_canon_sha256":"157dfd0a3ab32faf27d20e52a1489769dfc9593677b376d5d8199f0a70db4b16"},"schema_version":"1.0"},"canonical_sha256":"e5a00a91985c957697c41ea7171bd1f0f530e740cfa27a5a252b2961bdb7cde4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:44.644842Z","signature_b64":"4AUxjzbb1e1kcAu7QtNx1fY7BQQ0B6lYugLnHsCqaqFlXOXoDs8DS5qkY8mnq6nHByeWwkK70fcSP1Kwebf0AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5a00a91985c957697c41ea7171bd1f0f530e740cfa27a5a252b2961bdb7cde4","last_reissued_at":"2026-05-18T00:52:44.644203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:44.644203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.3746","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yyU94NSqzF4frQm0JLOjk4yZW+HQ706BFlSljCT+lW26wX1gj1C1+2U4LOvqQ4JHXvZQ39fu+MbUrMwzqhTWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:06:55.619655Z"},"content_sha256":"982af03dfe0be22bbfb2705ca3eaa06146536c48c85cff267940bbbbf5df34e0","schema_version":"1.0","event_id":"sha256:982af03dfe0be22bbfb2705ca3eaa06146536c48c85cff267940bbbbf5df34e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4WQAVEMYLSKXNF6ED2TROG6R6D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Lyapunov spectrum of relative transfer operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Manuel Stadlbauer, M\\'ario Bessa","submitted_at":"2011-08-18T13:04:09Z","abstract_excerpt":"We analyze the Lyapunov spectrum of the relative Ruelle operator associated with a skew product whose base is an ergodic automorphism and whose fibers are full shifts. We prove that these operators can be approximated in the $C^0$-topology by positive matrices with an associated dominated splitting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3746","kind":"arxiv","version":4},"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":"2026-05-18T00:52:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WEZZRNF2Y+/24gxCkjnkVWM8AMY02L4AS0zEESIfLtOQ075tEB2mXKI2VRyq6UEv0UYfSLp8O9NUeeJ9uBeSBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:06:55.620338Z"},"content_sha256":"ceaa80bfc412cc10941c753d9c6cf3bc0015c7263ec2239b6f800a2c1e79b031","schema_version":"1.0","event_id":"sha256:ceaa80bfc412cc10941c753d9c6cf3bc0015c7263ec2239b6f800a2c1e79b031"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4WQAVEMYLSKXNF6ED2TROG6R6D/bundle.json","state_url":"https://pith.science/pith/4WQAVEMYLSKXNF6ED2TROG6R6D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4WQAVEMYLSKXNF6ED2TROG6R6D/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":"2026-06-12T00:06:55Z","links":{"resolver":"https://pith.science/pith/4WQAVEMYLSKXNF6ED2TROG6R6D","bundle":"https://pith.science/pith/4WQAVEMYLSKXNF6ED2TROG6R6D/bundle.json","state":"https://pith.science/pith/4WQAVEMYLSKXNF6ED2TROG6R6D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4WQAVEMYLSKXNF6ED2TROG6R6D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4WQAVEMYLSKXNF6ED2TROG6R6D","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":"157dfd0a3ab32faf27d20e52a1489769dfc9593677b376d5d8199f0a70db4b16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-18T13:04:09Z","title_canon_sha256":"e936bf37fc7a4762d459f5fad55a85ea9e25bbaed92a832cd277e7f55af448fd"},"schema_version":"1.0","source":{"id":"1108.3746","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.3746","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"arxiv_version","alias_value":"1108.3746v4","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3746","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"pith_short_12","alias_value":"4WQAVEMYLSKX","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4WQAVEMYLSKXNF6E","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4WQAVEMY","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:ceaa80bfc412cc10941c753d9c6cf3bc0015c7263ec2239b6f800a2c1e79b031","target":"graph","created_at":"2026-05-18T00:52:44Z","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 analyze the Lyapunov spectrum of the relative Ruelle operator associated with a skew product whose base is an ergodic automorphism and whose fibers are full shifts. We prove that these operators can be approximated in the $C^0$-topology by positive matrices with an associated dominated splitting.","authors_text":"Manuel Stadlbauer, M\\'ario Bessa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-18T13:04:09Z","title":"On the Lyapunov spectrum of relative transfer operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3746","kind":"arxiv","version":4},"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":"sha256:982af03dfe0be22bbfb2705ca3eaa06146536c48c85cff267940bbbbf5df34e0","target":"record","created_at":"2026-05-18T00:52:44Z","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":"157dfd0a3ab32faf27d20e52a1489769dfc9593677b376d5d8199f0a70db4b16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-08-18T13:04:09Z","title_canon_sha256":"e936bf37fc7a4762d459f5fad55a85ea9e25bbaed92a832cd277e7f55af448fd"},"schema_version":"1.0","source":{"id":"1108.3746","kind":"arxiv","version":4}},"canonical_sha256":"e5a00a91985c957697c41ea7171bd1f0f530e740cfa27a5a252b2961bdb7cde4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5a00a91985c957697c41ea7171bd1f0f530e740cfa27a5a252b2961bdb7cde4","first_computed_at":"2026-05-18T00:52:44.644203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:44.644203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4AUxjzbb1e1kcAu7QtNx1fY7BQQ0B6lYugLnHsCqaqFlXOXoDs8DS5qkY8mnq6nHByeWwkK70fcSP1Kwebf0AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:44.644842Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.3746","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:982af03dfe0be22bbfb2705ca3eaa06146536c48c85cff267940bbbbf5df34e0","sha256:ceaa80bfc412cc10941c753d9c6cf3bc0015c7263ec2239b6f800a2c1e79b031"],"state_sha256":"d36a2b3e794aa7b14b05aeb4bff140c8c99a300fa957842a1baf9295e49a8b06"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"84C5UCeglL6fh8tyDi9XqFOxm/HH/yvHR/CCQrNhrpZAKX/oZ95U8R3w7gKa9t8UlJQlIplUOBXP8QytSi0wCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T00:06:55.624085Z","bundle_sha256":"7db607454e5a46dced273a887c5962f789f11fe984aea1597cbd798bc29c9cce"}}