{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:SL2HLULQDUNJOBKJXGB5WBY2QR","short_pith_number":"pith:SL2HLULQ","canonical_record":{"source":{"id":"2506.02855","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-06-03T13:23:35Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"977490348575fa0c2b1e64933a62aee3187f73f065eee816106661b2f94e99ce","abstract_canon_sha256":"fd52f3934f862b999bb3da4f07805e73ba0bc4aa0598cbef96bd93e810a512b1"},"schema_version":"1.0"},"canonical_sha256":"92f475d1701d1a970549b983db071a847465c4b1a9bc103e49247e646665597b","source":{"kind":"arxiv","id":"2506.02855","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.02855","created_at":"2026-07-05T11:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"2506.02855v2","created_at":"2026-07-05T11:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02855","created_at":"2026-07-05T11:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"SL2HLULQDUNJ","created_at":"2026-07-05T11:38:29Z"},{"alias_kind":"pith_short_16","alias_value":"SL2HLULQDUNJOBKJ","created_at":"2026-07-05T11:38:29Z"},{"alias_kind":"pith_short_8","alias_value":"SL2HLULQ","created_at":"2026-07-05T11:38:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:SL2HLULQDUNJOBKJXGB5WBY2QR","target":"record","payload":{"canonical_record":{"source":{"id":"2506.02855","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-06-03T13:23:35Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"977490348575fa0c2b1e64933a62aee3187f73f065eee816106661b2f94e99ce","abstract_canon_sha256":"fd52f3934f862b999bb3da4f07805e73ba0bc4aa0598cbef96bd93e810a512b1"},"schema_version":"1.0"},"canonical_sha256":"92f475d1701d1a970549b983db071a847465c4b1a9bc103e49247e646665597b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:29.895377Z","signature_b64":"dQSOdnWwUWkr0siJmr02qEUwWwkSOI62y0I1unor1LKd49KQQ6upthVAohimJu0vR8nLBONqvCwWTbfZ04qgCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92f475d1701d1a970549b983db071a847465c4b1a9bc103e49247e646665597b","last_reissued_at":"2026-07-05T11:38:29.894867Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:29.894867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.02855","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":"2026-07-05T11:38:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rPYah+MRR3CLreP8CwhH0DkI7IMrXCfGXL+Y9QSgC2ZLRxr82hFjzuYK6c1XD3uf7h+1tvH9fekWaoYkXzotAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T03:59:09.572523Z"},"content_sha256":"a4f1fb1bd0eafb4cdcb36e3d7b9ddc79bdf879a1d280fed447bd9ac0fc6398ee","schema_version":"1.0","event_id":"sha256:a4f1fb1bd0eafb4cdcb36e3d7b9ddc79bdf879a1d280fed447bd9ac0fc6398ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:SL2HLULQDUNJOBKJXGB5WBY2QR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pugh's global linearization for the nonautonomous unbounded system with $\\mu$-dichotomy via Lyapunov theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Weijie Lu, Yonghui Xia","submitted_at":"2025-06-03T13:23:35Z","abstract_excerpt":"The classical global linearization theorem for autonomous system given in [C. Pugh, Amer. J. Math., 91 (1969) 363-367] requires that nonlinear system with hyperbolicity satisfies boundedness and Lipschitz continuity.In this paper, we establish an {\\em unbounded} global linearization theorem for nonautonomous systems subject to unbounded Lipschitz perturbations, under the assumption that the linear system admits a nonuniform $\\mu$-dichotomy (more general than classical exponential dichotomy). To this end, we first develop a comprehensive Lyapunov function framework for systems exhibiting nonuni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02855","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/2506.02855/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":"2026-07-05T11:38:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3SR7LHuOva5WKn0CGS2LgSH3LTmOHmHNkwtXaS02e1cx91QB+lZSNAsTpQ1Hxj5EJEFhc9wB0TJ/uFLellP1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T03:59:09.573019Z"},"content_sha256":"99193ddf4b301adc6ae34b570333b3e6cbf677ee4d18ed869a93ea18e5538929","schema_version":"1.0","event_id":"sha256:99193ddf4b301adc6ae34b570333b3e6cbf677ee4d18ed869a93ea18e5538929"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SL2HLULQDUNJOBKJXGB5WBY2QR/bundle.json","state_url":"https://pith.science/pith/SL2HLULQDUNJOBKJXGB5WBY2QR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SL2HLULQDUNJOBKJXGB5WBY2QR/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":"2026-08-10T03:59:09Z","links":{"resolver":"https://pith.science/pith/SL2HLULQDUNJOBKJXGB5WBY2QR","bundle":"https://pith.science/pith/SL2HLULQDUNJOBKJXGB5WBY2QR/bundle.json","state":"https://pith.science/pith/SL2HLULQDUNJOBKJXGB5WBY2QR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SL2HLULQDUNJOBKJXGB5WBY2QR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:SL2HLULQDUNJOBKJXGB5WBY2QR","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":"fd52f3934f862b999bb3da4f07805e73ba0bc4aa0598cbef96bd93e810a512b1","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-06-03T13:23:35Z","title_canon_sha256":"977490348575fa0c2b1e64933a62aee3187f73f065eee816106661b2f94e99ce"},"schema_version":"1.0","source":{"id":"2506.02855","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.02855","created_at":"2026-07-05T11:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"2506.02855v2","created_at":"2026-07-05T11:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02855","created_at":"2026-07-05T11:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"SL2HLULQDUNJ","created_at":"2026-07-05T11:38:29Z"},{"alias_kind":"pith_short_16","alias_value":"SL2HLULQDUNJOBKJ","created_at":"2026-07-05T11:38:29Z"},{"alias_kind":"pith_short_8","alias_value":"SL2HLULQ","created_at":"2026-07-05T11:38:29Z"}],"graph_snapshots":[{"event_id":"sha256:99193ddf4b301adc6ae34b570333b3e6cbf677ee4d18ed869a93ea18e5538929","target":"graph","created_at":"2026-07-05T11:38:29Z","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/2506.02855/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The classical global linearization theorem for autonomous system given in [C. Pugh, Amer. J. Math., 91 (1969) 363-367] requires that nonlinear system with hyperbolicity satisfies boundedness and Lipschitz continuity.In this paper, we establish an {\\em unbounded} global linearization theorem for nonautonomous systems subject to unbounded Lipschitz perturbations, under the assumption that the linear system admits a nonuniform $\\mu$-dichotomy (more general than classical exponential dichotomy). To this end, we first develop a comprehensive Lyapunov function framework for systems exhibiting nonuni","authors_text":"Weijie Lu, Yonghui Xia","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-06-03T13:23:35Z","title":"Pugh's global linearization for the nonautonomous unbounded system with $\\mu$-dichotomy via Lyapunov theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02855","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:a4f1fb1bd0eafb4cdcb36e3d7b9ddc79bdf879a1d280fed447bd9ac0fc6398ee","target":"record","created_at":"2026-07-05T11:38:29Z","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":"fd52f3934f862b999bb3da4f07805e73ba0bc4aa0598cbef96bd93e810a512b1","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-06-03T13:23:35Z","title_canon_sha256":"977490348575fa0c2b1e64933a62aee3187f73f065eee816106661b2f94e99ce"},"schema_version":"1.0","source":{"id":"2506.02855","kind":"arxiv","version":2}},"canonical_sha256":"92f475d1701d1a970549b983db071a847465c4b1a9bc103e49247e646665597b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92f475d1701d1a970549b983db071a847465c4b1a9bc103e49247e646665597b","first_computed_at":"2026-07-05T11:38:29.894867Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:38:29.894867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dQSOdnWwUWkr0siJmr02qEUwWwkSOI62y0I1unor1LKd49KQQ6upthVAohimJu0vR8nLBONqvCwWTbfZ04qgCg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:38:29.895377Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.02855","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4f1fb1bd0eafb4cdcb36e3d7b9ddc79bdf879a1d280fed447bd9ac0fc6398ee","sha256:99193ddf4b301adc6ae34b570333b3e6cbf677ee4d18ed869a93ea18e5538929"],"state_sha256":"bee802b803b4728e6eeb123a03dca3b0a08d8dfb53891b06b418d8992389c3d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F/6aTqdPf8OgNoOx1BbC/uTXerBC3yOj+MMz4/QTM9iJbV8mD97WeBx5PS/6XR8TYKSDEoGYS5lBJrXSHLjDCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T03:59:09.579165Z","bundle_sha256":"a0fb924758e96c6961dd27e987f26f34f1674a90eb390f97cdf7e66d0b87db40"}}