{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:Z3MAZ52VGMFDI7Q4CNM5WAGZHB","short_pith_number":"pith:Z3MAZ52V","canonical_record":{"source":{"id":"1710.06662","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-18T10:20:52Z","cross_cats_sorted":[],"title_canon_sha256":"e559efd4a60dd5cf41f471af5b2414a0f633230064a6dc3e4f970893eddc341f","abstract_canon_sha256":"15c564cc6acdd9e5d158d27d8183002b353b640c00b1bc13bb7a975d17b2a108"},"schema_version":"1.0"},"canonical_sha256":"ced80cf755330a347e1c1359db00d93851bddfed20009935362d2db81b4f6626","source":{"kind":"arxiv","id":"1710.06662","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06662","created_at":"2026-05-17T23:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06662v2","created_at":"2026-05-17T23:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06662","created_at":"2026-05-17T23:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"Z3MAZ52VGMFD","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z3MAZ52VGMFDI7Q4","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z3MAZ52V","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:Z3MAZ52VGMFDI7Q4CNM5WAGZHB","target":"record","payload":{"canonical_record":{"source":{"id":"1710.06662","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-18T10:20:52Z","cross_cats_sorted":[],"title_canon_sha256":"e559efd4a60dd5cf41f471af5b2414a0f633230064a6dc3e4f970893eddc341f","abstract_canon_sha256":"15c564cc6acdd9e5d158d27d8183002b353b640c00b1bc13bb7a975d17b2a108"},"schema_version":"1.0"},"canonical_sha256":"ced80cf755330a347e1c1359db00d93851bddfed20009935362d2db81b4f6626","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:18.300943Z","signature_b64":"SzNvgZNR90nQoFcKpuq94GdN/Cg5ISEJkJCMXZD8avlBVPY+LW+B/TUYpOad1FPCkWwP0hsIjM0hghlPcKGzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ced80cf755330a347e1c1359db00d93851bddfed20009935362d2db81b4f6626","last_reissued_at":"2026-05-17T23:41:18.300262Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:18.300262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.06662","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":"2026-05-17T23:41:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+A5VFe5RBs7tCU710gfKTAYYZzU0o0Wc7mPp7pHOpd5IBGtREWu1macsSqOLjW816ubREllUppXvB3lDJTwVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:54:53.842452Z"},"content_sha256":"ac1701a2de8c8d302d7fc4ef609a185942aacf4b33cc012fc9a0a613884d83d3","schema_version":"1.0","event_id":"sha256:ac1701a2de8c8d302d7fc4ef609a185942aacf4b33cc012fc9a0a613884d83d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:Z3MAZ52VGMFDI7Q4CNM5WAGZHB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Smooth Linearization of Nonautonomous Difference Equations with a Nonuniform Dichotomy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Davor Dragicevic, Weinian Zhang, Wenmeng Zhang","submitted_at":"2017-10-18T10:20:52Z","abstract_excerpt":"In this paper we give a smooth linearization theorem for nonautonomous difference equations with a nonuniform strong exponential dichotomy. The linear part of such a nonautonomous difference equation is defined by a sequence of invertible linear operators on $\\mathbb{R}^d$. Reducing the linear part to a bounded linear operator on a Banach space, we discuss the spectrum and its spectral gaps. Then we obtain a gap condition for $C^1$ linearization of such a nonautonomous difference equation. We finally extend the result to the infinite dimensional case. Our theorems improve known results even in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06662","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":""},"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":"2026-05-17T23:41:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4fhN1KlYabtpX7+/6T852d6XElJspJSjwgCniOvyVjtFezsVfDeTHy80+NUFY5fgd1c3jXh3IPtTzFgcQw59BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:54:53.842817Z"},"content_sha256":"0e485c3254477b3927f3e737bb8ed44c8160ae2bc31f08c61345a3d351dc5a37","schema_version":"1.0","event_id":"sha256:0e485c3254477b3927f3e737bb8ed44c8160ae2bc31f08c61345a3d351dc5a37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z3MAZ52VGMFDI7Q4CNM5WAGZHB/bundle.json","state_url":"https://pith.science/pith/Z3MAZ52VGMFDI7Q4CNM5WAGZHB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z3MAZ52VGMFDI7Q4CNM5WAGZHB/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":"2026-05-30T23:54:53Z","links":{"resolver":"https://pith.science/pith/Z3MAZ52VGMFDI7Q4CNM5WAGZHB","bundle":"https://pith.science/pith/Z3MAZ52VGMFDI7Q4CNM5WAGZHB/bundle.json","state":"https://pith.science/pith/Z3MAZ52VGMFDI7Q4CNM5WAGZHB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z3MAZ52VGMFDI7Q4CNM5WAGZHB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Z3MAZ52VGMFDI7Q4CNM5WAGZHB","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":"15c564cc6acdd9e5d158d27d8183002b353b640c00b1bc13bb7a975d17b2a108","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-18T10:20:52Z","title_canon_sha256":"e559efd4a60dd5cf41f471af5b2414a0f633230064a6dc3e4f970893eddc341f"},"schema_version":"1.0","source":{"id":"1710.06662","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06662","created_at":"2026-05-17T23:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06662v2","created_at":"2026-05-17T23:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06662","created_at":"2026-05-17T23:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"Z3MAZ52VGMFD","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z3MAZ52VGMFDI7Q4","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z3MAZ52V","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:0e485c3254477b3927f3e737bb8ed44c8160ae2bc31f08c61345a3d351dc5a37","target":"graph","created_at":"2026-05-17T23:41:18Z","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 give a smooth linearization theorem for nonautonomous difference equations with a nonuniform strong exponential dichotomy. The linear part of such a nonautonomous difference equation is defined by a sequence of invertible linear operators on $\\mathbb{R}^d$. Reducing the linear part to a bounded linear operator on a Banach space, we discuss the spectrum and its spectral gaps. Then we obtain a gap condition for $C^1$ linearization of such a nonautonomous difference equation. We finally extend the result to the infinite dimensional case. Our theorems improve known results even in","authors_text":"Davor Dragicevic, Weinian Zhang, Wenmeng Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-18T10:20:52Z","title":"Smooth Linearization of Nonautonomous Difference Equations with a Nonuniform Dichotomy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06662","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:ac1701a2de8c8d302d7fc4ef609a185942aacf4b33cc012fc9a0a613884d83d3","target":"record","created_at":"2026-05-17T23:41:18Z","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":"15c564cc6acdd9e5d158d27d8183002b353b640c00b1bc13bb7a975d17b2a108","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-18T10:20:52Z","title_canon_sha256":"e559efd4a60dd5cf41f471af5b2414a0f633230064a6dc3e4f970893eddc341f"},"schema_version":"1.0","source":{"id":"1710.06662","kind":"arxiv","version":2}},"canonical_sha256":"ced80cf755330a347e1c1359db00d93851bddfed20009935362d2db81b4f6626","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ced80cf755330a347e1c1359db00d93851bddfed20009935362d2db81b4f6626","first_computed_at":"2026-05-17T23:41:18.300262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:18.300262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SzNvgZNR90nQoFcKpuq94GdN/Cg5ISEJkJCMXZD8avlBVPY+LW+B/TUYpOad1FPCkWwP0hsIjM0hghlPcKGzDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:18.300943Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.06662","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac1701a2de8c8d302d7fc4ef609a185942aacf4b33cc012fc9a0a613884d83d3","sha256:0e485c3254477b3927f3e737bb8ed44c8160ae2bc31f08c61345a3d351dc5a37"],"state_sha256":"668d8fe81b486f323df4abea07e51e4a7275b6f9abccea8229eec624dc81eadc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uf2BZBlvxIyTOR7LNg6q+B5UBtagfOkLM1dMx0m9i/rQs0M428/HbM1FKe3uD6G6Umr4wYekE6srVeMBGwvpBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:54:53.844865Z","bundle_sha256":"ebc3a935d85a20073bdf73df6202a07025c7d502879e2f6c14c7d813e7a14b9f"}}