{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VSDC6FC6YGN6P2LARUXEGN5DQC","short_pith_number":"pith:VSDC6FC6","canonical_record":{"source":{"id":"1606.05159","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-16T12:27:23Z","cross_cats_sorted":[],"title_canon_sha256":"db950215d5ad325efb75dfad3a3f1446c55524f79d638758601c5a70af361251","abstract_canon_sha256":"9bdf67905aa022623c71f9439836ca6bc1bdf2a124ef83ccace253f706f5e03c"},"schema_version":"1.0"},"canonical_sha256":"ac862f145ec19be7e9608d2e4337a380b0a033cf8d7801e53beabcb5caa80e1b","source":{"kind":"arxiv","id":"1606.05159","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.05159","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"arxiv_version","alias_value":"1606.05159v2","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05159","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"pith_short_12","alias_value":"VSDC6FC6YGN6","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VSDC6FC6YGN6P2LA","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VSDC6FC6","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VSDC6FC6YGN6P2LARUXEGN5DQC","target":"record","payload":{"canonical_record":{"source":{"id":"1606.05159","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-16T12:27:23Z","cross_cats_sorted":[],"title_canon_sha256":"db950215d5ad325efb75dfad3a3f1446c55524f79d638758601c5a70af361251","abstract_canon_sha256":"9bdf67905aa022623c71f9439836ca6bc1bdf2a124ef83ccace253f706f5e03c"},"schema_version":"1.0"},"canonical_sha256":"ac862f145ec19be7e9608d2e4337a380b0a033cf8d7801e53beabcb5caa80e1b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:36.617936Z","signature_b64":"ZCqT3kw+b7q5opRbcMkwiMdWcPSTbEiJ5jUFMDJOZBlA5NMAlhDLU1E37QWrNpnmw6E8XbHt5XExDSL6+bWlCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac862f145ec19be7e9608d2e4337a380b0a033cf8d7801e53beabcb5caa80e1b","last_reissued_at":"2026-05-17T23:46:36.617389Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:36.617389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.05159","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":"2026-05-17T23:46:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q7KQ/MAkj0AZc94jiQWhGtysC96o7UaNJ7H4YxEv1tfCOd13M1khx0BYt87AhGCE/JUZtplYTdP0Pd08h2RaDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:00:13.668675Z"},"content_sha256":"570245cd6db9d140af0b33db3d2275ebe40011f9f213820d16e1b5dccaae2a83","schema_version":"1.0","event_id":"sha256:570245cd6db9d140af0b33db3d2275ebe40011f9f213820d16e1b5dccaae2a83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VSDC6FC6YGN6P2LARUXEGN5DQC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Admissible Banach function spaces for linear dynamics with nonuniform behavior on the half-line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Liviu Horia Popescu, Nicolae Lupa","submitted_at":"2016-06-16T12:27:23Z","abstract_excerpt":"For nonuniform exponentially bounded evolution families on the half-line we introduce a class of Banach function spaces on which we define nonuniform evolution semigroups. We completely characterize nonuniform exponential stability in terms of invertibility of the corresponding generators. We emphasize that in particular our results apply to all linear differential equations with bounded operator and finite Lyapunov exponent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05159","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":"2026-05-17T23:46:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hIg/IJcnmEvdw3F4tnNzPDLZoFxNWfD+2MjwTmciJSeo18NqiQhz3je6HMs4GwlDkpYqfWb8h8ef8M2UtW2DBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:00:13.669009Z"},"content_sha256":"2c5528776bd2e4f3847a135a97e08ede14ba96a9f9f233170bb5864effd205a0","schema_version":"1.0","event_id":"sha256:2c5528776bd2e4f3847a135a97e08ede14ba96a9f9f233170bb5864effd205a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VSDC6FC6YGN6P2LARUXEGN5DQC/bundle.json","state_url":"https://pith.science/pith/VSDC6FC6YGN6P2LARUXEGN5DQC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VSDC6FC6YGN6P2LARUXEGN5DQC/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":"2026-06-27T03:00:13Z","links":{"resolver":"https://pith.science/pith/VSDC6FC6YGN6P2LARUXEGN5DQC","bundle":"https://pith.science/pith/VSDC6FC6YGN6P2LARUXEGN5DQC/bundle.json","state":"https://pith.science/pith/VSDC6FC6YGN6P2LARUXEGN5DQC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VSDC6FC6YGN6P2LARUXEGN5DQC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VSDC6FC6YGN6P2LARUXEGN5DQC","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":"9bdf67905aa022623c71f9439836ca6bc1bdf2a124ef83ccace253f706f5e03c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-16T12:27:23Z","title_canon_sha256":"db950215d5ad325efb75dfad3a3f1446c55524f79d638758601c5a70af361251"},"schema_version":"1.0","source":{"id":"1606.05159","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.05159","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"arxiv_version","alias_value":"1606.05159v2","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05159","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"pith_short_12","alias_value":"VSDC6FC6YGN6","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VSDC6FC6YGN6P2LA","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VSDC6FC6","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:2c5528776bd2e4f3847a135a97e08ede14ba96a9f9f233170bb5864effd205a0","target":"graph","created_at":"2026-05-17T23:46:36Z","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":"For nonuniform exponentially bounded evolution families on the half-line we introduce a class of Banach function spaces on which we define nonuniform evolution semigroups. We completely characterize nonuniform exponential stability in terms of invertibility of the corresponding generators. We emphasize that in particular our results apply to all linear differential equations with bounded operator and finite Lyapunov exponent.","authors_text":"Liviu Horia Popescu, Nicolae Lupa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-16T12:27:23Z","title":"Admissible Banach function spaces for linear dynamics with nonuniform behavior on the half-line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05159","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":"sha256:570245cd6db9d140af0b33db3d2275ebe40011f9f213820d16e1b5dccaae2a83","target":"record","created_at":"2026-05-17T23:46:36Z","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":"9bdf67905aa022623c71f9439836ca6bc1bdf2a124ef83ccace253f706f5e03c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-16T12:27:23Z","title_canon_sha256":"db950215d5ad325efb75dfad3a3f1446c55524f79d638758601c5a70af361251"},"schema_version":"1.0","source":{"id":"1606.05159","kind":"arxiv","version":2}},"canonical_sha256":"ac862f145ec19be7e9608d2e4337a380b0a033cf8d7801e53beabcb5caa80e1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac862f145ec19be7e9608d2e4337a380b0a033cf8d7801e53beabcb5caa80e1b","first_computed_at":"2026-05-17T23:46:36.617389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:36.617389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZCqT3kw+b7q5opRbcMkwiMdWcPSTbEiJ5jUFMDJOZBlA5NMAlhDLU1E37QWrNpnmw6E8XbHt5XExDSL6+bWlCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:36.617936Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.05159","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:570245cd6db9d140af0b33db3d2275ebe40011f9f213820d16e1b5dccaae2a83","sha256:2c5528776bd2e4f3847a135a97e08ede14ba96a9f9f233170bb5864effd205a0"],"state_sha256":"d9f077197772fc4fdbec9fd278080cbb8055c6706f8479c23028546449cdb48b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aJW5baoYb3wl68tGjON4OmoXpGOEHrwmHtvSccHj9j9OJ0Us4w4mkQ+VCuQSGx3boHhpndU9eEa2cs//TlOQAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T03:00:13.671082Z","bundle_sha256":"6eec68d646c0ce25cf59ef4ddbd220a44c5a864dec9f477cd534b37a452f4ce4"}}