{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:3L5YPVRYYXELXPCWCFZN52WHF4","short_pith_number":"pith:3L5YPVRY","canonical_record":{"source":{"id":"1109.4856","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-22T15:48:49Z","cross_cats_sorted":["math.IT","nlin.SI"],"title_canon_sha256":"439ee16030aa771284746b30f15f04dcd28b9243297c9e59d4915db9685c20e9","abstract_canon_sha256":"fc49a0cf05883332647672d91a51a83151c3bb813e810b48068b34528ad6d097"},"schema_version":"1.0"},"canonical_sha256":"dafb87d638c5c8bbbc561172deeac72f07c7c45c6567da55cf86618d604f280f","source":{"kind":"arxiv","id":"1109.4856","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4856","created_at":"2026-05-18T03:59:01Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4856v2","created_at":"2026-05-18T03:59:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4856","created_at":"2026-05-18T03:59:01Z"},{"alias_kind":"pith_short_12","alias_value":"3L5YPVRYYXEL","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3L5YPVRYYXELXPCW","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3L5YPVRY","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:3L5YPVRYYXELXPCWCFZN52WHF4","target":"record","payload":{"canonical_record":{"source":{"id":"1109.4856","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-22T15:48:49Z","cross_cats_sorted":["math.IT","nlin.SI"],"title_canon_sha256":"439ee16030aa771284746b30f15f04dcd28b9243297c9e59d4915db9685c20e9","abstract_canon_sha256":"fc49a0cf05883332647672d91a51a83151c3bb813e810b48068b34528ad6d097"},"schema_version":"1.0"},"canonical_sha256":"dafb87d638c5c8bbbc561172deeac72f07c7c45c6567da55cf86618d604f280f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:01.413953Z","signature_b64":"i0t90pJAq1R7yxM1yy115eCtF0lzleAZ7n/hKw67H74iKD0Ic9J+9aEmuBLtjoWVLv5Gn3eYG7EZG5by7AiiAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dafb87d638c5c8bbbc561172deeac72f07c7c45c6567da55cf86618d604f280f","last_reissued_at":"2026-05-18T03:59:01.413393Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:01.413393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.4856","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":"2026-05-18T03:59:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9/wRjXaCoQYVvOMfjqrIc7nCyRSpg7yqVXB2DnY0Hf1Hchi+3C5Mz8zd++qidJemyWcWpW9xCC4b+HdMKTxjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T22:25:57.404247Z"},"content_sha256":"42ecfdac5601fc087af7215e907fd7e054b51e3d47a4652ec6c8e0dbb9e2f781","schema_version":"1.0","event_id":"sha256:42ecfdac5601fc087af7215e907fd7e054b51e3d47a4652ec6c8e0dbb9e2f781"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:3L5YPVRYYXELXPCWCFZN52WHF4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Information Loss in Memoryless Systems: The Multivariate Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","nlin.SI"],"primary_cat":"cs.IT","authors_text":"Bernhard C. Geiger, Gernot Kubin","submitted_at":"2011-09-22T15:48:49Z","abstract_excerpt":"In this work we give a concise definition of information loss from a system-theoretic point of view. Based on this definition, we analyze the information loss in static input-output systems subject to a continuous-valued input. For a certain class of multiple-input, multiple-output systems the information loss is quantified. An interpretation of this loss is accompanied by upper bounds which are simple to evaluate.\n  Finally, a class of systems is identified for which the information loss is necessarily infinite. Quantizers and limiters are shown to belong to this class."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4856","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":"2026-05-18T03:59:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ITxUk0c6hmYvgyzv/s7diWuKVVPs2Rik0csgPiETEa9Xp6N0lTu/I1Re30kpf5AT+aLFmB/DDP9RtO4M+kS4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T22:25:57.404934Z"},"content_sha256":"1d5b2305ed9d501d0568c6f054f71ba15e558d806098d6bef18c4ece55ceeab8","schema_version":"1.0","event_id":"sha256:1d5b2305ed9d501d0568c6f054f71ba15e558d806098d6bef18c4ece55ceeab8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3L5YPVRYYXELXPCWCFZN52WHF4/bundle.json","state_url":"https://pith.science/pith/3L5YPVRYYXELXPCWCFZN52WHF4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3L5YPVRYYXELXPCWCFZN52WHF4/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":"2026-05-20T22:25:57Z","links":{"resolver":"https://pith.science/pith/3L5YPVRYYXELXPCWCFZN52WHF4","bundle":"https://pith.science/pith/3L5YPVRYYXELXPCWCFZN52WHF4/bundle.json","state":"https://pith.science/pith/3L5YPVRYYXELXPCWCFZN52WHF4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3L5YPVRYYXELXPCWCFZN52WHF4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3L5YPVRYYXELXPCWCFZN52WHF4","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":"fc49a0cf05883332647672d91a51a83151c3bb813e810b48068b34528ad6d097","cross_cats_sorted":["math.IT","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-22T15:48:49Z","title_canon_sha256":"439ee16030aa771284746b30f15f04dcd28b9243297c9e59d4915db9685c20e9"},"schema_version":"1.0","source":{"id":"1109.4856","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4856","created_at":"2026-05-18T03:59:01Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4856v2","created_at":"2026-05-18T03:59:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4856","created_at":"2026-05-18T03:59:01Z"},{"alias_kind":"pith_short_12","alias_value":"3L5YPVRYYXEL","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3L5YPVRYYXELXPCW","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3L5YPVRY","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:1d5b2305ed9d501d0568c6f054f71ba15e558d806098d6bef18c4ece55ceeab8","target":"graph","created_at":"2026-05-18T03:59:01Z","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 work we give a concise definition of information loss from a system-theoretic point of view. Based on this definition, we analyze the information loss in static input-output systems subject to a continuous-valued input. For a certain class of multiple-input, multiple-output systems the information loss is quantified. An interpretation of this loss is accompanied by upper bounds which are simple to evaluate.\n  Finally, a class of systems is identified for which the information loss is necessarily infinite. Quantizers and limiters are shown to belong to this class.","authors_text":"Bernhard C. Geiger, Gernot Kubin","cross_cats":["math.IT","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-22T15:48:49Z","title":"On the Information Loss in Memoryless Systems: The Multivariate Case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4856","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":"sha256:42ecfdac5601fc087af7215e907fd7e054b51e3d47a4652ec6c8e0dbb9e2f781","target":"record","created_at":"2026-05-18T03:59:01Z","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":"fc49a0cf05883332647672d91a51a83151c3bb813e810b48068b34528ad6d097","cross_cats_sorted":["math.IT","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-22T15:48:49Z","title_canon_sha256":"439ee16030aa771284746b30f15f04dcd28b9243297c9e59d4915db9685c20e9"},"schema_version":"1.0","source":{"id":"1109.4856","kind":"arxiv","version":2}},"canonical_sha256":"dafb87d638c5c8bbbc561172deeac72f07c7c45c6567da55cf86618d604f280f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dafb87d638c5c8bbbc561172deeac72f07c7c45c6567da55cf86618d604f280f","first_computed_at":"2026-05-18T03:59:01.413393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:01.413393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i0t90pJAq1R7yxM1yy115eCtF0lzleAZ7n/hKw67H74iKD0Ic9J+9aEmuBLtjoWVLv5Gn3eYG7EZG5by7AiiAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:01.413953Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4856","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42ecfdac5601fc087af7215e907fd7e054b51e3d47a4652ec6c8e0dbb9e2f781","sha256:1d5b2305ed9d501d0568c6f054f71ba15e558d806098d6bef18c4ece55ceeab8"],"state_sha256":"d63f87b1d18f3f6d92bb26a0f10940d431d9c80bc9d2e95a331295af9707691c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xnQuWEHsfhjLrHGs2fyMYj7z76A7loHMXX0FYOrc8s5Mn3XildiKF5I80YrebQX9mc6alAa3p907flAdVo3OAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T22:25:57.408826Z","bundle_sha256":"f581fca24cae338d2d0007a98cc19bdc07afb5c5854f1d33b7da3061f2440a55"}}