{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AUSSW2J6VOCEBAB74RWWKJ3OAJ","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":"ce0b387c5d952cf0e3a0df32f66bdf99ef06636e38964d632f23bd0d5f262c39","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-03-30T12:49:58Z","title_canon_sha256":"ef447daadfbfd7f41bda98045e9283eb3fc5ee6113f24b30f7560bed0ded22bd"},"schema_version":"1.0","source":{"id":"1203.6791","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6791","created_at":"2026-05-18T03:58:52Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6791v1","created_at":"2026-05-18T03:58:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6791","created_at":"2026-05-18T03:58:52Z"},{"alias_kind":"pith_short_12","alias_value":"AUSSW2J6VOCE","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AUSSW2J6VOCEBAB7","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AUSSW2J6","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:804773b57c6653740554ee2317d4b2e373dd980f49831ff3e9db6b045ae7d902","target":"graph","created_at":"2026-05-18T03:58:52Z","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 introduce a relative variant of information loss to characterize the behavior of deterministic input-output systems. We show that the relative loss is closely related to Renyi's information dimension. We provide an upper bound for continuous input random variables and an exact result for a class of functions (comprising quantizers) with infinite absolute information loss. A connection between relative information loss and reconstruction error is investigated.","authors_text":"Bernhard C. Geiger, Gernot Kubin","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-03-30T12:49:58Z","title":"Relative Information Loss - An Introduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6791","kind":"arxiv","version":1},"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":"sha256:5e161e66444ab75769ba0529f70a29a8d312609e02a5264154d39f2a3ec1a4e5","target":"record","created_at":"2026-05-18T03:58:52Z","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":"ce0b387c5d952cf0e3a0df32f66bdf99ef06636e38964d632f23bd0d5f262c39","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-03-30T12:49:58Z","title_canon_sha256":"ef447daadfbfd7f41bda98045e9283eb3fc5ee6113f24b30f7560bed0ded22bd"},"schema_version":"1.0","source":{"id":"1203.6791","kind":"arxiv","version":1}},"canonical_sha256":"05252b693eab8440803fe46d65276e026e85d384be4ae74736bfe11f6fdab950","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05252b693eab8440803fe46d65276e026e85d384be4ae74736bfe11f6fdab950","first_computed_at":"2026-05-18T03:58:52.258055Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:52.258055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a8YB15ueCVg8XQDD/qXmBh3EryLBf32dW86iS47p8s7be93U2FxWoLUp6AONTQWw/9afyU/+RP6JN+aLQOnjDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:52.258726Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.6791","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e161e66444ab75769ba0529f70a29a8d312609e02a5264154d39f2a3ec1a4e5","sha256:804773b57c6653740554ee2317d4b2e373dd980f49831ff3e9db6b045ae7d902"],"state_sha256":"08cfb706f0cdea2edcdddb2fe7b02864642e8c80520d3c484d33302537c0bbe0"}