{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:LL34C5YI4G5EVRQPGZO6ZI3PKC","short_pith_number":"pith:LL34C5YI","schema_version":"1.0","canonical_sha256":"5af7c17708e1ba4ac60f365deca36f508e9785578072d45dc44eea12725dcb60","source":{"kind":"arxiv","id":"1205.4933","version":1},"attestation_state":"computed","paper":{"title":"Compressed Sensing on the Image of Bilinear Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Peter Jung, Philipp Walk","submitted_at":"2012-05-22T14:52:48Z","abstract_excerpt":"For several communication models, the dispersive part of a communication channel is described by a bilinear operation $T$ between the possible sets of input signals and channel parameters. The received channel output has then to be identified from the image $T(X,Y)$ of the input signal difference sets $X$ and the channel state sets $Y$. The main goal in this contribution is to characterize the compressibility of $T(X,Y)$ with respect to an ambient dimension $N$. In this paper we show that a restricted norm multiplicativity of $T$ on all canonical subspaces $X$ and $Y$ with dimension $S$ resp. "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1205.4933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-05-22T14:52:48Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3a2d0335e7fe41b0547a1a82480f870bbe6155f7ed8855c8e1da57618667d70f","abstract_canon_sha256":"38d90d99df9920cfa2d6ed9d37b292c2045d902dcc283f9b7d2979d48023e6da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:10.068097Z","signature_b64":"EeqOuIvhCKmXQQlYxTteD39i6sHOdYBvkdYpHsIwvRXjoFHhce+XJCuNlVvTH/X89MGgqXuP4v5Bp0fyoC20CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5af7c17708e1ba4ac60f365deca36f508e9785578072d45dc44eea12725dcb60","last_reissued_at":"2026-05-18T02:21:10.067589Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:10.067589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Compressed Sensing on the Image of Bilinear Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Peter Jung, Philipp Walk","submitted_at":"2012-05-22T14:52:48Z","abstract_excerpt":"For several communication models, the dispersive part of a communication channel is described by a bilinear operation $T$ between the possible sets of input signals and channel parameters. The received channel output has then to be identified from the image $T(X,Y)$ of the input signal difference sets $X$ and the channel state sets $Y$. The main goal in this contribution is to characterize the compressibility of $T(X,Y)$ with respect to an ambient dimension $N$. In this paper we show that a restricted norm multiplicativity of $T$ on all canonical subspaces $X$ and $Y$ with dimension $S$ resp. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4933","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1205.4933","created_at":"2026-05-18T02:21:10.067659+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.4933v1","created_at":"2026-05-18T02:21:10.067659+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4933","created_at":"2026-05-18T02:21:10.067659+00:00"},{"alias_kind":"pith_short_12","alias_value":"LL34C5YI4G5E","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"LL34C5YI4G5EVRQP","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"LL34C5YI","created_at":"2026-05-18T12:27:14.488303+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LL34C5YI4G5EVRQPGZO6ZI3PKC","json":"https://pith.science/pith/LL34C5YI4G5EVRQPGZO6ZI3PKC.json","graph_json":"https://pith.science/api/pith-number/LL34C5YI4G5EVRQPGZO6ZI3PKC/graph.json","events_json":"https://pith.science/api/pith-number/LL34C5YI4G5EVRQPGZO6ZI3PKC/events.json","paper":"https://pith.science/paper/LL34C5YI"},"agent_actions":{"view_html":"https://pith.science/pith/LL34C5YI4G5EVRQPGZO6ZI3PKC","download_json":"https://pith.science/pith/LL34C5YI4G5EVRQPGZO6ZI3PKC.json","view_paper":"https://pith.science/paper/LL34C5YI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.4933&json=true","fetch_graph":"https://pith.science/api/pith-number/LL34C5YI4G5EVRQPGZO6ZI3PKC/graph.json","fetch_events":"https://pith.science/api/pith-number/LL34C5YI4G5EVRQPGZO6ZI3PKC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LL34C5YI4G5EVRQPGZO6ZI3PKC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LL34C5YI4G5EVRQPGZO6ZI3PKC/action/storage_attestation","attest_author":"https://pith.science/pith/LL34C5YI4G5EVRQPGZO6ZI3PKC/action/author_attestation","sign_citation":"https://pith.science/pith/LL34C5YI4G5EVRQPGZO6ZI3PKC/action/citation_signature","submit_replication":"https://pith.science/pith/LL34C5YI4G5EVRQPGZO6ZI3PKC/action/replication_record"}},"created_at":"2026-05-18T02:21:10.067659+00:00","updated_at":"2026-05-18T02:21:10.067659+00:00"}