{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:D2G73OY5HRT555HK2IZ5BZ7HS7","short_pith_number":"pith:D2G73OY5","canonical_record":{"source":{"id":"1212.3359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-13T22:30:40Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1f671519059cccab9e933dbcc23d4f48a897cbc989b2370933d2b4c348edb076","abstract_canon_sha256":"f5298f270fefaf2ebcdaa02d34e537bc378b822cf3033d6e55b4d445af99e891"},"schema_version":"1.0"},"canonical_sha256":"1e8dfdbb1d3c67def4ead233d0e7e797e45b025da77c964edd4725dc5ac76358","source":{"kind":"arxiv","id":"1212.3359","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3359","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3359v1","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3359","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"D2G73OY5HRT5","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"D2G73OY5HRT555HK","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"D2G73OY5","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:D2G73OY5HRT555HK2IZ5BZ7HS7","target":"record","payload":{"canonical_record":{"source":{"id":"1212.3359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-13T22:30:40Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1f671519059cccab9e933dbcc23d4f48a897cbc989b2370933d2b4c348edb076","abstract_canon_sha256":"f5298f270fefaf2ebcdaa02d34e537bc378b822cf3033d6e55b4d445af99e891"},"schema_version":"1.0"},"canonical_sha256":"1e8dfdbb1d3c67def4ead233d0e7e797e45b025da77c964edd4725dc5ac76358","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:24.884190Z","signature_b64":"28JLG5Ev1LJ0Tq9AlMCqG3DMwVwxE4AfH30QA+etT3LwsS4LGnOU42gIVQPy8w74SyVgRMVozsqtXffRvEGlBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e8dfdbb1d3c67def4ead233d0e7e797e45b025da77c964edd4725dc5ac76358","last_reissued_at":"2026-05-18T03:38:24.883506Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:24.883506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.3359","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:38:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FzmI7DfjS3AfA0p6FT7zOVveNXAXpv9TVtOzWy5P05BZQN4AUI3PING3WX6nVtiQqeDxUqt8DGaFwiXdeTAzDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:19:42.407297Z"},"content_sha256":"a99548bcaa83a40c9965ad96fae2064e00697231465db7eb88bfae77b0fb9302","schema_version":"1.0","event_id":"sha256:a99548bcaa83a40c9965ad96fae2064e00697231465db7eb88bfae77b0fb9302"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:D2G73OY5HRT555HK2IZ5BZ7HS7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matrix Design for Optimal Sensing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hema Kumari Achanta, Soura Dasgupta, Weiyu Xu","submitted_at":"2012-12-13T22:30:40Z","abstract_excerpt":"We design optimal $2 \\times N$ ($2 <N$) matrices, with unit columns, so that the maximum condition number of all the submatrices comprising 3 columns is minimized. The problem has two applications. When estimating a 2-dimensional signal by using only three of $N$ observations at a given time, this minimizes the worst-case achievable estimation error. It also captures the problem of optimum sensor placement for monitoring a source located in a plane, when only a minimum number of required sensors are active at any given time. For arbitrary $N\\geq3$, we derive the optimal matrices which minimize"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3359","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:38:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x+FkLOyOhfgPAjUaKbXP+jFTbLN+VhLzjHLetYgwjdYgepxtwDrnfzKc6SFlEQ38NFQdhLWR1reUoJZgU9m5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:19:42.407996Z"},"content_sha256":"b8d4238225bad53299301ec3e4e99658b12f7a9fd29dfd9eabdfc38bfab9d41d","schema_version":"1.0","event_id":"sha256:b8d4238225bad53299301ec3e4e99658b12f7a9fd29dfd9eabdfc38bfab9d41d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D2G73OY5HRT555HK2IZ5BZ7HS7/bundle.json","state_url":"https://pith.science/pith/D2G73OY5HRT555HK2IZ5BZ7HS7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D2G73OY5HRT555HK2IZ5BZ7HS7/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":"2026-05-27T11:19:42Z","links":{"resolver":"https://pith.science/pith/D2G73OY5HRT555HK2IZ5BZ7HS7","bundle":"https://pith.science/pith/D2G73OY5HRT555HK2IZ5BZ7HS7/bundle.json","state":"https://pith.science/pith/D2G73OY5HRT555HK2IZ5BZ7HS7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D2G73OY5HRT555HK2IZ5BZ7HS7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:D2G73OY5HRT555HK2IZ5BZ7HS7","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":"f5298f270fefaf2ebcdaa02d34e537bc378b822cf3033d6e55b4d445af99e891","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-13T22:30:40Z","title_canon_sha256":"1f671519059cccab9e933dbcc23d4f48a897cbc989b2370933d2b4c348edb076"},"schema_version":"1.0","source":{"id":"1212.3359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3359","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3359v1","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3359","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"D2G73OY5HRT5","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"D2G73OY5HRT555HK","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"D2G73OY5","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:b8d4238225bad53299301ec3e4e99658b12f7a9fd29dfd9eabdfc38bfab9d41d","target":"graph","created_at":"2026-05-18T03:38:24Z","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 design optimal $2 \\times N$ ($2 <N$) matrices, with unit columns, so that the maximum condition number of all the submatrices comprising 3 columns is minimized. The problem has two applications. When estimating a 2-dimensional signal by using only three of $N$ observations at a given time, this minimizes the worst-case achievable estimation error. It also captures the problem of optimum sensor placement for monitoring a source located in a plane, when only a minimum number of required sensors are active at any given time. For arbitrary $N\\geq3$, we derive the optimal matrices which minimize","authors_text":"Hema Kumari Achanta, Soura Dasgupta, Weiyu Xu","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-13T22:30:40Z","title":"Matrix Design for Optimal Sensing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3359","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:a99548bcaa83a40c9965ad96fae2064e00697231465db7eb88bfae77b0fb9302","target":"record","created_at":"2026-05-18T03:38:24Z","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":"f5298f270fefaf2ebcdaa02d34e537bc378b822cf3033d6e55b4d445af99e891","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-13T22:30:40Z","title_canon_sha256":"1f671519059cccab9e933dbcc23d4f48a897cbc989b2370933d2b4c348edb076"},"schema_version":"1.0","source":{"id":"1212.3359","kind":"arxiv","version":1}},"canonical_sha256":"1e8dfdbb1d3c67def4ead233d0e7e797e45b025da77c964edd4725dc5ac76358","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e8dfdbb1d3c67def4ead233d0e7e797e45b025da77c964edd4725dc5ac76358","first_computed_at":"2026-05-18T03:38:24.883506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:24.883506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"28JLG5Ev1LJ0Tq9AlMCqG3DMwVwxE4AfH30QA+etT3LwsS4LGnOU42gIVQPy8w74SyVgRMVozsqtXffRvEGlBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:24.884190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a99548bcaa83a40c9965ad96fae2064e00697231465db7eb88bfae77b0fb9302","sha256:b8d4238225bad53299301ec3e4e99658b12f7a9fd29dfd9eabdfc38bfab9d41d"],"state_sha256":"742b3e2e2d2d93f35b4e4102c104edc06c4e3209c3a44d2e3bf1f3c37607819c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tjqhmXgAWqdw8p+EpBzBMl0vDJ2TGG9C+RzKnVXxXM4QREsOjhvIoJMpwueC9wdJI1soABclY2ba3CwI8WpBDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:19:42.411751Z","bundle_sha256":"a708e6f8d3a707aacaac85a41c3518ea4b3ca6dab163c5b6c2f4831a11d82603"}}