{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TUF3VQICABY3ZTEXZJCWXULYER","short_pith_number":"pith:TUF3VQIC","canonical_record":{"source":{"id":"1501.02353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-10T13:33:09Z","cross_cats_sorted":[],"title_canon_sha256":"e742fcbdd6dcabe79b27029da075fb154fc55ef609c1e24304611c4cfd18d834","abstract_canon_sha256":"cdc2e7eac15e187d79b4651b7eb59207e32a20d3c31539cb67bd1ff5ca2362f1"},"schema_version":"1.0"},"canonical_sha256":"9d0bbac1020071bccc97ca456bd178247578e672153ca59328a9fc7d1ddda0ba","source":{"kind":"arxiv","id":"1501.02353","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02353","created_at":"2026-05-18T01:01:01Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02353v1","created_at":"2026-05-18T01:01:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02353","created_at":"2026-05-18T01:01:01Z"},{"alias_kind":"pith_short_12","alias_value":"TUF3VQICABY3","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TUF3VQICABY3ZTEX","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TUF3VQIC","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TUF3VQICABY3ZTEXZJCWXULYER","target":"record","payload":{"canonical_record":{"source":{"id":"1501.02353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-10T13:33:09Z","cross_cats_sorted":[],"title_canon_sha256":"e742fcbdd6dcabe79b27029da075fb154fc55ef609c1e24304611c4cfd18d834","abstract_canon_sha256":"cdc2e7eac15e187d79b4651b7eb59207e32a20d3c31539cb67bd1ff5ca2362f1"},"schema_version":"1.0"},"canonical_sha256":"9d0bbac1020071bccc97ca456bd178247578e672153ca59328a9fc7d1ddda0ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:01.960869Z","signature_b64":"aIyN98DVFpen2WNhV3E4SuYU4oOiDymmEhUvuG0gA4mfgHmJ5ZsWxOA+sVAkqHdrBp0Z98hm9VvC4OFttG0PDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d0bbac1020071bccc97ca456bd178247578e672153ca59328a9fc7d1ddda0ba","last_reissued_at":"2026-05-18T01:01:01.960164Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:01.960164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.02353","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":"2026-05-18T01:01:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FUJEmZDYdwVFktf1df0sd6J5E8GwqcLrcwFcbfrQN1812T/sIlRGuIOF6epK6vJ4q1uj7iNcWgEn39JBA5eQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:10:10.047313Z"},"content_sha256":"64e2985e11c9f4eaccb1c5e99772e7b2dbbe70d1eba25dac9536cd99103901d5","schema_version":"1.0","event_id":"sha256:64e2985e11c9f4eaccb1c5e99772e7b2dbbe70d1eba25dac9536cd99103901d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TUF3VQICABY3ZTEXZJCWXULYER","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Structured inverse least-squares problem for structured matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Bibhas Adhikari, Rafikul Alam","submitted_at":"2015-01-10T13:33:09Z","abstract_excerpt":"Given a pair of matrices X and B and an appropriate class of structured matrices S, we provide a complete solution of the structured inverse least-squares problem $min_{A\\in_S} \\|AX-B\\|_F$. Indeed, we determine all solutions of the structured inverse least squares problem as well as those solutions which have the smallest norm. We show that there are infinitely many smallest norm solutions of the least squares problem for the spectral norm whereas the smallest norm solution is unique for the Frobenius norm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02353","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":"2026-05-18T01:01:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3zgGyyI1ct4QLUTgB38Ya61wDr0RDD4d+9Qt8LfihxmSLLCIb5ixGmyQOhMJNUxEXUFG9c8Y+3CTBJrABwxHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:10:10.047683Z"},"content_sha256":"47b4d3737ef57287e8da9c080303048fb4c2491afccb8be15b537f94125400e9","schema_version":"1.0","event_id":"sha256:47b4d3737ef57287e8da9c080303048fb4c2491afccb8be15b537f94125400e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TUF3VQICABY3ZTEXZJCWXULYER/bundle.json","state_url":"https://pith.science/pith/TUF3VQICABY3ZTEXZJCWXULYER/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TUF3VQICABY3ZTEXZJCWXULYER/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":"2026-06-25T12:10:10Z","links":{"resolver":"https://pith.science/pith/TUF3VQICABY3ZTEXZJCWXULYER","bundle":"https://pith.science/pith/TUF3VQICABY3ZTEXZJCWXULYER/bundle.json","state":"https://pith.science/pith/TUF3VQICABY3ZTEXZJCWXULYER/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TUF3VQICABY3ZTEXZJCWXULYER/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TUF3VQICABY3ZTEXZJCWXULYER","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":"cdc2e7eac15e187d79b4651b7eb59207e32a20d3c31539cb67bd1ff5ca2362f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-10T13:33:09Z","title_canon_sha256":"e742fcbdd6dcabe79b27029da075fb154fc55ef609c1e24304611c4cfd18d834"},"schema_version":"1.0","source":{"id":"1501.02353","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02353","created_at":"2026-05-18T01:01:01Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02353v1","created_at":"2026-05-18T01:01:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02353","created_at":"2026-05-18T01:01:01Z"},{"alias_kind":"pith_short_12","alias_value":"TUF3VQICABY3","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TUF3VQICABY3ZTEX","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TUF3VQIC","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:47b4d3737ef57287e8da9c080303048fb4c2491afccb8be15b537f94125400e9","target":"graph","created_at":"2026-05-18T01:01:01Z","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":"Given a pair of matrices X and B and an appropriate class of structured matrices S, we provide a complete solution of the structured inverse least-squares problem $min_{A\\in_S} \\|AX-B\\|_F$. Indeed, we determine all solutions of the structured inverse least squares problem as well as those solutions which have the smallest norm. We show that there are infinitely many smallest norm solutions of the least squares problem for the spectral norm whereas the smallest norm solution is unique for the Frobenius norm.","authors_text":"Bibhas Adhikari, Rafikul Alam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-10T13:33:09Z","title":"Structured inverse least-squares problem for structured matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02353","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":"sha256:64e2985e11c9f4eaccb1c5e99772e7b2dbbe70d1eba25dac9536cd99103901d5","target":"record","created_at":"2026-05-18T01:01:01Z","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":"cdc2e7eac15e187d79b4651b7eb59207e32a20d3c31539cb67bd1ff5ca2362f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-10T13:33:09Z","title_canon_sha256":"e742fcbdd6dcabe79b27029da075fb154fc55ef609c1e24304611c4cfd18d834"},"schema_version":"1.0","source":{"id":"1501.02353","kind":"arxiv","version":1}},"canonical_sha256":"9d0bbac1020071bccc97ca456bd178247578e672153ca59328a9fc7d1ddda0ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d0bbac1020071bccc97ca456bd178247578e672153ca59328a9fc7d1ddda0ba","first_computed_at":"2026-05-18T01:01:01.960164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:01.960164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aIyN98DVFpen2WNhV3E4SuYU4oOiDymmEhUvuG0gA4mfgHmJ5ZsWxOA+sVAkqHdrBp0Z98hm9VvC4OFttG0PDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:01.960869Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.02353","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64e2985e11c9f4eaccb1c5e99772e7b2dbbe70d1eba25dac9536cd99103901d5","sha256:47b4d3737ef57287e8da9c080303048fb4c2491afccb8be15b537f94125400e9"],"state_sha256":"71d7332079ef59ea62c88dedb3f765f0ceb5fef3ae1a6f6b90ea08dc7d76c9b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KCmie3+h8FbPLQDhnSUeWbp3IDvl0hGc7QIdniDPNYqBqn0nWIKlEGZmXoHrYkVbbVqu3x1p0qnquY1HqlVpBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T12:10:10.049548Z","bundle_sha256":"c3bee740549da4636f4d3d04c6002598131562b13aa5e92ed9d7fff8397d94ec"}}