{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3FIUEKPJYYQOHHTZIFTTEV7GTD","short_pith_number":"pith:3FIUEKPJ","canonical_record":{"source":{"id":"1505.00947","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-05T10:39:06Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"0032cb8e0ded49abf93394915f72a10bdf27d62022520a9a61c32439ea19528f","abstract_canon_sha256":"a935227f4e2d4ed5d18bc37fb21a98e1c904870f1ddfb2dd3c5d6988e96de324"},"schema_version":"1.0"},"canonical_sha256":"d9514229e9c620e39e7941673257e698d0a46e80d2e96c082b09f745686c9508","source":{"kind":"arxiv","id":"1505.00947","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00947","created_at":"2026-05-18T00:10:14Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00947v1","created_at":"2026-05-18T00:10:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00947","created_at":"2026-05-18T00:10:14Z"},{"alias_kind":"pith_short_12","alias_value":"3FIUEKPJYYQO","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3FIUEKPJYYQOHHTZ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3FIUEKPJ","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3FIUEKPJYYQOHHTZIFTTEV7GTD","target":"record","payload":{"canonical_record":{"source":{"id":"1505.00947","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-05T10:39:06Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"0032cb8e0ded49abf93394915f72a10bdf27d62022520a9a61c32439ea19528f","abstract_canon_sha256":"a935227f4e2d4ed5d18bc37fb21a98e1c904870f1ddfb2dd3c5d6988e96de324"},"schema_version":"1.0"},"canonical_sha256":"d9514229e9c620e39e7941673257e698d0a46e80d2e96c082b09f745686c9508","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:14.281573Z","signature_b64":"3LZQgPoK6wvDqD+vRXVArtrJAaVpZsW3h4LiBTVtI7sHQpx1gpua4OhiGIXkKA0D11bD5251MrQNQEG1oBBoDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9514229e9c620e39e7941673257e698d0a46e80d2e96c082b09f745686c9508","last_reissued_at":"2026-05-18T00:10:14.280733Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:14.280733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.00947","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":"2026-05-18T00:10:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2uFPP6z4VfNGUQtOpFYDVtOz73r/zPp6TC2uWmQEgDj5ZOPEMD+FrllCKBcpU3BfPZOIg0D5cml3M7C7XtsTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T12:59:25.392216Z"},"content_sha256":"99acc22cccaf61448d0edcbed3793a0f08bc43c94bb96fb79a3f895f4392075b","schema_version":"1.0","event_id":"sha256:99acc22cccaf61448d0edcbed3793a0f08bc43c94bb96fb79a3f895f4392075b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3FIUEKPJYYQOHHTZIFTTEV7GTD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Colocated MIMO Radar Waveform Design for Transmit Beampattern Formation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Haisheng Xu, Jian Wang, Jian Yuan, Rick S. Blum","submitted_at":"2015-05-05T10:39:06Z","abstract_excerpt":"In this paper, colocated MIMO radar waveform design is considered by minimizing the integrated side-lobe level to obtain beam patterns with lower side-lobe levels than competing methods. First, a quadratic programming problem is formulated to design beam patterns by using the criteria for a minimal integrated side-lobe level. A theorem is derived that provides a closed-form analytical optimal solution that appears to be an extension of the Rayleigh quotient minimization for a possibly singular matrix in quadratic form. Such singularities are shown to occur in the problem of interest, but proof"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00947","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":"2026-05-18T00:10:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CAPhRfkYvobQPTBTq+h6WPhpUkx3iZBCnZsifO2S0CCiXEd7UGHZvNpv029yeq3/PSjYnpdBjETvNQthRjwrBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T12:59:25.392573Z"},"content_sha256":"dc53545d41270f7fa2027f268eae1b93600ff34a7f8297796817d0c56e8ab5ed","schema_version":"1.0","event_id":"sha256:dc53545d41270f7fa2027f268eae1b93600ff34a7f8297796817d0c56e8ab5ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3FIUEKPJYYQOHHTZIFTTEV7GTD/bundle.json","state_url":"https://pith.science/pith/3FIUEKPJYYQOHHTZIFTTEV7GTD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3FIUEKPJYYQOHHTZIFTTEV7GTD/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":"2026-06-04T12:59:25Z","links":{"resolver":"https://pith.science/pith/3FIUEKPJYYQOHHTZIFTTEV7GTD","bundle":"https://pith.science/pith/3FIUEKPJYYQOHHTZIFTTEV7GTD/bundle.json","state":"https://pith.science/pith/3FIUEKPJYYQOHHTZIFTTEV7GTD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3FIUEKPJYYQOHHTZIFTTEV7GTD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3FIUEKPJYYQOHHTZIFTTEV7GTD","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":"a935227f4e2d4ed5d18bc37fb21a98e1c904870f1ddfb2dd3c5d6988e96de324","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-05T10:39:06Z","title_canon_sha256":"0032cb8e0ded49abf93394915f72a10bdf27d62022520a9a61c32439ea19528f"},"schema_version":"1.0","source":{"id":"1505.00947","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00947","created_at":"2026-05-18T00:10:14Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00947v1","created_at":"2026-05-18T00:10:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00947","created_at":"2026-05-18T00:10:14Z"},{"alias_kind":"pith_short_12","alias_value":"3FIUEKPJYYQO","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3FIUEKPJYYQOHHTZ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3FIUEKPJ","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:dc53545d41270f7fa2027f268eae1b93600ff34a7f8297796817d0c56e8ab5ed","target":"graph","created_at":"2026-05-18T00:10:14Z","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 paper, colocated MIMO radar waveform design is considered by minimizing the integrated side-lobe level to obtain beam patterns with lower side-lobe levels than competing methods. First, a quadratic programming problem is formulated to design beam patterns by using the criteria for a minimal integrated side-lobe level. A theorem is derived that provides a closed-form analytical optimal solution that appears to be an extension of the Rayleigh quotient minimization for a possibly singular matrix in quadratic form. Such singularities are shown to occur in the problem of interest, but proof","authors_text":"Haisheng Xu, Jian Wang, Jian Yuan, Rick S. Blum","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-05T10:39:06Z","title":"Colocated MIMO Radar Waveform Design for Transmit Beampattern Formation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00947","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":"sha256:99acc22cccaf61448d0edcbed3793a0f08bc43c94bb96fb79a3f895f4392075b","target":"record","created_at":"2026-05-18T00:10:14Z","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":"a935227f4e2d4ed5d18bc37fb21a98e1c904870f1ddfb2dd3c5d6988e96de324","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-05-05T10:39:06Z","title_canon_sha256":"0032cb8e0ded49abf93394915f72a10bdf27d62022520a9a61c32439ea19528f"},"schema_version":"1.0","source":{"id":"1505.00947","kind":"arxiv","version":1}},"canonical_sha256":"d9514229e9c620e39e7941673257e698d0a46e80d2e96c082b09f745686c9508","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9514229e9c620e39e7941673257e698d0a46e80d2e96c082b09f745686c9508","first_computed_at":"2026-05-18T00:10:14.280733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:14.280733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3LZQgPoK6wvDqD+vRXVArtrJAaVpZsW3h4LiBTVtI7sHQpx1gpua4OhiGIXkKA0D11bD5251MrQNQEG1oBBoDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:14.281573Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.00947","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99acc22cccaf61448d0edcbed3793a0f08bc43c94bb96fb79a3f895f4392075b","sha256:dc53545d41270f7fa2027f268eae1b93600ff34a7f8297796817d0c56e8ab5ed"],"state_sha256":"56ed29aa3b1f148e49c34981cebce704cff2d9f5bf8cb4cbc33f0a688c66f593"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ep+ZE6353xoer1Hc9GcZNi/BZNlqSSQc1hXtssxGupZZc9TRaHhcAcYssFPd+KJK6HrhvsXSkz/syWCFN699Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T12:59:25.394505Z","bundle_sha256":"cf63494ef4af2b26458066cf10437bfbd79682b16371bb93fb92a201208d6d52"}}