{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SVG7YSDBTY34YWYUVNKMWSBBMK","short_pith_number":"pith:SVG7YSDB","canonical_record":{"source":{"id":"1705.04048","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-11T07:38:46Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a2d742fc2621a4871afb1ca0899ce26f12d163f45a0473910194b16f9a3921d9","abstract_canon_sha256":"49a6fb30f38ee8750dd5bbbbb8c446dadca6e7a1160734955856be06f5815877"},"schema_version":"1.0"},"canonical_sha256":"954dfc48619e37cc5b14ab54cb482162b9cb9d84b0b2145087c50073e62cab78","source":{"kind":"arxiv","id":"1705.04048","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04048","created_at":"2026-05-18T00:28:06Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04048v2","created_at":"2026-05-18T00:28:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04048","created_at":"2026-05-18T00:28:06Z"},{"alias_kind":"pith_short_12","alias_value":"SVG7YSDBTY34","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SVG7YSDBTY34YWYU","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SVG7YSDB","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SVG7YSDBTY34YWYUVNKMWSBBMK","target":"record","payload":{"canonical_record":{"source":{"id":"1705.04048","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-11T07:38:46Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a2d742fc2621a4871afb1ca0899ce26f12d163f45a0473910194b16f9a3921d9","abstract_canon_sha256":"49a6fb30f38ee8750dd5bbbbb8c446dadca6e7a1160734955856be06f5815877"},"schema_version":"1.0"},"canonical_sha256":"954dfc48619e37cc5b14ab54cb482162b9cb9d84b0b2145087c50073e62cab78","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:06.990281Z","signature_b64":"s8EZQY2cYnjIqmOi8/pTkHV6b/rna99CWaMy34zCVIFy/nkd6fUOVePE1T4L58OHlYteXgztYOEQc4mFwp/dCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"954dfc48619e37cc5b14ab54cb482162b9cb9d84b0b2145087c50073e62cab78","last_reissued_at":"2026-05-18T00:28:06.989653Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:06.989653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.04048","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:28:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FTEeehZ9eiCpPvchxIFbKMDZTJcswVkBUVb/IhtH6BA75AtvpOf4tyErCrW1TfK+44pSS4nCiF4r3IJmMBuUAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:07:27.910071Z"},"content_sha256":"79db079ced632fae0fc8f37bdce9b48ab0ea317f4ec461926b0bd929b430b9f8","schema_version":"1.0","event_id":"sha256:79db079ced632fae0fc8f37bdce9b48ab0ea317f4ec461926b0bd929b430b9f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SVG7YSDBTY34YWYUVNKMWSBBMK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Phaseless compressive sensing using partial support information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jun Yu, Zhiyong Zhou","submitted_at":"2017-05-11T07:38:46Z","abstract_excerpt":"We study the recovery conditions of weighted $\\ell_1$ minimization for real-valued signal reconstruction from phaseless compressive sensing measurements when partial support information is available. A strong restricted isometry property condition is provided to ensure the stable recovery. Moreover, we present the weighted null space property as the sufficient and necessary condition for the success of $k$-sparse phaseless recovery via weighted $\\ell_1$ minimization. Numerical experiments are conducted to illustrate our results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04048","kind":"arxiv","version":2},"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":"2026-05-18T00:28:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XLVcvvGo3/1D4eW+0EooXBQGdbK/1iYLBl26mLIKIxjThlyEWRsyripcg5K4PcdoYqf9Fi8zq/XQL2t9RRVzCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:07:27.910765Z"},"content_sha256":"36a88395807297e2752aac02be99e13f529b952f792ce37703d56b60edd3178c","schema_version":"1.0","event_id":"sha256:36a88395807297e2752aac02be99e13f529b952f792ce37703d56b60edd3178c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SVG7YSDBTY34YWYUVNKMWSBBMK/bundle.json","state_url":"https://pith.science/pith/SVG7YSDBTY34YWYUVNKMWSBBMK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SVG7YSDBTY34YWYUVNKMWSBBMK/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":"2026-05-26T18:07:27Z","links":{"resolver":"https://pith.science/pith/SVG7YSDBTY34YWYUVNKMWSBBMK","bundle":"https://pith.science/pith/SVG7YSDBTY34YWYUVNKMWSBBMK/bundle.json","state":"https://pith.science/pith/SVG7YSDBTY34YWYUVNKMWSBBMK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SVG7YSDBTY34YWYUVNKMWSBBMK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SVG7YSDBTY34YWYUVNKMWSBBMK","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":"49a6fb30f38ee8750dd5bbbbb8c446dadca6e7a1160734955856be06f5815877","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-11T07:38:46Z","title_canon_sha256":"a2d742fc2621a4871afb1ca0899ce26f12d163f45a0473910194b16f9a3921d9"},"schema_version":"1.0","source":{"id":"1705.04048","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04048","created_at":"2026-05-18T00:28:06Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04048v2","created_at":"2026-05-18T00:28:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04048","created_at":"2026-05-18T00:28:06Z"},{"alias_kind":"pith_short_12","alias_value":"SVG7YSDBTY34","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SVG7YSDBTY34YWYU","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SVG7YSDB","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:36a88395807297e2752aac02be99e13f529b952f792ce37703d56b60edd3178c","target":"graph","created_at":"2026-05-18T00:28:06Z","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 study the recovery conditions of weighted $\\ell_1$ minimization for real-valued signal reconstruction from phaseless compressive sensing measurements when partial support information is available. A strong restricted isometry property condition is provided to ensure the stable recovery. Moreover, we present the weighted null space property as the sufficient and necessary condition for the success of $k$-sparse phaseless recovery via weighted $\\ell_1$ minimization. Numerical experiments are conducted to illustrate our results.","authors_text":"Jun Yu, Zhiyong Zhou","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-11T07:38:46Z","title":"Phaseless compressive sensing using partial support information"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04048","kind":"arxiv","version":2},"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":"sha256:79db079ced632fae0fc8f37bdce9b48ab0ea317f4ec461926b0bd929b430b9f8","target":"record","created_at":"2026-05-18T00:28:06Z","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":"49a6fb30f38ee8750dd5bbbbb8c446dadca6e7a1160734955856be06f5815877","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-11T07:38:46Z","title_canon_sha256":"a2d742fc2621a4871afb1ca0899ce26f12d163f45a0473910194b16f9a3921d9"},"schema_version":"1.0","source":{"id":"1705.04048","kind":"arxiv","version":2}},"canonical_sha256":"954dfc48619e37cc5b14ab54cb482162b9cb9d84b0b2145087c50073e62cab78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"954dfc48619e37cc5b14ab54cb482162b9cb9d84b0b2145087c50073e62cab78","first_computed_at":"2026-05-18T00:28:06.989653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:06.989653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s8EZQY2cYnjIqmOi8/pTkHV6b/rna99CWaMy34zCVIFy/nkd6fUOVePE1T4L58OHlYteXgztYOEQc4mFwp/dCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:06.990281Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.04048","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79db079ced632fae0fc8f37bdce9b48ab0ea317f4ec461926b0bd929b430b9f8","sha256:36a88395807297e2752aac02be99e13f529b952f792ce37703d56b60edd3178c"],"state_sha256":"820e1de43a24f26e5d5462c628e06d3a4d33116965e49f88b804ac4b00cdb735"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q5fCbc2d4aV/aV5w+dSD9Fg/HYWd5wL/Ev3XMxZGrGf0Y6eJw7XrnyvmBCcMMrrEZ/TtUegOiPavZdjX2Fp7Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T18:07:27.913874Z","bundle_sha256":"c28dd2a7ce848b0a9d7fce1d85b4e8c1ed1ef9129f25cc830513e4b3581c0d69"}}