{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:STRWFVBVA2HT5PPHG3HRN7LT5D","short_pith_number":"pith:STRWFVBV","canonical_record":{"source":{"id":"2507.07557","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-07-10T08:56:11Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1fe77f564e01bee13b47cfb352fbebe3a5e8ef9332a8a171fb6eccca52f7cc73","abstract_canon_sha256":"592b8bfcdf10f1bf3078069d6e7165c5ddbcff69e98e3b45f4efbaf9e598d068"},"schema_version":"1.0"},"canonical_sha256":"94e362d435068f3ebde736cf16fd73e8c918c309a3c7e91214f5ffadfd3c8b26","source":{"kind":"arxiv","id":"2507.07557","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.07557","created_at":"2026-07-05T11:35:00Z"},{"alias_kind":"arxiv_version","alias_value":"2507.07557v1","created_at":"2026-07-05T11:35:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.07557","created_at":"2026-07-05T11:35:00Z"},{"alias_kind":"pith_short_12","alias_value":"STRWFVBVA2HT","created_at":"2026-07-05T11:35:00Z"},{"alias_kind":"pith_short_16","alias_value":"STRWFVBVA2HT5PPH","created_at":"2026-07-05T11:35:00Z"},{"alias_kind":"pith_short_8","alias_value":"STRWFVBV","created_at":"2026-07-05T11:35:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:STRWFVBVA2HT5PPHG3HRN7LT5D","target":"record","payload":{"canonical_record":{"source":{"id":"2507.07557","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-07-10T08:56:11Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1fe77f564e01bee13b47cfb352fbebe3a5e8ef9332a8a171fb6eccca52f7cc73","abstract_canon_sha256":"592b8bfcdf10f1bf3078069d6e7165c5ddbcff69e98e3b45f4efbaf9e598d068"},"schema_version":"1.0"},"canonical_sha256":"94e362d435068f3ebde736cf16fd73e8c918c309a3c7e91214f5ffadfd3c8b26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:35:00.643360Z","signature_b64":"xrxu/RDgT7UUWeC5/s8MIgiTYio50lVosHUovC9VSKEhDqv8O788tzlm+i6y7c54sB30CfRmwCUSfRP1Oqt8Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94e362d435068f3ebde736cf16fd73e8c918c309a3c7e91214f5ffadfd3c8b26","last_reissued_at":"2026-07-05T11:35:00.642871Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:35:00.642871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.07557","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":"2026-07-05T11:35:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D8kTZuQOsSlS7+qYU4zS+hiw37uQzAZ4HDFZK76RqcrcS/71vrAsevG/zgMOQgXO2D1bQ2ZUaHTksq7uO7sTBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T07:30:47.136921Z"},"content_sha256":"4eed019f70617c417f3d17465dad0a608ad5cc605309d89ef422bc1c2f7d4f67","schema_version":"1.0","event_id":"sha256:4eed019f70617c417f3d17465dad0a608ad5cc605309d89ef422bc1c2f7d4f67"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:STRWFVBVA2HT5PPHG3HRN7LT5D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparse Signal Recovery From Quadratic Systems with Full-Rank Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jinming Wen, Meng Huang, Yi Hu","submitted_at":"2025-07-10T08:56:11Z","abstract_excerpt":"In signal processing and data recovery, reconstructing a signal from quadratic measurements poses a significant challenge, particularly in high-dimensional settings where measurements $m$ is far less than the signal dimension $n$ (i.e., $m \\ll n$). This paper addresses this problem by exploiting signal sparsity. Using tools from algebraic geometry, we derive theoretical recovery guarantees for sparse quadratic systems, showing that $m\\ge 2s$ (real case) and $m\\ge 4s-2$ (complex case) generic measurements suffice to uniquely recover all $s$-sparse signals. Under a Gaussian measurement model, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.07557","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.07557/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:35:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gmUZxgPENBZjnDIIh7zWL6x1AsLkQZ6Hg7KyOBUU/akhVpdsFgZETtW2vo3UwjLRovqoJZAeYtkMn0bVrJoiCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T07:30:47.137476Z"},"content_sha256":"c17bbd6366f9889f83c3d24953b39dab113c8462779ceb0c045c00d0177cc73e","schema_version":"1.0","event_id":"sha256:c17bbd6366f9889f83c3d24953b39dab113c8462779ceb0c045c00d0177cc73e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/STRWFVBVA2HT5PPHG3HRN7LT5D/bundle.json","state_url":"https://pith.science/pith/STRWFVBVA2HT5PPHG3HRN7LT5D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/STRWFVBVA2HT5PPHG3HRN7LT5D/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":"2026-08-07T07:30:47Z","links":{"resolver":"https://pith.science/pith/STRWFVBVA2HT5PPHG3HRN7LT5D","bundle":"https://pith.science/pith/STRWFVBVA2HT5PPHG3HRN7LT5D/bundle.json","state":"https://pith.science/pith/STRWFVBVA2HT5PPHG3HRN7LT5D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/STRWFVBVA2HT5PPHG3HRN7LT5D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:STRWFVBVA2HT5PPHG3HRN7LT5D","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":"592b8bfcdf10f1bf3078069d6e7165c5ddbcff69e98e3b45f4efbaf9e598d068","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-07-10T08:56:11Z","title_canon_sha256":"1fe77f564e01bee13b47cfb352fbebe3a5e8ef9332a8a171fb6eccca52f7cc73"},"schema_version":"1.0","source":{"id":"2507.07557","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.07557","created_at":"2026-07-05T11:35:00Z"},{"alias_kind":"arxiv_version","alias_value":"2507.07557v1","created_at":"2026-07-05T11:35:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.07557","created_at":"2026-07-05T11:35:00Z"},{"alias_kind":"pith_short_12","alias_value":"STRWFVBVA2HT","created_at":"2026-07-05T11:35:00Z"},{"alias_kind":"pith_short_16","alias_value":"STRWFVBVA2HT5PPH","created_at":"2026-07-05T11:35:00Z"},{"alias_kind":"pith_short_8","alias_value":"STRWFVBV","created_at":"2026-07-05T11:35:00Z"}],"graph_snapshots":[{"event_id":"sha256:c17bbd6366f9889f83c3d24953b39dab113c8462779ceb0c045c00d0177cc73e","target":"graph","created_at":"2026-07-05T11:35:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.07557/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In signal processing and data recovery, reconstructing a signal from quadratic measurements poses a significant challenge, particularly in high-dimensional settings where measurements $m$ is far less than the signal dimension $n$ (i.e., $m \\ll n$). This paper addresses this problem by exploiting signal sparsity. Using tools from algebraic geometry, we derive theoretical recovery guarantees for sparse quadratic systems, showing that $m\\ge 2s$ (real case) and $m\\ge 4s-2$ (complex case) generic measurements suffice to uniquely recover all $s$-sparse signals. Under a Gaussian measurement model, we","authors_text":"Jinming Wen, Meng Huang, Yi Hu","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-07-10T08:56:11Z","title":"Sparse Signal Recovery From Quadratic Systems with Full-Rank Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.07557","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":"sha256:4eed019f70617c417f3d17465dad0a608ad5cc605309d89ef422bc1c2f7d4f67","target":"record","created_at":"2026-07-05T11:35:00Z","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":"592b8bfcdf10f1bf3078069d6e7165c5ddbcff69e98e3b45f4efbaf9e598d068","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-07-10T08:56:11Z","title_canon_sha256":"1fe77f564e01bee13b47cfb352fbebe3a5e8ef9332a8a171fb6eccca52f7cc73"},"schema_version":"1.0","source":{"id":"2507.07557","kind":"arxiv","version":1}},"canonical_sha256":"94e362d435068f3ebde736cf16fd73e8c918c309a3c7e91214f5ffadfd3c8b26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94e362d435068f3ebde736cf16fd73e8c918c309a3c7e91214f5ffadfd3c8b26","first_computed_at":"2026-07-05T11:35:00.642871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:35:00.642871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xrxu/RDgT7UUWeC5/s8MIgiTYio50lVosHUovC9VSKEhDqv8O788tzlm+i6y7c54sB30CfRmwCUSfRP1Oqt8Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:35:00.643360Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.07557","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4eed019f70617c417f3d17465dad0a608ad5cc605309d89ef422bc1c2f7d4f67","sha256:c17bbd6366f9889f83c3d24953b39dab113c8462779ceb0c045c00d0177cc73e"],"state_sha256":"cd74ad87e47e9b6ee98d49953dfa141b41a8abee716422380f3e94fa15ed98a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZJTNyHkHYuw1ZRqbiaA9Q68kF/jOUNDXcQ+4y5EOVdoOU6Y4p5bhYs5wO51f3A4mVwFNTLgjeDUGVCVpDN1NCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T07:30:47.146259Z","bundle_sha256":"190b8bbf54273b14bf3621b530261873e368b249a5f5cc30d7394dd5b2002435"}}