{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GOEDLSFJUOAHSTA44NP7SHB4LE","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":"e85f9f32d8f3956e9971b50ed03121f9d3e0e11478b4254b885a47e317d02879","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-17T05:02:45Z","title_canon_sha256":"70cb347dddf409a8457016bb451eaf4b58c358b5fc849a291c4f0cd9b9e9b4fd"},"schema_version":"1.0","source":{"id":"1212.3886","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3886","created_at":"2026-05-18T03:38:22Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3886v1","created_at":"2026-05-18T03:38:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3886","created_at":"2026-05-18T03:38:22Z"},{"alias_kind":"pith_short_12","alias_value":"GOEDLSFJUOAH","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GOEDLSFJUOAHSTA4","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GOEDLSFJ","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:923f4be9a1bb954df7b253388062752796444c2d1b544e8eece96b1040ed9fdf","target":"graph","created_at":"2026-05-18T03:38:22Z","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":"A mono-component is a real-valued signal of finite energy that has non-negative instantaneous frequencies, which may be defined as the derivative of the phase function of the given real-valued signal through the approach of canonical amplitude-phase modulation. We study in this article how the amplitude is determined by its phase in a canonical amplitude-phase modulation. Our finding is that such an amplitude can be perfectly reconstructed by a sampling formula using the so-called generalized sampling functions and their Hilbert transforms. The regularity of such an amplitude is identified to ","authors_text":"Luoqing Li, Qiuhui Chen, Yi Wang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-17T05:02:45Z","title":"Amplitudes of mono-components and representation by generalized sampling functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3886","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":"sha256:40dfadf61a0748ace5dbed89a4cbc3d6f0508370d6bf994ed402569fb21472d0","target":"record","created_at":"2026-05-18T03:38:22Z","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":"e85f9f32d8f3956e9971b50ed03121f9d3e0e11478b4254b885a47e317d02879","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-12-17T05:02:45Z","title_canon_sha256":"70cb347dddf409a8457016bb451eaf4b58c358b5fc849a291c4f0cd9b9e9b4fd"},"schema_version":"1.0","source":{"id":"1212.3886","kind":"arxiv","version":1}},"canonical_sha256":"338835c8a9a380794c1ce35ff91c3c593592890dc10f52a1ecc61db97518236a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"338835c8a9a380794c1ce35ff91c3c593592890dc10f52a1ecc61db97518236a","first_computed_at":"2026-05-18T03:38:22.162187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:22.162187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"10qMQ1UpbWFTrBoH+cP9F9wS+WseRyRVebw/LjY8aya0uoQaA+2jvem8EnrdRiu031vh0BShuehmUhXDlEdICw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:22.162684Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3886","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40dfadf61a0748ace5dbed89a4cbc3d6f0508370d6bf994ed402569fb21472d0","sha256:923f4be9a1bb954df7b253388062752796444c2d1b544e8eece96b1040ed9fdf"],"state_sha256":"cf1f7de66ec3840ffb9d4955a295af487856f23f7231ee5abb9326bde2a68ad8"}