{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:3CUJMUIWBPHAXL65FEDADZUUGQ","short_pith_number":"pith:3CUJMUIW","canonical_record":{"source":{"id":"2208.04880","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"eess.SY","submitted_at":"2022-08-09T16:14:42Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"e514962b07fe1345c8a29c259a24920c080200a044e696a39ff6748eadcef00a","abstract_canon_sha256":"edb466ba2baa6ee7b38d5e52d0f28262697a1606698091936a66dcd18efb0969"},"schema_version":"1.0"},"canonical_sha256":"d8a89651160bce0bafdd290601e6943439f43b6dbd114265d815ee0ed130a97d","source":{"kind":"arxiv","id":"2208.04880","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.04880","created_at":"2026-07-05T04:47:20Z"},{"alias_kind":"arxiv_version","alias_value":"2208.04880v1","created_at":"2026-07-05T04:47:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.04880","created_at":"2026-07-05T04:47:20Z"},{"alias_kind":"pith_short_12","alias_value":"3CUJMUIWBPHA","created_at":"2026-07-05T04:47:20Z"},{"alias_kind":"pith_short_16","alias_value":"3CUJMUIWBPHAXL65","created_at":"2026-07-05T04:47:20Z"},{"alias_kind":"pith_short_8","alias_value":"3CUJMUIW","created_at":"2026-07-05T04:47:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:3CUJMUIWBPHAXL65FEDADZUUGQ","target":"record","payload":{"canonical_record":{"source":{"id":"2208.04880","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"eess.SY","submitted_at":"2022-08-09T16:14:42Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"e514962b07fe1345c8a29c259a24920c080200a044e696a39ff6748eadcef00a","abstract_canon_sha256":"edb466ba2baa6ee7b38d5e52d0f28262697a1606698091936a66dcd18efb0969"},"schema_version":"1.0"},"canonical_sha256":"d8a89651160bce0bafdd290601e6943439f43b6dbd114265d815ee0ed130a97d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:47:20.216370Z","signature_b64":"nKnjlMuFoLsniNHEjCKwKjEawz9tkxhwZOJUxXFxhIbApp7SAgOzSnzxqhCGdjnUU6XvlBgf3v8NXFIGtsoTAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8a89651160bce0bafdd290601e6943439f43b6dbd114265d815ee0ed130a97d","last_reissued_at":"2026-07-05T04:47:20.216015Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:47:20.216015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.04880","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":"2026-07-05T04:47:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uJVGopGOLbJXCsUKu/LAKL2cST563Nm6DDl9UINvw/IeZsqlwP8tptHgDE2qLt7a17ueel3c9HUnd50C57cHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T13:44:59.055607Z"},"content_sha256":"b02872c4d7b316cb5fb64948786400285d2704fb57919af8236bf356fef630ca","schema_version":"1.0","event_id":"sha256:b02872c4d7b316cb5fb64948786400285d2704fb57919af8236bf356fef630ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:3CUJMUIWBPHAXL65FEDADZUUGQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Loop Shaping with Scaled Relative Graphs","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"eess.SY","authors_text":"Fulvio Forni, Rodolphe Sepulchre, Thomas Chaffey","submitted_at":"2022-08-09T16:14:42Z","abstract_excerpt":"The Scaled Relative Graph (SRG) is a generalization of the Nyquist diagram that may be plotted for nonlinear operators, and allows nonlinear robustness margins to be defined graphically. This abstract explores techniques for shaping the SRG of an operator in order to maximize these robustness margins."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.04880","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/2208.04880/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":"2026-07-05T04:47:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BRRJEhAoXi646GJX+W9uRDJeBxLtVvKZGpThY7a54gmxyfB0HtK1vX2Lnfh45VH3Lu0kgJYljR3kHNgjlbRbBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T13:44:59.056153Z"},"content_sha256":"670a0d8cbe71f1d38d7da828414522f33073cd511d8f99438bb469679e53575f","schema_version":"1.0","event_id":"sha256:670a0d8cbe71f1d38d7da828414522f33073cd511d8f99438bb469679e53575f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3CUJMUIWBPHAXL65FEDADZUUGQ/bundle.json","state_url":"https://pith.science/pith/3CUJMUIWBPHAXL65FEDADZUUGQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3CUJMUIWBPHAXL65FEDADZUUGQ/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":"2026-08-13T13:44:59Z","links":{"resolver":"https://pith.science/pith/3CUJMUIWBPHAXL65FEDADZUUGQ","bundle":"https://pith.science/pith/3CUJMUIWBPHAXL65FEDADZUUGQ/bundle.json","state":"https://pith.science/pith/3CUJMUIWBPHAXL65FEDADZUUGQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3CUJMUIWBPHAXL65FEDADZUUGQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:3CUJMUIWBPHAXL65FEDADZUUGQ","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":"edb466ba2baa6ee7b38d5e52d0f28262697a1606698091936a66dcd18efb0969","cross_cats_sorted":["cs.SY"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"eess.SY","submitted_at":"2022-08-09T16:14:42Z","title_canon_sha256":"e514962b07fe1345c8a29c259a24920c080200a044e696a39ff6748eadcef00a"},"schema_version":"1.0","source":{"id":"2208.04880","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.04880","created_at":"2026-07-05T04:47:20Z"},{"alias_kind":"arxiv_version","alias_value":"2208.04880v1","created_at":"2026-07-05T04:47:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.04880","created_at":"2026-07-05T04:47:20Z"},{"alias_kind":"pith_short_12","alias_value":"3CUJMUIWBPHA","created_at":"2026-07-05T04:47:20Z"},{"alias_kind":"pith_short_16","alias_value":"3CUJMUIWBPHAXL65","created_at":"2026-07-05T04:47:20Z"},{"alias_kind":"pith_short_8","alias_value":"3CUJMUIW","created_at":"2026-07-05T04:47:20Z"}],"graph_snapshots":[{"event_id":"sha256:670a0d8cbe71f1d38d7da828414522f33073cd511d8f99438bb469679e53575f","target":"graph","created_at":"2026-07-05T04:47:20Z","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/2208.04880/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Scaled Relative Graph (SRG) is a generalization of the Nyquist diagram that may be plotted for nonlinear operators, and allows nonlinear robustness margins to be defined graphically. This abstract explores techniques for shaping the SRG of an operator in order to maximize these robustness margins.","authors_text":"Fulvio Forni, Rodolphe Sepulchre, Thomas Chaffey","cross_cats":["cs.SY"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"eess.SY","submitted_at":"2022-08-09T16:14:42Z","title":"Loop Shaping with Scaled Relative Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.04880","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:b02872c4d7b316cb5fb64948786400285d2704fb57919af8236bf356fef630ca","target":"record","created_at":"2026-07-05T04:47:20Z","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":"edb466ba2baa6ee7b38d5e52d0f28262697a1606698091936a66dcd18efb0969","cross_cats_sorted":["cs.SY"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"eess.SY","submitted_at":"2022-08-09T16:14:42Z","title_canon_sha256":"e514962b07fe1345c8a29c259a24920c080200a044e696a39ff6748eadcef00a"},"schema_version":"1.0","source":{"id":"2208.04880","kind":"arxiv","version":1}},"canonical_sha256":"d8a89651160bce0bafdd290601e6943439f43b6dbd114265d815ee0ed130a97d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8a89651160bce0bafdd290601e6943439f43b6dbd114265d815ee0ed130a97d","first_computed_at":"2026-07-05T04:47:20.216015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:47:20.216015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nKnjlMuFoLsniNHEjCKwKjEawz9tkxhwZOJUxXFxhIbApp7SAgOzSnzxqhCGdjnUU6XvlBgf3v8NXFIGtsoTAA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:47:20.216370Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.04880","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b02872c4d7b316cb5fb64948786400285d2704fb57919af8236bf356fef630ca","sha256:670a0d8cbe71f1d38d7da828414522f33073cd511d8f99438bb469679e53575f"],"state_sha256":"fddf01e1c9da1d6c8746c9dc8c40e492570890bd05419428c0069e0d14465e27"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k86AHHgugiAHZM0XQBJsy6fyOq31PJ+7hXFOxal5a1fTNVy3nYKiZhIB3B3LOLWC0VxBEVFXjw1Lqdb1B9DdDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T13:44:59.060026Z","bundle_sha256":"58b6e86691c74cbf0136e23a00487e6af9e73e2f1c43b8402e4246a5b99f8a62"}}