{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:M7ITHC54DHAEZULNKFOQZ4LHE7","short_pith_number":"pith:M7ITHC54","canonical_record":{"source":{"id":"2104.14183","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-04-29T08:01:35Z","cross_cats_sorted":[],"title_canon_sha256":"971dd914e034d0d004c2fc2541716f7334cac95538c1bfc4633183337bc8f9f7","abstract_canon_sha256":"fafaeac7a1339d0366f63d089e1f85a520bba8e8c80743c2bf36c2659ac88201"},"schema_version":"1.0"},"canonical_sha256":"67d1338bbc19c04cd16d515d0cf16727fdc132809601d468e35aeb32e27f8cb2","source":{"kind":"arxiv","id":"2104.14183","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.14183","created_at":"2026-07-05T02:36:13Z"},{"alias_kind":"arxiv_version","alias_value":"2104.14183v1","created_at":"2026-07-05T02:36:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.14183","created_at":"2026-07-05T02:36:13Z"},{"alias_kind":"pith_short_12","alias_value":"M7ITHC54DHAE","created_at":"2026-07-05T02:36:13Z"},{"alias_kind":"pith_short_16","alias_value":"M7ITHC54DHAEZULN","created_at":"2026-07-05T02:36:13Z"},{"alias_kind":"pith_short_8","alias_value":"M7ITHC54","created_at":"2026-07-05T02:36:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:M7ITHC54DHAEZULNKFOQZ4LHE7","target":"record","payload":{"canonical_record":{"source":{"id":"2104.14183","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-04-29T08:01:35Z","cross_cats_sorted":[],"title_canon_sha256":"971dd914e034d0d004c2fc2541716f7334cac95538c1bfc4633183337bc8f9f7","abstract_canon_sha256":"fafaeac7a1339d0366f63d089e1f85a520bba8e8c80743c2bf36c2659ac88201"},"schema_version":"1.0"},"canonical_sha256":"67d1338bbc19c04cd16d515d0cf16727fdc132809601d468e35aeb32e27f8cb2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:36:13.996698Z","signature_b64":"141zgkxtj/Jd3ktpSkMwrWN2v16XyOhV19xTmeDZFhUr3glrx+0dCuoI3XMuPyjYQ0oS6VaUAvH8qh5izJH5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67d1338bbc19c04cd16d515d0cf16727fdc132809601d468e35aeb32e27f8cb2","last_reissued_at":"2026-07-05T02:36:13.996225Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:36:13.996225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2104.14183","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":"2026-07-05T02:36:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A2TTvmDlztzjJKFq8EXGNc3JXOINyrVmcITKo41rztpJcjZ/hraYZ0yP7Fv4i7DnQph+wlMKE4Om41yMcz/OCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T16:37:12.807510Z"},"content_sha256":"8dbecc5e42bc07e0799226ad67ef670721d04ddea4b1b42677c29addd9d64307","schema_version":"1.0","event_id":"sha256:8dbecc5e42bc07e0799226ad67ef670721d04ddea4b1b42677c29addd9d64307"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:M7ITHC54DHAEZULNKFOQZ4LHE7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exponential convergence towards consensus for non-symmetric linear first-order systems in finite and infinite dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"CaGE), Emmanuel Tr\\'elat (LJLL (UMR\\_7598), Francesco Salvarani (PULV), Laurent Boudin (LJLL (UMR\\_7598))","submitted_at":"2021-04-29T08:01:35Z","abstract_excerpt":"We consider finite and infinite-dimensional first-order consensus systems with timeconstant interaction coefficients. For symmetric coefficients, convergence to consensus is classically established by proving, for instance, that the usual variance is an exponentially decreasing Lyapunov function. We investigate here the convergence to consensus in the non-symmetric case: we identify a positive weight which allows to define a weighted mean corresponding to the consensus, and obtain exponential convergence towards consensus. Moreover, we compute the sharp exponential decay rate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.14183","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/2104.14183/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":"2026-07-05T02:36:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sSyv5NIIxwL8pP8PWq1S6PW3UEqPrh90m5CtDIg+ULxqXIxTdQf55MWUB7u4F+ovtoXMIaFBRN187ovy56v2DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T16:37:12.808005Z"},"content_sha256":"6035ca47d8ca8f0e5e292e4b32abd41f7ba4a0e7b9840d2f5ba5e053804d3dd7","schema_version":"1.0","event_id":"sha256:6035ca47d8ca8f0e5e292e4b32abd41f7ba4a0e7b9840d2f5ba5e053804d3dd7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M7ITHC54DHAEZULNKFOQZ4LHE7/bundle.json","state_url":"https://pith.science/pith/M7ITHC54DHAEZULNKFOQZ4LHE7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M7ITHC54DHAEZULNKFOQZ4LHE7/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":"2026-08-04T16:37:12Z","links":{"resolver":"https://pith.science/pith/M7ITHC54DHAEZULNKFOQZ4LHE7","bundle":"https://pith.science/pith/M7ITHC54DHAEZULNKFOQZ4LHE7/bundle.json","state":"https://pith.science/pith/M7ITHC54DHAEZULNKFOQZ4LHE7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M7ITHC54DHAEZULNKFOQZ4LHE7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:M7ITHC54DHAEZULNKFOQZ4LHE7","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":"fafaeac7a1339d0366f63d089e1f85a520bba8e8c80743c2bf36c2659ac88201","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-04-29T08:01:35Z","title_canon_sha256":"971dd914e034d0d004c2fc2541716f7334cac95538c1bfc4633183337bc8f9f7"},"schema_version":"1.0","source":{"id":"2104.14183","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.14183","created_at":"2026-07-05T02:36:13Z"},{"alias_kind":"arxiv_version","alias_value":"2104.14183v1","created_at":"2026-07-05T02:36:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.14183","created_at":"2026-07-05T02:36:13Z"},{"alias_kind":"pith_short_12","alias_value":"M7ITHC54DHAE","created_at":"2026-07-05T02:36:13Z"},{"alias_kind":"pith_short_16","alias_value":"M7ITHC54DHAEZULN","created_at":"2026-07-05T02:36:13Z"},{"alias_kind":"pith_short_8","alias_value":"M7ITHC54","created_at":"2026-07-05T02:36:13Z"}],"graph_snapshots":[{"event_id":"sha256:6035ca47d8ca8f0e5e292e4b32abd41f7ba4a0e7b9840d2f5ba5e053804d3dd7","target":"graph","created_at":"2026-07-05T02:36:13Z","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/2104.14183/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider finite and infinite-dimensional first-order consensus systems with timeconstant interaction coefficients. For symmetric coefficients, convergence to consensus is classically established by proving, for instance, that the usual variance is an exponentially decreasing Lyapunov function. We investigate here the convergence to consensus in the non-symmetric case: we identify a positive weight which allows to define a weighted mean corresponding to the consensus, and obtain exponential convergence towards consensus. Moreover, we compute the sharp exponential decay rate.","authors_text":"CaGE), Emmanuel Tr\\'elat (LJLL (UMR\\_7598), Francesco Salvarani (PULV), Laurent Boudin (LJLL (UMR\\_7598))","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-04-29T08:01:35Z","title":"Exponential convergence towards consensus for non-symmetric linear first-order systems in finite and infinite dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.14183","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":"sha256:8dbecc5e42bc07e0799226ad67ef670721d04ddea4b1b42677c29addd9d64307","target":"record","created_at":"2026-07-05T02:36:13Z","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":"fafaeac7a1339d0366f63d089e1f85a520bba8e8c80743c2bf36c2659ac88201","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-04-29T08:01:35Z","title_canon_sha256":"971dd914e034d0d004c2fc2541716f7334cac95538c1bfc4633183337bc8f9f7"},"schema_version":"1.0","source":{"id":"2104.14183","kind":"arxiv","version":1}},"canonical_sha256":"67d1338bbc19c04cd16d515d0cf16727fdc132809601d468e35aeb32e27f8cb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67d1338bbc19c04cd16d515d0cf16727fdc132809601d468e35aeb32e27f8cb2","first_computed_at":"2026-07-05T02:36:13.996225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:36:13.996225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"141zgkxtj/Jd3ktpSkMwrWN2v16XyOhV19xTmeDZFhUr3glrx+0dCuoI3XMuPyjYQ0oS6VaUAvH8qh5izJH5Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:36:13.996698Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.14183","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8dbecc5e42bc07e0799226ad67ef670721d04ddea4b1b42677c29addd9d64307","sha256:6035ca47d8ca8f0e5e292e4b32abd41f7ba4a0e7b9840d2f5ba5e053804d3dd7"],"state_sha256":"77d783e473c2730ac38e6f0abb6ad9e7d6cb1911d9ecd3e1fd907f673c61bda9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6stVvlXSXBlK9+scTfNwFGMfNin9t0BmqNCpRTBYe2LA2cdGVVMAzUuVmF/wU1IP/vA0M8IvY4az6dISU37DBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T16:37:12.811728Z","bundle_sha256":"c8bc4253c5b60dd19081c0f3dc43022ff04c3f0605cf558e142277575f3a1ae2"}}