{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HD3WBKVWZVSB2FXDVY2WLOSF2L","short_pith_number":"pith:HD3WBKVW","canonical_record":{"source":{"id":"1804.06068","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-17T06:44:16Z","cross_cats_sorted":[],"title_canon_sha256":"dd99276b42e85b93ab4bc4e4ebf5ce9047b189c55ce3861a6b5d509ff0f934ed","abstract_canon_sha256":"ee088c62dde49f32ceff3c66c67dca9b07088446a6353e16c4a22433378a3768"},"schema_version":"1.0"},"canonical_sha256":"38f760aab6cd641d16e3ae3565ba45d2f72c5860af9dc49719683a5a7a15bfc3","source":{"kind":"arxiv","id":"1804.06068","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06068","created_at":"2026-05-18T00:18:21Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06068v1","created_at":"2026-05-18T00:18:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06068","created_at":"2026-05-18T00:18:21Z"},{"alias_kind":"pith_short_12","alias_value":"HD3WBKVWZVSB","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HD3WBKVWZVSB2FXD","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HD3WBKVW","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HD3WBKVWZVSB2FXDVY2WLOSF2L","target":"record","payload":{"canonical_record":{"source":{"id":"1804.06068","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-17T06:44:16Z","cross_cats_sorted":[],"title_canon_sha256":"dd99276b42e85b93ab4bc4e4ebf5ce9047b189c55ce3861a6b5d509ff0f934ed","abstract_canon_sha256":"ee088c62dde49f32ceff3c66c67dca9b07088446a6353e16c4a22433378a3768"},"schema_version":"1.0"},"canonical_sha256":"38f760aab6cd641d16e3ae3565ba45d2f72c5860af9dc49719683a5a7a15bfc3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:21.824424Z","signature_b64":"KeJBMEXoBesBk6+wHIgvKFPrnqJwiW4N4YASm4gVMBYzQikEJjvayKdNgPOND+34jJDsHSTUBBWwz/34hgzxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38f760aab6cd641d16e3ae3565ba45d2f72c5860af9dc49719683a5a7a15bfc3","last_reissued_at":"2026-05-18T00:18:21.823795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:21.823795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.06068","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":"2026-05-18T00:18:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bxfd4J9vd4cnh+SjgBBE9H9Zrv2geBmsOqoJNdW+kmEb7e6PYL3PqA/91c0THNeOAbm2AgndiBQq/1DLK5yPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:34:51.659566Z"},"content_sha256":"2f746b0419848ed05b1443be981d98ab19cfa817da71ba16eaf284379169805c","schema_version":"1.0","event_id":"sha256:2f746b0419848ed05b1443be981d98ab19cfa817da71ba16eaf284379169805c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HD3WBKVWZVSB2FXDVY2WLOSF2L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positivity, monotonicity, and consensus on Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Cyrus Mostajeran, Rodolphe Sepulchre","submitted_at":"2018-04-17T06:44:16Z","abstract_excerpt":"Dynamical systems whose linearizations along trajectories are positive in the sense that they infinitesimally contract a smooth cone field are called differentially positive. The property can be thought of as a generalization of monotonicity, which is differential positivity in a linear space with respect to a constant cone field. Differential positivity places significant constraints on the asymptotic behavior of trajectories under mild technical conditions. This paper studies differentially positive systems defined on Lie groups. The geometry of a Lie group allows for the generation of invar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06068","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":""},"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":"2026-05-18T00:18:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J1lkXn/+7qq8QWpjKR/ZJIntLV7LfHLszQCO4cxcZyFV0kU+r2z3/hJ5Rf25NmCk77RIKVCFAS5kE9B47IKgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:34:51.660270Z"},"content_sha256":"37053b8b408ba17787a4f47041829eb92968cc07e99fb64c16cb44b8d8d450f8","schema_version":"1.0","event_id":"sha256:37053b8b408ba17787a4f47041829eb92968cc07e99fb64c16cb44b8d8d450f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HD3WBKVWZVSB2FXDVY2WLOSF2L/bundle.json","state_url":"https://pith.science/pith/HD3WBKVWZVSB2FXDVY2WLOSF2L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HD3WBKVWZVSB2FXDVY2WLOSF2L/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":"2026-05-30T23:34:51Z","links":{"resolver":"https://pith.science/pith/HD3WBKVWZVSB2FXDVY2WLOSF2L","bundle":"https://pith.science/pith/HD3WBKVWZVSB2FXDVY2WLOSF2L/bundle.json","state":"https://pith.science/pith/HD3WBKVWZVSB2FXDVY2WLOSF2L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HD3WBKVWZVSB2FXDVY2WLOSF2L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HD3WBKVWZVSB2FXDVY2WLOSF2L","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":"ee088c62dde49f32ceff3c66c67dca9b07088446a6353e16c4a22433378a3768","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-17T06:44:16Z","title_canon_sha256":"dd99276b42e85b93ab4bc4e4ebf5ce9047b189c55ce3861a6b5d509ff0f934ed"},"schema_version":"1.0","source":{"id":"1804.06068","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06068","created_at":"2026-05-18T00:18:21Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06068v1","created_at":"2026-05-18T00:18:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06068","created_at":"2026-05-18T00:18:21Z"},{"alias_kind":"pith_short_12","alias_value":"HD3WBKVWZVSB","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HD3WBKVWZVSB2FXD","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HD3WBKVW","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:37053b8b408ba17787a4f47041829eb92968cc07e99fb64c16cb44b8d8d450f8","target":"graph","created_at":"2026-05-18T00:18:21Z","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":"Dynamical systems whose linearizations along trajectories are positive in the sense that they infinitesimally contract a smooth cone field are called differentially positive. The property can be thought of as a generalization of monotonicity, which is differential positivity in a linear space with respect to a constant cone field. Differential positivity places significant constraints on the asymptotic behavior of trajectories under mild technical conditions. This paper studies differentially positive systems defined on Lie groups. The geometry of a Lie group allows for the generation of invar","authors_text":"Cyrus Mostajeran, Rodolphe Sepulchre","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-17T06:44:16Z","title":"Positivity, monotonicity, and consensus on Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06068","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":"sha256:2f746b0419848ed05b1443be981d98ab19cfa817da71ba16eaf284379169805c","target":"record","created_at":"2026-05-18T00:18:21Z","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":"ee088c62dde49f32ceff3c66c67dca9b07088446a6353e16c4a22433378a3768","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-17T06:44:16Z","title_canon_sha256":"dd99276b42e85b93ab4bc4e4ebf5ce9047b189c55ce3861a6b5d509ff0f934ed"},"schema_version":"1.0","source":{"id":"1804.06068","kind":"arxiv","version":1}},"canonical_sha256":"38f760aab6cd641d16e3ae3565ba45d2f72c5860af9dc49719683a5a7a15bfc3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38f760aab6cd641d16e3ae3565ba45d2f72c5860af9dc49719683a5a7a15bfc3","first_computed_at":"2026-05-18T00:18:21.823795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:21.823795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KeJBMEXoBesBk6+wHIgvKFPrnqJwiW4N4YASm4gVMBYzQikEJjvayKdNgPOND+34jJDsHSTUBBWwz/34hgzxDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:21.824424Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.06068","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f746b0419848ed05b1443be981d98ab19cfa817da71ba16eaf284379169805c","sha256:37053b8b408ba17787a4f47041829eb92968cc07e99fb64c16cb44b8d8d450f8"],"state_sha256":"84e9d7545800bf937f2e05327ae56ce6f6a73e7f3f55c3af88015ebcc33bc1f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JVoof2K/VJicPWrPJbmnWQ68Sy/BoiEHT8xReI0vqKh19qehqAF9h+MXp5I/oGs+WGVrZQRJoWsGmNMyE2J5Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:34:51.664337Z","bundle_sha256":"29ab62267e941f3cb9aeaf9d4a81dd5600592d5a2a8e3f6e4c2e509e730655ba"}}