{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:3EFDDUHZT7SVTQOF56NDYSM4QQ","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":"57ee19a21d5891d27d050d504a8012316952a29204bc08166acc484c5bbe9642","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-06-13T06:59:55Z","title_canon_sha256":"25a0e7732b0dcd163e750e3675293ad9bdaf12d3f7369def709b36b72b3ca47e"},"schema_version":"1.0","source":{"id":"2206.05931","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.05931","created_at":"2026-07-05T05:22:29Z"},{"alias_kind":"arxiv_version","alias_value":"2206.05931v2","created_at":"2026-07-05T05:22:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.05931","created_at":"2026-07-05T05:22:29Z"},{"alias_kind":"pith_short_12","alias_value":"3EFDDUHZT7SV","created_at":"2026-07-05T05:22:29Z"},{"alias_kind":"pith_short_16","alias_value":"3EFDDUHZT7SVTQOF","created_at":"2026-07-05T05:22:29Z"},{"alias_kind":"pith_short_8","alias_value":"3EFDDUHZ","created_at":"2026-07-05T05:22:29Z"}],"graph_snapshots":[{"event_id":"sha256:fea5d28bfeababf938102bc74db3bf1f241114f2b74f9b7af08083f2b0b87d46","target":"graph","created_at":"2026-07-05T05:22:29Z","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/2206.05931/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the small-time global null controllability of the generalized Burgers' equations $y_t + \\gamma |y|^{\\gamma-1}y_x-y_{xx}=u(t)$ on the segment $[0,1]$. The scalar control $u(t)$ is uniform in space and plays a role similar to the pressure in higher dimension. We set a right Dirichlet boundary condition $y(t,1)=0$, and allow a left boundary control $y(t,0)=v(t)$. Under the assumption $\\gamma>3/2$ we prove that the system is small-time global null controllable. Our proof relies on the return method and a careful analysis of the shape and dissipation of a boundary layer.","authors_text":"CaGE ), R\\'emi Robin (LJLL","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-06-13T06:59:55Z","title":"Small-time global null controllability of generalized Burgers' equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.05931","kind":"arxiv","version":2},"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:b4f012c46590548bc90409117a31cb9046ea9218bc0e08947f429fa1eedb81ed","target":"record","created_at":"2026-07-05T05:22:29Z","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":"57ee19a21d5891d27d050d504a8012316952a29204bc08166acc484c5bbe9642","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-06-13T06:59:55Z","title_canon_sha256":"25a0e7732b0dcd163e750e3675293ad9bdaf12d3f7369def709b36b72b3ca47e"},"schema_version":"1.0","source":{"id":"2206.05931","kind":"arxiv","version":2}},"canonical_sha256":"d90a31d0f99fe559c1c5ef9a3c499c841b5e8cc349ef032fadef5507bb156e3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d90a31d0f99fe559c1c5ef9a3c499c841b5e8cc349ef032fadef5507bb156e3b","first_computed_at":"2026-07-05T05:22:29.708528Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:22:29.708528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DNI7YLQ6QaiO90WDiozSFS01WWjUPxAxb/Dm9H5UumNYx/kD2fjaDM7wKXZE+js6PrD6uBr7gJwq4768bKUUBw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:22:29.708991Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.05931","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4f012c46590548bc90409117a31cb9046ea9218bc0e08947f429fa1eedb81ed","sha256:fea5d28bfeababf938102bc74db3bf1f241114f2b74f9b7af08083f2b0b87d46"],"state_sha256":"b1f2d2379e43b85ae05ba1eee128e9001ffebb2c1caa1918d827e3222f365ed8"}