{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MVZWK2BZEIYCWOJNVDLWZC7N65","short_pith_number":"pith:MVZWK2BZ","canonical_record":{"source":{"id":"1301.2987","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-01-14T14:35:26Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"fe12df400c7044456c33eea784dcec8b305ca042e7fc5014ce540fa2ee2d4867","abstract_canon_sha256":"ef166d04ac9242bf35c4bbcb43e306abd18392b72487666a36e0bfe6d6f9818f"},"schema_version":"1.0"},"canonical_sha256":"657365683922302b392da8d76c8bedf760a263bfac1245e627aaf337b9f521bc","source":{"kind":"arxiv","id":"1301.2987","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2987","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2987v1","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2987","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"pith_short_12","alias_value":"MVZWK2BZEIYC","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MVZWK2BZEIYCWOJN","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MVZWK2BZ","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MVZWK2BZEIYCWOJNVDLWZC7N65","target":"record","payload":{"canonical_record":{"source":{"id":"1301.2987","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-01-14T14:35:26Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"fe12df400c7044456c33eea784dcec8b305ca042e7fc5014ce540fa2ee2d4867","abstract_canon_sha256":"ef166d04ac9242bf35c4bbcb43e306abd18392b72487666a36e0bfe6d6f9818f"},"schema_version":"1.0"},"canonical_sha256":"657365683922302b392da8d76c8bedf760a263bfac1245e627aaf337b9f521bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:47.575868Z","signature_b64":"oVhQ2UCdLz8rlCWO8Lz8dkhU+1s+CcogQQNJvIdr/mGi1tRwL/ssdm0V0/y3QGTV8GFj1Gkzox6s/Nyh+uj3AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"657365683922302b392da8d76c8bedf760a263bfac1245e627aaf337b9f521bc","last_reissued_at":"2026-05-18T00:26:47.575171Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:47.575171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.2987","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":"2026-05-18T00:26:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m5j7YxOdc3aae4H6wYDuvLOLNK+kTuTr5cWBrdNwEaFCX2+1zr7lFuE2ezSaYS9M0Fa5DPUVMUSppaqkUcRODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:12:33.592431Z"},"content_sha256":"ff533a54361c2c59485bcdede9f320f7174dbf8d090f6baec14b100a9b3bba3f","schema_version":"1.0","event_id":"sha256:ff533a54361c2c59485bcdede9f320f7174dbf8d090f6baec14b100a9b3bba3f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MVZWK2BZEIYCWOJNVDLWZC7N65","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast global null controllability for a viscous Burgers' equation despite the presence of a boundary layer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Fr\\'ed\\'eric Marbach","submitted_at":"2013-01-14T14:35:26Z","abstract_excerpt":"In this work, we are interested in the small time global null controllability for the viscous Burgers' equation y_t - y_xx + y y_x = u(t) on the line segment [0,1]. The second-hand side is a scalar control playing a role similar to that of a pressure. We set y(t,1) = 0 and restrict ourselves to using only two controls (namely the interior one u(t) and the boundary one y(t,0)). In this setting, we show that small time global null controllability still holds by taking advantage of both hyperbolic and parabolic behaviors of our system. We use the Cole-Hopf transform and Fourier series to derive p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2987","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":"2026-05-18T00:26:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pOhfAbL26eUhtqcEcYTFvTwosAgdyzBcsscmSyV+E2v0Zo5hib3/K5vkhWwsc4YXPg3Yi83Em5Q9KwdUpptRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:12:33.593034Z"},"content_sha256":"91cb9eddcdb3f07a279f86aaf5bd45a59825a9e25a4f2775adf205e6cb7dd19b","schema_version":"1.0","event_id":"sha256:91cb9eddcdb3f07a279f86aaf5bd45a59825a9e25a4f2775adf205e6cb7dd19b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MVZWK2BZEIYCWOJNVDLWZC7N65/bundle.json","state_url":"https://pith.science/pith/MVZWK2BZEIYCWOJNVDLWZC7N65/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MVZWK2BZEIYCWOJNVDLWZC7N65/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":"2026-06-05T18:12:33Z","links":{"resolver":"https://pith.science/pith/MVZWK2BZEIYCWOJNVDLWZC7N65","bundle":"https://pith.science/pith/MVZWK2BZEIYCWOJNVDLWZC7N65/bundle.json","state":"https://pith.science/pith/MVZWK2BZEIYCWOJNVDLWZC7N65/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MVZWK2BZEIYCWOJNVDLWZC7N65/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MVZWK2BZEIYCWOJNVDLWZC7N65","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":"ef166d04ac9242bf35c4bbcb43e306abd18392b72487666a36e0bfe6d6f9818f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-01-14T14:35:26Z","title_canon_sha256":"fe12df400c7044456c33eea784dcec8b305ca042e7fc5014ce540fa2ee2d4867"},"schema_version":"1.0","source":{"id":"1301.2987","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2987","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2987v1","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2987","created_at":"2026-05-18T00:26:47Z"},{"alias_kind":"pith_short_12","alias_value":"MVZWK2BZEIYC","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MVZWK2BZEIYCWOJN","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MVZWK2BZ","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:91cb9eddcdb3f07a279f86aaf5bd45a59825a9e25a4f2775adf205e6cb7dd19b","target":"graph","created_at":"2026-05-18T00:26:47Z","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":"In this work, we are interested in the small time global null controllability for the viscous Burgers' equation y_t - y_xx + y y_x = u(t) on the line segment [0,1]. The second-hand side is a scalar control playing a role similar to that of a pressure. We set y(t,1) = 0 and restrict ourselves to using only two controls (namely the interior one u(t) and the boundary one y(t,0)). In this setting, we show that small time global null controllability still holds by taking advantage of both hyperbolic and parabolic behaviors of our system. We use the Cole-Hopf transform and Fourier series to derive p","authors_text":"Fr\\'ed\\'eric Marbach","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-01-14T14:35:26Z","title":"Fast global null controllability for a viscous Burgers' equation despite the presence of a boundary layer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2987","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:ff533a54361c2c59485bcdede9f320f7174dbf8d090f6baec14b100a9b3bba3f","target":"record","created_at":"2026-05-18T00:26:47Z","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":"ef166d04ac9242bf35c4bbcb43e306abd18392b72487666a36e0bfe6d6f9818f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-01-14T14:35:26Z","title_canon_sha256":"fe12df400c7044456c33eea784dcec8b305ca042e7fc5014ce540fa2ee2d4867"},"schema_version":"1.0","source":{"id":"1301.2987","kind":"arxiv","version":1}},"canonical_sha256":"657365683922302b392da8d76c8bedf760a263bfac1245e627aaf337b9f521bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"657365683922302b392da8d76c8bedf760a263bfac1245e627aaf337b9f521bc","first_computed_at":"2026-05-18T00:26:47.575171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:47.575171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oVhQ2UCdLz8rlCWO8Lz8dkhU+1s+CcogQQNJvIdr/mGi1tRwL/ssdm0V0/y3QGTV8GFj1Gkzox6s/Nyh+uj3AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:47.575868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2987","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff533a54361c2c59485bcdede9f320f7174dbf8d090f6baec14b100a9b3bba3f","sha256:91cb9eddcdb3f07a279f86aaf5bd45a59825a9e25a4f2775adf205e6cb7dd19b"],"state_sha256":"3d4a38c1a73c2153132788dc91b83b1cc92d749d051255e9e3878b4a97e3e02b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tCGgGwFiNqjoGvsgFvZCVTcowqjBFnFTISMbsv1X/blKW6TrujsQB4srN3r1MIKPNcAoxzmYlRkB8CEWghKIDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T18:12:33.596413Z","bundle_sha256":"c085624c3c4490c5073beb9ea70521ec3c17c6c3aa034c0ffffb3172aa5627c1"}}