{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CT2NITFKPMHUWCAVGTK6OFTTZ5","short_pith_number":"pith:CT2NITFK","canonical_record":{"source":{"id":"1110.5164","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-24T08:49:16Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"5dcd48c1c840fff471f4801b18e234dc75ede02dd049f4da59192049ef5a5d46","abstract_canon_sha256":"11c944e7429ecfb020a11a651180437d0ea511bd2f0d671c0a549c89bb60c6f3"},"schema_version":"1.0"},"canonical_sha256":"14f4d44caa7b0f4b081534d5e71673cf7ebb81521bba0cd56aef21dcc4af82d6","source":{"kind":"arxiv","id":"1110.5164","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5164","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5164v3","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5164","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"CT2NITFKPMHU","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CT2NITFKPMHUWCAV","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CT2NITFK","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CT2NITFKPMHUWCAVGTK6OFTTZ5","target":"record","payload":{"canonical_record":{"source":{"id":"1110.5164","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-24T08:49:16Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"5dcd48c1c840fff471f4801b18e234dc75ede02dd049f4da59192049ef5a5d46","abstract_canon_sha256":"11c944e7429ecfb020a11a651180437d0ea511bd2f0d671c0a549c89bb60c6f3"},"schema_version":"1.0"},"canonical_sha256":"14f4d44caa7b0f4b081534d5e71673cf7ebb81521bba0cd56aef21dcc4af82d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:53.655577Z","signature_b64":"BY1sX92Og3bjYg1cxR2kv/+sjWEadCDs4dI0c7ldav4myF4AhYtvJ66EIJlKY2AqY/nfHs1qPKW43t1smAXdCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14f4d44caa7b0f4b081534d5e71673cf7ebb81521bba0cd56aef21dcc4af82d6","last_reissued_at":"2026-05-18T01:17:53.654866Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:53.654866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.5164","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:17:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DfR2107e2oU8H+v/FLqHDzFLG+q0vVfq6V9/NW9tdU2U8h5P5i4EScxVyCzOwCAQm2hiQJwXYdGnp1H+IC5wAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:36:38.540709Z"},"content_sha256":"0ec0288a555b64927f641069f4908e03dc51ae3d312a74bc588eb81cc3d0b569","schema_version":"1.0","event_id":"sha256:0ec0288a555b64927f641069f4908e03dc51ae3d312a74bc588eb81cc3d0b569"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CT2NITFKPMHUWCAVGTK6OFTTZ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Carleman estimates for the Zaremba Boundary Condition and Stabilization of Waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Luc Robbiano, Pierre Cornilleau","submitted_at":"2011-10-24T08:49:16Z","abstract_excerpt":"In this paper, we shall prove a Carleman estimate for the so-called Zaremba problem. Using some techniques of interpolation and spectral estimates, we deduce a result of stabilization for the wave equation by means of a linear Neumann feedback on the boundary. This extends previous results from the literature: indeed, our logarithmic decay result is obtained while the part where the feedback is applied contacts the boundary zone driven by an homogeneous Dirichlet condition. We also derive a controllability result for the heat equation with the Zaremba boundary condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5164","kind":"arxiv","version":3},"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":"2026-05-18T01:17:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j/JqABgaoLwDXeKDgied7QHajSY4/KPgW+V50SOfpYPoZVRReS0v61nqJOUp+nfDANz76NPPY7e6c8OlCnMqAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:36:38.541059Z"},"content_sha256":"90a18e36623ecb076598e24748ec76cb0dbdda4f93074f1a94a27fc783787c14","schema_version":"1.0","event_id":"sha256:90a18e36623ecb076598e24748ec76cb0dbdda4f93074f1a94a27fc783787c14"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CT2NITFKPMHUWCAVGTK6OFTTZ5/bundle.json","state_url":"https://pith.science/pith/CT2NITFKPMHUWCAVGTK6OFTTZ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CT2NITFKPMHUWCAVGTK6OFTTZ5/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":"2026-06-23T19:36:38Z","links":{"resolver":"https://pith.science/pith/CT2NITFKPMHUWCAVGTK6OFTTZ5","bundle":"https://pith.science/pith/CT2NITFKPMHUWCAVGTK6OFTTZ5/bundle.json","state":"https://pith.science/pith/CT2NITFKPMHUWCAVGTK6OFTTZ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CT2NITFKPMHUWCAVGTK6OFTTZ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CT2NITFKPMHUWCAVGTK6OFTTZ5","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":"11c944e7429ecfb020a11a651180437d0ea511bd2f0d671c0a549c89bb60c6f3","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-24T08:49:16Z","title_canon_sha256":"5dcd48c1c840fff471f4801b18e234dc75ede02dd049f4da59192049ef5a5d46"},"schema_version":"1.0","source":{"id":"1110.5164","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5164","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5164v3","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5164","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"CT2NITFKPMHU","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CT2NITFKPMHUWCAV","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CT2NITFK","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:90a18e36623ecb076598e24748ec76cb0dbdda4f93074f1a94a27fc783787c14","target":"graph","created_at":"2026-05-18T01:17:53Z","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 paper, we shall prove a Carleman estimate for the so-called Zaremba problem. Using some techniques of interpolation and spectral estimates, we deduce a result of stabilization for the wave equation by means of a linear Neumann feedback on the boundary. This extends previous results from the literature: indeed, our logarithmic decay result is obtained while the part where the feedback is applied contacts the boundary zone driven by an homogeneous Dirichlet condition. We also derive a controllability result for the heat equation with the Zaremba boundary condition.","authors_text":"Luc Robbiano, Pierre Cornilleau","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-24T08:49:16Z","title":"Carleman estimates for the Zaremba Boundary Condition and Stabilization of Waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5164","kind":"arxiv","version":3},"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":"sha256:0ec0288a555b64927f641069f4908e03dc51ae3d312a74bc588eb81cc3d0b569","target":"record","created_at":"2026-05-18T01:17:53Z","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":"11c944e7429ecfb020a11a651180437d0ea511bd2f0d671c0a549c89bb60c6f3","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-24T08:49:16Z","title_canon_sha256":"5dcd48c1c840fff471f4801b18e234dc75ede02dd049f4da59192049ef5a5d46"},"schema_version":"1.0","source":{"id":"1110.5164","kind":"arxiv","version":3}},"canonical_sha256":"14f4d44caa7b0f4b081534d5e71673cf7ebb81521bba0cd56aef21dcc4af82d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14f4d44caa7b0f4b081534d5e71673cf7ebb81521bba0cd56aef21dcc4af82d6","first_computed_at":"2026-05-18T01:17:53.654866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:53.654866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BY1sX92Og3bjYg1cxR2kv/+sjWEadCDs4dI0c7ldav4myF4AhYtvJ66EIJlKY2AqY/nfHs1qPKW43t1smAXdCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:53.655577Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.5164","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ec0288a555b64927f641069f4908e03dc51ae3d312a74bc588eb81cc3d0b569","sha256:90a18e36623ecb076598e24748ec76cb0dbdda4f93074f1a94a27fc783787c14"],"state_sha256":"a8710c67a1d6c53285e94b37d1f7664a718c95580e5b0635abb61d1e61776de1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KSt9WvPvOVpTIlUVV4UrQfO5qwQS9pmrdu0xDhTaZgyWmW03z991GtKLItprHqKKfwdmr13xhUmr6sufXqF5CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T19:36:38.543092Z","bundle_sha256":"78aa05d8cade4ac0a939b6889ce115d1b76213950e9f2e0da89d96fd4d4fda0a"}}