{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:OVDZDRWNFXCH2PHA6N3RQ7I5S3","short_pith_number":"pith:OVDZDRWN","canonical_record":{"source":{"id":"2506.18634","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-23T13:37:30Z","cross_cats_sorted":[],"title_canon_sha256":"cb83a5b2b65ed761b601805e28ce1440bb66be34f11fa93e0a22b21854866f73","abstract_canon_sha256":"62d92f84eb82b26880b3431b305b50977a8a9655b3429f87c2ded17678df2fc4"},"schema_version":"1.0"},"canonical_sha256":"754791c6cd2dc47d3ce0f377187d1d96c24535fcd315071cf9d49f9c9f961ad5","source":{"kind":"arxiv","id":"2506.18634","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.18634","created_at":"2026-07-05T11:25:53Z"},{"alias_kind":"arxiv_version","alias_value":"2506.18634v1","created_at":"2026-07-05T11:25:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.18634","created_at":"2026-07-05T11:25:53Z"},{"alias_kind":"pith_short_12","alias_value":"OVDZDRWNFXCH","created_at":"2026-07-05T11:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"OVDZDRWNFXCH2PHA","created_at":"2026-07-05T11:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"OVDZDRWN","created_at":"2026-07-05T11:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:OVDZDRWNFXCH2PHA6N3RQ7I5S3","target":"record","payload":{"canonical_record":{"source":{"id":"2506.18634","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-23T13:37:30Z","cross_cats_sorted":[],"title_canon_sha256":"cb83a5b2b65ed761b601805e28ce1440bb66be34f11fa93e0a22b21854866f73","abstract_canon_sha256":"62d92f84eb82b26880b3431b305b50977a8a9655b3429f87c2ded17678df2fc4"},"schema_version":"1.0"},"canonical_sha256":"754791c6cd2dc47d3ce0f377187d1d96c24535fcd315071cf9d49f9c9f961ad5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:25:53.410902Z","signature_b64":"1k11Yh1tB0KVRrqD+GN3GrHdd65xkHsxw7IRKhJhMkAIixErz6RWtk/h9ym/23l2TDnIleI5gz7BtJPZXH/UCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"754791c6cd2dc47d3ce0f377187d1d96c24535fcd315071cf9d49f9c9f961ad5","last_reissued_at":"2026-07-05T11:25:53.410443Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:25:53.410443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.18634","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":"2026-07-05T11:25:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AYFSG8TtLA1mq6llN3fzMdO6f+5gVz4N/xykAoXJWBL0X+1Cnzwi5KlTgKR4wFendyFRCTRhod0hTDjHa8zUAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T22:57:03.723061Z"},"content_sha256":"6afb194e800503f830b6cf027a2de41539d08619a96f6c43d2cf92f15a324cec","schema_version":"1.0","event_id":"sha256:6afb194e800503f830b6cf027a2de41539d08619a96f6c43d2cf92f15a324cec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:OVDZDRWNFXCH2PHA6N3RQ7I5S3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stabilization of Quasilinear Parabolic Equations by Cubic Feedback at Boundary with Estimated Region of Attraction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"E Witrant (GIPSA-INFINITY), M Krstic (UC San Diego), M Maghenem (GIPSA-INFINITY), Mohamed Camil Belhadjoudja (GIPSA-INFINITY)","submitted_at":"2025-06-23T13:37:30Z","abstract_excerpt":"For quasilinear parabolic partial differential equations (PDEs) that exhibit finite-time blow up in open loop, i.e., under null boundary conditions, we provide an estimate of the region of attraction under cubic feedback laws applied at the boundary, using boundary measurements. We guarantee: 1-L 2 and H 1 exponential stability of the origin with an estimate of the region of attraction. 2-Convergence of the H 2 and the C 1 norms of the solutions to zero. 3-Existence and uniqueness of complete classical solutions. 4-Positivity of the solutions starting from positive initial conditions. Unlike e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.18634","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/2506.18634/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":"2026-07-05T11:25:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qFf9VdVUHf7mjJwFlW7FZjhUeUaAQpfJNv4wGlws4pPyyQLQy4hlvFw/yPZ+jkxNUHOv8mXusz9Rtp1/AcxYCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T22:57:03.723799Z"},"content_sha256":"0fd770d02dd3bda276aca4aaf920bda22f7d821d03c54ee45a07b8d125633375","schema_version":"1.0","event_id":"sha256:0fd770d02dd3bda276aca4aaf920bda22f7d821d03c54ee45a07b8d125633375"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OVDZDRWNFXCH2PHA6N3RQ7I5S3/bundle.json","state_url":"https://pith.science/pith/OVDZDRWNFXCH2PHA6N3RQ7I5S3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OVDZDRWNFXCH2PHA6N3RQ7I5S3/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":"2026-08-18T22:57:03Z","links":{"resolver":"https://pith.science/pith/OVDZDRWNFXCH2PHA6N3RQ7I5S3","bundle":"https://pith.science/pith/OVDZDRWNFXCH2PHA6N3RQ7I5S3/bundle.json","state":"https://pith.science/pith/OVDZDRWNFXCH2PHA6N3RQ7I5S3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OVDZDRWNFXCH2PHA6N3RQ7I5S3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:OVDZDRWNFXCH2PHA6N3RQ7I5S3","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":"62d92f84eb82b26880b3431b305b50977a8a9655b3429f87c2ded17678df2fc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-23T13:37:30Z","title_canon_sha256":"cb83a5b2b65ed761b601805e28ce1440bb66be34f11fa93e0a22b21854866f73"},"schema_version":"1.0","source":{"id":"2506.18634","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.18634","created_at":"2026-07-05T11:25:53Z"},{"alias_kind":"arxiv_version","alias_value":"2506.18634v1","created_at":"2026-07-05T11:25:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.18634","created_at":"2026-07-05T11:25:53Z"},{"alias_kind":"pith_short_12","alias_value":"OVDZDRWNFXCH","created_at":"2026-07-05T11:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"OVDZDRWNFXCH2PHA","created_at":"2026-07-05T11:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"OVDZDRWN","created_at":"2026-07-05T11:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:0fd770d02dd3bda276aca4aaf920bda22f7d821d03c54ee45a07b8d125633375","target":"graph","created_at":"2026-07-05T11:25:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.18634/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For quasilinear parabolic partial differential equations (PDEs) that exhibit finite-time blow up in open loop, i.e., under null boundary conditions, we provide an estimate of the region of attraction under cubic feedback laws applied at the boundary, using boundary measurements. We guarantee: 1-L 2 and H 1 exponential stability of the origin with an estimate of the region of attraction. 2-Convergence of the H 2 and the C 1 norms of the solutions to zero. 3-Existence and uniqueness of complete classical solutions. 4-Positivity of the solutions starting from positive initial conditions. Unlike e","authors_text":"E Witrant (GIPSA-INFINITY), M Krstic (UC San Diego), M Maghenem (GIPSA-INFINITY), Mohamed Camil Belhadjoudja (GIPSA-INFINITY)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-23T13:37:30Z","title":"Stabilization of Quasilinear Parabolic Equations by Cubic Feedback at Boundary with Estimated Region of Attraction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.18634","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":"sha256:6afb194e800503f830b6cf027a2de41539d08619a96f6c43d2cf92f15a324cec","target":"record","created_at":"2026-07-05T11:25:53Z","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":"62d92f84eb82b26880b3431b305b50977a8a9655b3429f87c2ded17678df2fc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-23T13:37:30Z","title_canon_sha256":"cb83a5b2b65ed761b601805e28ce1440bb66be34f11fa93e0a22b21854866f73"},"schema_version":"1.0","source":{"id":"2506.18634","kind":"arxiv","version":1}},"canonical_sha256":"754791c6cd2dc47d3ce0f377187d1d96c24535fcd315071cf9d49f9c9f961ad5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"754791c6cd2dc47d3ce0f377187d1d96c24535fcd315071cf9d49f9c9f961ad5","first_computed_at":"2026-07-05T11:25:53.410443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:25:53.410443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1k11Yh1tB0KVRrqD+GN3GrHdd65xkHsxw7IRKhJhMkAIixErz6RWtk/h9ym/23l2TDnIleI5gz7BtJPZXH/UCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:25:53.410902Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.18634","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6afb194e800503f830b6cf027a2de41539d08619a96f6c43d2cf92f15a324cec","sha256:0fd770d02dd3bda276aca4aaf920bda22f7d821d03c54ee45a07b8d125633375"],"state_sha256":"47c021457d9ef0d12291c45c3f0656a42f1f9ec78c18572a6b42ecf02b39d3bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OOoPSwypqLDILLL0XUPo6cJoaz5n6WGRog5oXNYAqTEMWEMqZKqzLmRDMdLLhDAuneTaVgMuCByX/I73weFECg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T22:57:03.730831Z","bundle_sha256":"9962f4cb0f0983396ec393560be6192e4b49216dd4a3bba70ad39ed09476aca2"}}