{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6TYWMWVQEONISN3GJJEC2HI5N5","short_pith_number":"pith:6TYWMWVQ","canonical_record":{"source":{"id":"1801.02353","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-08T09:32:34Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"6f917e5323a74d92261ff08a4030daf38cb6ec4192a9a68abf9056d0ae722ab1","abstract_canon_sha256":"c91eb17015704b314e973365336dfb8adb34cc475021023785e3df3bd618247f"},"schema_version":"1.0"},"canonical_sha256":"f4f1665ab0239a8937664a482d1d1d6f7b0f18c1e707029806614ca47d30361a","source":{"kind":"arxiv","id":"1801.02353","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.02353","created_at":"2026-05-18T00:04:30Z"},{"alias_kind":"arxiv_version","alias_value":"1801.02353v2","created_at":"2026-05-18T00:04:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02353","created_at":"2026-05-18T00:04:30Z"},{"alias_kind":"pith_short_12","alias_value":"6TYWMWVQEONI","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6TYWMWVQEONISN3G","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6TYWMWVQ","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6TYWMWVQEONISN3GJJEC2HI5N5","target":"record","payload":{"canonical_record":{"source":{"id":"1801.02353","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-08T09:32:34Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"6f917e5323a74d92261ff08a4030daf38cb6ec4192a9a68abf9056d0ae722ab1","abstract_canon_sha256":"c91eb17015704b314e973365336dfb8adb34cc475021023785e3df3bd618247f"},"schema_version":"1.0"},"canonical_sha256":"f4f1665ab0239a8937664a482d1d1d6f7b0f18c1e707029806614ca47d30361a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:30.410514Z","signature_b64":"YKUOAT7yJjCVi+Jvc2fwpiO/ZMH/DHQtZjGrJfXd6sbRFgPag1JOEenERH5XycEAXH69Dn2Cn20GalJpYNS3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4f1665ab0239a8937664a482d1d1d6f7b0f18c1e707029806614ca47d30361a","last_reissued_at":"2026-05-18T00:04:30.410035Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:30.410035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.02353","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z1uADKIBu+eArW7MuiwS7rr4k8w/vfUwK9dFGjvGJC2XewZoyjNVuYNbDijn6C0QltjBGmshbZA6tla2u0BuBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T02:58:08.479338Z"},"content_sha256":"ba98b58743327fd2d1db8696c832291a64ed3c546a8025fa6d1c95a628607ee5","schema_version":"1.0","event_id":"sha256:ba98b58743327fd2d1db8696c832291a64ed3c546a8025fa6d1c95a628607ee5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6TYWMWVQEONISN3GJJEC2HI5N5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exponential stability of general 1-D quasilinear systems with source terms for the $C^1$ norm under boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Amaury Hayat","submitted_at":"2018-01-08T09:32:34Z","abstract_excerpt":"We address the question of the exponential stability for the $C^{1}$ norm of general 1-D quasilinear systems with source terms under boundary conditions. To reach this aim, we introduce the notion of basic $C^{1}$ Lyapunov functions, a generic kind of exponentially decreasing function whose existence ensures the exponential stability of the system for the $C^{1}$ norm. We show that the existence of a basic $C^{1}$ Lyapunov function is subject to two conditions: an interior condition, intrinsic to the system, and a condition on the boundary controls. We give explicit sufficient interior and bou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02353","kind":"arxiv","version":2},"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":"2026-05-18T00:04:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bT5UhZH2YhQQz1PjyuhTNgctdiaVdfvryEF98Vo1S7ip+fVYKso5jFWMINainS7sdvv4aybiUsbb/c4W4bmzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T02:58:08.480081Z"},"content_sha256":"e3aba7ea649e3a3018994bbb346852ab24cf19b7cd3fd6de9427fe171c1ab4ff","schema_version":"1.0","event_id":"sha256:e3aba7ea649e3a3018994bbb346852ab24cf19b7cd3fd6de9427fe171c1ab4ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6TYWMWVQEONISN3GJJEC2HI5N5/bundle.json","state_url":"https://pith.science/pith/6TYWMWVQEONISN3GJJEC2HI5N5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6TYWMWVQEONISN3GJJEC2HI5N5/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":"2026-06-12T02:58:08Z","links":{"resolver":"https://pith.science/pith/6TYWMWVQEONISN3GJJEC2HI5N5","bundle":"https://pith.science/pith/6TYWMWVQEONISN3GJJEC2HI5N5/bundle.json","state":"https://pith.science/pith/6TYWMWVQEONISN3GJJEC2HI5N5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6TYWMWVQEONISN3GJJEC2HI5N5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6TYWMWVQEONISN3GJJEC2HI5N5","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":"c91eb17015704b314e973365336dfb8adb34cc475021023785e3df3bd618247f","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-08T09:32:34Z","title_canon_sha256":"6f917e5323a74d92261ff08a4030daf38cb6ec4192a9a68abf9056d0ae722ab1"},"schema_version":"1.0","source":{"id":"1801.02353","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.02353","created_at":"2026-05-18T00:04:30Z"},{"alias_kind":"arxiv_version","alias_value":"1801.02353v2","created_at":"2026-05-18T00:04:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02353","created_at":"2026-05-18T00:04:30Z"},{"alias_kind":"pith_short_12","alias_value":"6TYWMWVQEONI","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6TYWMWVQEONISN3G","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6TYWMWVQ","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:e3aba7ea649e3a3018994bbb346852ab24cf19b7cd3fd6de9427fe171c1ab4ff","target":"graph","created_at":"2026-05-18T00:04:30Z","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":"We address the question of the exponential stability for the $C^{1}$ norm of general 1-D quasilinear systems with source terms under boundary conditions. To reach this aim, we introduce the notion of basic $C^{1}$ Lyapunov functions, a generic kind of exponentially decreasing function whose existence ensures the exponential stability of the system for the $C^{1}$ norm. We show that the existence of a basic $C^{1}$ Lyapunov function is subject to two conditions: an interior condition, intrinsic to the system, and a condition on the boundary controls. We give explicit sufficient interior and bou","authors_text":"Amaury Hayat","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-08T09:32:34Z","title":"Exponential stability of general 1-D quasilinear systems with source terms for the $C^1$ norm under boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02353","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:ba98b58743327fd2d1db8696c832291a64ed3c546a8025fa6d1c95a628607ee5","target":"record","created_at":"2026-05-18T00:04:30Z","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":"c91eb17015704b314e973365336dfb8adb34cc475021023785e3df3bd618247f","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-08T09:32:34Z","title_canon_sha256":"6f917e5323a74d92261ff08a4030daf38cb6ec4192a9a68abf9056d0ae722ab1"},"schema_version":"1.0","source":{"id":"1801.02353","kind":"arxiv","version":2}},"canonical_sha256":"f4f1665ab0239a8937664a482d1d1d6f7b0f18c1e707029806614ca47d30361a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4f1665ab0239a8937664a482d1d1d6f7b0f18c1e707029806614ca47d30361a","first_computed_at":"2026-05-18T00:04:30.410035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:30.410035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YKUOAT7yJjCVi+Jvc2fwpiO/ZMH/DHQtZjGrJfXd6sbRFgPag1JOEenERH5XycEAXH69Dn2Cn20GalJpYNS3CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:30.410514Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.02353","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba98b58743327fd2d1db8696c832291a64ed3c546a8025fa6d1c95a628607ee5","sha256:e3aba7ea649e3a3018994bbb346852ab24cf19b7cd3fd6de9427fe171c1ab4ff"],"state_sha256":"710346d101085736ed316f2373645e355d00a11e5b1bfa443ce4801bfb5a8600"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TJ6QVAGs4ssH3+GTBqiZf8p/TMoijtFiwnQxw0kZB3seIhjoCkPsVOLH2uYv/dZ1zL8P9k6Ywr2kNPORiLUFDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T02:58:08.484849Z","bundle_sha256":"66241e67b8408151990a6e7d270641ed6388ec01413e7261fd0710fbaf39b8aa"}}