{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:VKARMIH7D7NW475Y3DIRCIV3VA","short_pith_number":"pith:VKARMIH7","canonical_record":{"source":{"id":"1205.2459","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-11T08:35:27Z","cross_cats_sorted":[],"title_canon_sha256":"189f81d7133320d22a4a22a67b87832e908ffdd42bda5eb52a41af255f05d481","abstract_canon_sha256":"ed6bddd5658850dd110094833c88a0788b25e85f31669fd62be50791911a97dd"},"schema_version":"1.0"},"canonical_sha256":"aa811620ff1fdb6e7fb8d8d11122bba82a0e966fa97373ae722bb295fdbabd38","source":{"kind":"arxiv","id":"1205.2459","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2459","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2459v4","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2459","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"pith_short_12","alias_value":"VKARMIH7D7NW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VKARMIH7D7NW475Y","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VKARMIH7","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:VKARMIH7D7NW475Y3DIRCIV3VA","target":"record","payload":{"canonical_record":{"source":{"id":"1205.2459","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-11T08:35:27Z","cross_cats_sorted":[],"title_canon_sha256":"189f81d7133320d22a4a22a67b87832e908ffdd42bda5eb52a41af255f05d481","abstract_canon_sha256":"ed6bddd5658850dd110094833c88a0788b25e85f31669fd62be50791911a97dd"},"schema_version":"1.0"},"canonical_sha256":"aa811620ff1fdb6e7fb8d8d11122bba82a0e966fa97373ae722bb295fdbabd38","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:55.088947Z","signature_b64":"RolmF9UskmPryk7SEcJAAVZEZlYzzo78GC+ayVU3CGbuv+q/dgQRibxn9UNUg325XHbJ49Fz9ZijLqEeqT4yAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa811620ff1fdb6e7fb8d8d11122bba82a0e966fa97373ae722bb295fdbabd38","last_reissued_at":"2026-05-18T03:05:55.088339Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:55.088339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.2459","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:05:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XpBXHY6e7AbkOwpah/9/DEBw5WIVxe7kuv/arPXqWXBtBaVn3om+Oyk/4bNRXw/wYmSAflDYAmsyfpjbvB+wDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:50:42.402257Z"},"content_sha256":"460a9c7224daa066db35efa353b0c0e786c27d2c275cf431c30dde1d4e408e8b","schema_version":"1.0","event_id":"sha256:460a9c7224daa066db35efa353b0c0e786c27d2c275cf431c30dde1d4e408e8b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:VKARMIH7D7NW475Y3DIRCIV3VA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stabilization for the semilinear wave equation with geometric control condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Camille Laurent (LJLL), Romain Joly (IF)","submitted_at":"2012-05-11T08:35:27Z","abstract_excerpt":"In this article, we prove the exponential stabilization of the semilinear wave equation with a damping effective in a zone satisfying the geometric control condition only. The nonlinearity is assumed to be subcritical, defocusing and analytic. The main novelty compared to previous results, is the proof of a unique continuation result in large time for some undamped equation. The idea is to use an asymptotic smoothing effect proved by Hale and Raugel in the context of dynamical systems. Then, once the analyticity in time is proved, we apply a unique continuation result with partial analyticity "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2459","kind":"arxiv","version":4},"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":"2026-05-18T03:05:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CdIAJ3DdUMJSKbJat4fbmdlEbR6X2RdcBvDJ1/ZUC9STNhSnQ/Ail2U03iqQ88xItarT6neBKAQHXIRb3UrUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:50:42.402625Z"},"content_sha256":"a3296e42df8276b6b8220cb5cd526a6487aeb8b4dcf6f1f94be783b8054bbe48","schema_version":"1.0","event_id":"sha256:a3296e42df8276b6b8220cb5cd526a6487aeb8b4dcf6f1f94be783b8054bbe48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VKARMIH7D7NW475Y3DIRCIV3VA/bundle.json","state_url":"https://pith.science/pith/VKARMIH7D7NW475Y3DIRCIV3VA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VKARMIH7D7NW475Y3DIRCIV3VA/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":"2026-06-25T18:50:42Z","links":{"resolver":"https://pith.science/pith/VKARMIH7D7NW475Y3DIRCIV3VA","bundle":"https://pith.science/pith/VKARMIH7D7NW475Y3DIRCIV3VA/bundle.json","state":"https://pith.science/pith/VKARMIH7D7NW475Y3DIRCIV3VA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VKARMIH7D7NW475Y3DIRCIV3VA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VKARMIH7D7NW475Y3DIRCIV3VA","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":"ed6bddd5658850dd110094833c88a0788b25e85f31669fd62be50791911a97dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-11T08:35:27Z","title_canon_sha256":"189f81d7133320d22a4a22a67b87832e908ffdd42bda5eb52a41af255f05d481"},"schema_version":"1.0","source":{"id":"1205.2459","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2459","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2459v4","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2459","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"pith_short_12","alias_value":"VKARMIH7D7NW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VKARMIH7D7NW475Y","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VKARMIH7","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:a3296e42df8276b6b8220cb5cd526a6487aeb8b4dcf6f1f94be783b8054bbe48","target":"graph","created_at":"2026-05-18T03:05:55Z","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 article, we prove the exponential stabilization of the semilinear wave equation with a damping effective in a zone satisfying the geometric control condition only. The nonlinearity is assumed to be subcritical, defocusing and analytic. The main novelty compared to previous results, is the proof of a unique continuation result in large time for some undamped equation. The idea is to use an asymptotic smoothing effect proved by Hale and Raugel in the context of dynamical systems. Then, once the analyticity in time is proved, we apply a unique continuation result with partial analyticity ","authors_text":"Camille Laurent (LJLL), Romain Joly (IF)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-11T08:35:27Z","title":"Stabilization for the semilinear wave equation with geometric control condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2459","kind":"arxiv","version":4},"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":"sha256:460a9c7224daa066db35efa353b0c0e786c27d2c275cf431c30dde1d4e408e8b","target":"record","created_at":"2026-05-18T03:05:55Z","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":"ed6bddd5658850dd110094833c88a0788b25e85f31669fd62be50791911a97dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-11T08:35:27Z","title_canon_sha256":"189f81d7133320d22a4a22a67b87832e908ffdd42bda5eb52a41af255f05d481"},"schema_version":"1.0","source":{"id":"1205.2459","kind":"arxiv","version":4}},"canonical_sha256":"aa811620ff1fdb6e7fb8d8d11122bba82a0e966fa97373ae722bb295fdbabd38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa811620ff1fdb6e7fb8d8d11122bba82a0e966fa97373ae722bb295fdbabd38","first_computed_at":"2026-05-18T03:05:55.088339Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:55.088339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RolmF9UskmPryk7SEcJAAVZEZlYzzo78GC+ayVU3CGbuv+q/dgQRibxn9UNUg325XHbJ49Fz9ZijLqEeqT4yAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:55.088947Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2459","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:460a9c7224daa066db35efa353b0c0e786c27d2c275cf431c30dde1d4e408e8b","sha256:a3296e42df8276b6b8220cb5cd526a6487aeb8b4dcf6f1f94be783b8054bbe48"],"state_sha256":"4eb8d8da6bbfe6ad970eab339f4d3079c98b8bec6d0a20699db414dc597062ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vSkEOZOcjureGiocvBbpgATINzZcPEpqDvco9DypnIyQHDJqpOGirJ3sMimcM1HtPoL41EvNKVDxJm/sauoSDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T18:50:42.404501Z","bundle_sha256":"35e67ebd4e0b61ebfbd5dc4981bdfb7d587f7bf0a26fb6d89eeadce2dcfe0f69"}}