{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:AGGIGND43XQJ6A7B3P3GWBH4UB","short_pith_number":"pith:AGGIGND4","canonical_record":{"source":{"id":"1403.3199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-13T08:49:27Z","cross_cats_sorted":[],"title_canon_sha256":"56ef7cc13c8cc8d305012e36dacb1dabecb61450cbadfc39581e3a44602d7105","abstract_canon_sha256":"500456d7351afdcf1416d31e1808aa06fcefc2ab31444de6cc451393dd5a809e"},"schema_version":"1.0"},"canonical_sha256":"018c83347cdde09f03e1dbf66b04fca07aa9d7956a839b37c5cdfbbdbfc6d1c9","source":{"kind":"arxiv","id":"1403.3199","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3199","created_at":"2026-05-18T02:56:31Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3199v1","created_at":"2026-05-18T02:56:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3199","created_at":"2026-05-18T02:56:31Z"},{"alias_kind":"pith_short_12","alias_value":"AGGIGND43XQJ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AGGIGND43XQJ6A7B","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AGGIGND4","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:AGGIGND43XQJ6A7B3P3GWBH4UB","target":"record","payload":{"canonical_record":{"source":{"id":"1403.3199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-13T08:49:27Z","cross_cats_sorted":[],"title_canon_sha256":"56ef7cc13c8cc8d305012e36dacb1dabecb61450cbadfc39581e3a44602d7105","abstract_canon_sha256":"500456d7351afdcf1416d31e1808aa06fcefc2ab31444de6cc451393dd5a809e"},"schema_version":"1.0"},"canonical_sha256":"018c83347cdde09f03e1dbf66b04fca07aa9d7956a839b37c5cdfbbdbfc6d1c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:31.631447Z","signature_b64":"CBtfDlsFqcIufttGoPPlBMDA/+RKsR1fvz5AuT6HFALJEXMLZKRsj+BQkBP3pAFoh+xSchT/bWNMXHFcJpJxDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"018c83347cdde09f03e1dbf66b04fca07aa9d7956a839b37c5cdfbbdbfc6d1c9","last_reissued_at":"2026-05-18T02:56:31.630747Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:31.630747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.3199","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":"2026-05-18T02:56:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"do7iTiX9uCq7LER5kXV4kXU2cuHQ0Y4ftVyFCosWbeZCf5WW0wD15d7wkIIBCNKWa/tBHQIMOjnNkzwkeOY6Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:40:16.132414Z"},"content_sha256":"f79361dd631ac2843cb39a24cbac0da928423a22f5a3f0051a58b97b915b5be2","schema_version":"1.0","event_id":"sha256:f79361dd631ac2843cb39a24cbac0da928423a22f5a3f0051a58b97b915b5be2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:AGGIGND43XQJ6A7B3P3GWBH4UB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The best decay rate of the damped plate equation in a square","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Abdelkader Sa\\\"idi, Ka\\\"is Ammari","submitted_at":"2014-03-13T08:49:27Z","abstract_excerpt":"In this paper we study the best decay rate of the solutions of a damped plate equation in a square and with a homogeneous Dirichlet boundary conditions. We show that the fastest decay rate is given by the supremum of the real part of the spectrum of the infinitesimal generator of the underlying semigroup, if the damping coefficient is in $L^\\infty(\\Omega).$ Moreover, we give some numerical illustrations by spectral computation of the spectrum associated to the damped plate equation. The numerical results obtained for various cases of damping are in a good agreement with theoretical ones. Compu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3199","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":"2026-05-18T02:56:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zDoW4AG/uDla8ee5mBl3kTByv8dCPemVd9kCXpY9Z5BXVza3j78LM/2+BDP7Ee5pSo9NFwofAw9rOX9fEFm+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:40:16.132762Z"},"content_sha256":"8a468653b94f1d47093f208a22effc4da2180462c4c910e57c90b4590cb9cba0","schema_version":"1.0","event_id":"sha256:8a468653b94f1d47093f208a22effc4da2180462c4c910e57c90b4590cb9cba0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AGGIGND43XQJ6A7B3P3GWBH4UB/bundle.json","state_url":"https://pith.science/pith/AGGIGND43XQJ6A7B3P3GWBH4UB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AGGIGND43XQJ6A7B3P3GWBH4UB/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":"2026-06-23T15:40:16Z","links":{"resolver":"https://pith.science/pith/AGGIGND43XQJ6A7B3P3GWBH4UB","bundle":"https://pith.science/pith/AGGIGND43XQJ6A7B3P3GWBH4UB/bundle.json","state":"https://pith.science/pith/AGGIGND43XQJ6A7B3P3GWBH4UB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AGGIGND43XQJ6A7B3P3GWBH4UB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AGGIGND43XQJ6A7B3P3GWBH4UB","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":"500456d7351afdcf1416d31e1808aa06fcefc2ab31444de6cc451393dd5a809e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-13T08:49:27Z","title_canon_sha256":"56ef7cc13c8cc8d305012e36dacb1dabecb61450cbadfc39581e3a44602d7105"},"schema_version":"1.0","source":{"id":"1403.3199","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3199","created_at":"2026-05-18T02:56:31Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3199v1","created_at":"2026-05-18T02:56:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3199","created_at":"2026-05-18T02:56:31Z"},{"alias_kind":"pith_short_12","alias_value":"AGGIGND43XQJ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AGGIGND43XQJ6A7B","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AGGIGND4","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:8a468653b94f1d47093f208a22effc4da2180462c4c910e57c90b4590cb9cba0","target":"graph","created_at":"2026-05-18T02:56:31Z","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 study the best decay rate of the solutions of a damped plate equation in a square and with a homogeneous Dirichlet boundary conditions. We show that the fastest decay rate is given by the supremum of the real part of the spectrum of the infinitesimal generator of the underlying semigroup, if the damping coefficient is in $L^\\infty(\\Omega).$ Moreover, we give some numerical illustrations by spectral computation of the spectrum associated to the damped plate equation. The numerical results obtained for various cases of damping are in a good agreement with theoretical ones. Compu","authors_text":"Abdelkader Sa\\\"idi, Ka\\\"is Ammari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-13T08:49:27Z","title":"The best decay rate of the damped plate equation in a square"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3199","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:f79361dd631ac2843cb39a24cbac0da928423a22f5a3f0051a58b97b915b5be2","target":"record","created_at":"2026-05-18T02:56:31Z","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":"500456d7351afdcf1416d31e1808aa06fcefc2ab31444de6cc451393dd5a809e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-13T08:49:27Z","title_canon_sha256":"56ef7cc13c8cc8d305012e36dacb1dabecb61450cbadfc39581e3a44602d7105"},"schema_version":"1.0","source":{"id":"1403.3199","kind":"arxiv","version":1}},"canonical_sha256":"018c83347cdde09f03e1dbf66b04fca07aa9d7956a839b37c5cdfbbdbfc6d1c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"018c83347cdde09f03e1dbf66b04fca07aa9d7956a839b37c5cdfbbdbfc6d1c9","first_computed_at":"2026-05-18T02:56:31.630747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:31.630747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CBtfDlsFqcIufttGoPPlBMDA/+RKsR1fvz5AuT6HFALJEXMLZKRsj+BQkBP3pAFoh+xSchT/bWNMXHFcJpJxDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:31.631447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.3199","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f79361dd631ac2843cb39a24cbac0da928423a22f5a3f0051a58b97b915b5be2","sha256:8a468653b94f1d47093f208a22effc4da2180462c4c910e57c90b4590cb9cba0"],"state_sha256":"c564dac80e255c64dc700eb10296fcb833ceb98de7a1027102c961aceee26aca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tFgJ+c8DVjcDVTrXL8kTivNrUH+iNwZbBkGDMDGvGzOiiQbUCLZrgXS0jvOQKhnHgl9HY2D83/Yx/iSmQSFlDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:40:16.134642Z","bundle_sha256":"cd9a80a27f0f153c12e78c61a9f5cc17d666dcd895a6a144cad97a17dc44d16d"}}