{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5G5FKOLJBKO6EQ4WCWUDZFDKOP","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":"c903a4fa43a42c8fb1be7a59e3e8d2e58a6220c98314a2b4c348164bcda8b98d","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-15T16:45:54Z","title_canon_sha256":"cdb3ecd183a4452846d8b4af73c5dc45d82c0b95fbef48e0fee3bcc9baff3df9"},"schema_version":"1.0","source":{"id":"1908.05631","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.05631","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"arxiv_version","alias_value":"1908.05631v3","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05631","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"pith_short_12","alias_value":"5G5FKOLJBKO6","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"pith_short_16","alias_value":"5G5FKOLJBKO6EQ4W","created_at":"2026-07-05T01:15:55Z"},{"alias_kind":"pith_short_8","alias_value":"5G5FKOLJ","created_at":"2026-07-05T01:15:55Z"}],"graph_snapshots":[{"event_id":"sha256:461412c4b4adf4b59b4c342c6a37de50871dc7968dadad70fbf4cf1297f55109","target":"graph","created_at":"2026-07-05T01:15:55Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.05631/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study decay rates for the energy of solutions of the damped wave equation on the torus. We consider dampings invariant in one direction and bounded above and below by multiples of $x^{\\beta}$ near the boundary of the support and show decay at rate $1/t^{\\frac{\\beta+2}{\\beta+3}}$. In the case where $W$ vanishes exactly like $x^{\\beta}$ this result is optimal by work of the second author. The proof uses a version of the Morawetz multiplier method.","authors_text":"Kiril Datchev, Perry Kleinhenz","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-15T16:45:54Z","title":"Sharp polynomial decay rates for the damped wave equation with H\\\"older-like damping"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05631","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":"sha256:190fd773f9b734118eebc9b3bae2bf0e141177f7368fff71e4d1546a4aa2f03a","target":"record","created_at":"2026-07-05T01:15:55Z","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":"c903a4fa43a42c8fb1be7a59e3e8d2e58a6220c98314a2b4c348164bcda8b98d","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-15T16:45:54Z","title_canon_sha256":"cdb3ecd183a4452846d8b4af73c5dc45d82c0b95fbef48e0fee3bcc9baff3df9"},"schema_version":"1.0","source":{"id":"1908.05631","kind":"arxiv","version":3}},"canonical_sha256":"e9ba5539690a9de2439615a83c946a73f33e9b8a6f942eec160ffd3ac64526fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9ba5539690a9de2439615a83c946a73f33e9b8a6f942eec160ffd3ac64526fc","first_computed_at":"2026-07-05T01:15:55.161421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:15:55.161421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8OVxiNtTx9qQzkpQb09+EKQtyg/eDsDXcNxqTJ5Bf2kSjzLN493CB15JoLUkDYXPbclJ5u2VJ/EvBvoISOAHDw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:15:55.161758Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.05631","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:190fd773f9b734118eebc9b3bae2bf0e141177f7368fff71e4d1546a4aa2f03a","sha256:461412c4b4adf4b59b4c342c6a37de50871dc7968dadad70fbf4cf1297f55109"],"state_sha256":"ce2db1c158f0f77792ea4e10968ebaea749e1790e3d7b8071ab6f72ca77dc4c0"}