{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GORD4R3ELU7JVJKBI2B5FLSON2","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":"0540c4f602b583a80e6ebe8c2d3c7029edb42e676b0d08b09dad82a84b0ccc20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-21T07:17:45Z","title_canon_sha256":"a5983dbf4ce189473ff213bb79081771ff03dec2fb6ec355782aff3f411546ee"},"schema_version":"1.0","source":{"id":"1607.06214","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06214","created_at":"2026-05-18T00:33:53Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06214v2","created_at":"2026-05-18T00:33:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06214","created_at":"2026-05-18T00:33:53Z"},{"alias_kind":"pith_short_12","alias_value":"GORD4R3ELU7J","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GORD4R3ELU7JVJKB","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GORD4R3E","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:52c4dd9dfbc35774986b4a32cfb9e5013f391c6efe70b21ffd52e894c84c5285","target":"graph","created_at":"2026-05-18T00:33:53Z","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"},"paper":{"abstract_excerpt":"We prove $L^{2}$ estimates and solvability for a variety of simply characteristic constant coefficient partial differential equations $P(D)u=f$. These estimates \\[||u||_{L^2(D_{r})}\\le C\\sqrt{d_{r}d_{s}} ||f||_{_{L^2(D_{s})}}\\] depend on geometric quantities - the diameters $d_{r}$ and $d_{s}$ of the regions $D_{r}$, where we estimate $u$, and $D_{s}$, the support of $f$ - rather than weights. As these geometric quantities transform simply under translations, rotations, and dilations, the corresponding estimates share the same properties. In particular, this implies that they transform appropr","authors_text":"Eemeli Bl\\r{a}sten, John Sylvester","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-21T07:17:45Z","title":"Translation-Invariant Estimates for Operators with Simple Characteristics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06214","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":"sha256:04057d040ac5c16f8053b7718fed167126c0c62160313d4d45faea3edc8edffe","target":"record","created_at":"2026-05-18T00:33:53Z","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":"0540c4f602b583a80e6ebe8c2d3c7029edb42e676b0d08b09dad82a84b0ccc20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-21T07:17:45Z","title_canon_sha256":"a5983dbf4ce189473ff213bb79081771ff03dec2fb6ec355782aff3f411546ee"},"schema_version":"1.0","source":{"id":"1607.06214","kind":"arxiv","version":2}},"canonical_sha256":"33a23e47645d3e9aa5414683d2ae4e6e8fe8e98eeff9048220044fe167b635e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33a23e47645d3e9aa5414683d2ae4e6e8fe8e98eeff9048220044fe167b635e9","first_computed_at":"2026-05-18T00:33:53.230603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:53.230603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TSneh0CFiPGTKcR3lye/gRCS72SosjzdIuPyjW1yEU/y63+24ictPAJo2YLXwWLgkaLtx+a/AjhEPd/DkMqOCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:53.231024Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.06214","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04057d040ac5c16f8053b7718fed167126c0c62160313d4d45faea3edc8edffe","sha256:52c4dd9dfbc35774986b4a32cfb9e5013f391c6efe70b21ffd52e894c84c5285"],"state_sha256":"a480094a0a2812c80522031c3d44a60d5ca1546e16ea6094a31ef073c2845be9"}