{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:DCSGZWEUKKY7HXOQNV5SCV2IR6","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":"a7129ea8d2c7872f5f2f997bddddf3a671fe46cf7233914bda1128974e7d01b0","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-03-21T10:41:54Z","title_canon_sha256":"a8fa7504bacc81db69c63278b6157c31613c51e4e629a2be1238a4c5674fe506"},"schema_version":"1.0","source":{"id":"0803.3140","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.3140","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"0803.3140v1","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.3140","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"DCSGZWEUKKY7","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"DCSGZWEUKKY7HXOQ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"DCSGZWEU","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:e244eb22076a02a2ee8c83fcee0edd0666c23bd6a2fc90473ab6b25404604cb7","target":"graph","created_at":"2026-05-18T01:11:55Z","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":"We prove sharp estimates for the dilation operator $f(x)\\longmapsto f(\\lambda x)$, when acting on Wiener amalgam spaces $W(L^p,L^q)$. Scaling arguments are also used to prove the sharpness of the known convolution and pointwise relations for modulation spaces $M^{p,q}$, as well as the optimality of an estimate for the Schr\\\"odinger propagator on modulation spaces.","authors_text":"Elena Cordero, Fabio Nicola","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-03-21T10:41:54Z","title":"Sharpness of some properties of Wiener amalgam and modulation spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.3140","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":"sha256:098fbe5066ef6674760aa039636aafdccdec56c66d447afbab2b44c30c618675","target":"record","created_at":"2026-05-18T01:11:55Z","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":"a7129ea8d2c7872f5f2f997bddddf3a671fe46cf7233914bda1128974e7d01b0","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-03-21T10:41:54Z","title_canon_sha256":"a8fa7504bacc81db69c63278b6157c31613c51e4e629a2be1238a4c5674fe506"},"schema_version":"1.0","source":{"id":"0803.3140","kind":"arxiv","version":1}},"canonical_sha256":"18a46cd89452b1f3ddd06d7b2157488fb16709d1b750c9996533c71c61b47adb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18a46cd89452b1f3ddd06d7b2157488fb16709d1b750c9996533c71c61b47adb","first_computed_at":"2026-05-18T01:11:55.658175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:55.658175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F5LkvNYV5tq9L5gVlo2M3EyxSZdXr8QAVpT6sbBGOKsQIKOgIrxF0J7eKu/aZXYoR+1vxa3OOMusm0pJAcWPCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:55.658541Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.3140","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:098fbe5066ef6674760aa039636aafdccdec56c66d447afbab2b44c30c618675","sha256:e244eb22076a02a2ee8c83fcee0edd0666c23bd6a2fc90473ab6b25404604cb7"],"state_sha256":"b34ca2d7e81b2d73b5783f448fcd1ac21a974f63f9defb2d3cba14f202070681"}