{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CSUAZF5O5G6PI4I2METGYHME4B","short_pith_number":"pith:CSUAZF5O","canonical_record":{"source":{"id":"1407.4086","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-07-15T18:24:19Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"bcf02e15dea8085b0b463a46b849e6c499962526981336733c943909226cfbe4","abstract_canon_sha256":"a0763e92ea83c56f9c13dd87afccac9775d2c3bb1291f78813076afe2480a008"},"schema_version":"1.0"},"canonical_sha256":"14a80c97aee9bcf4711a61266c1d84e07436b1a45dd0bc6a0938d6c2e0eef17d","source":{"kind":"arxiv","id":"1407.4086","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4086","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4086v1","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4086","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"CSUAZF5O5G6P","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CSUAZF5O5G6PI4I2","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CSUAZF5O","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CSUAZF5O5G6PI4I2METGYHME4B","target":"record","payload":{"canonical_record":{"source":{"id":"1407.4086","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-07-15T18:24:19Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"bcf02e15dea8085b0b463a46b849e6c499962526981336733c943909226cfbe4","abstract_canon_sha256":"a0763e92ea83c56f9c13dd87afccac9775d2c3bb1291f78813076afe2480a008"},"schema_version":"1.0"},"canonical_sha256":"14a80c97aee9bcf4711a61266c1d84e07436b1a45dd0bc6a0938d6c2e0eef17d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:31.951094Z","signature_b64":"L/X5ifvJ3h4bR7eZyNNl55z+XiQdOHrkjBFjeE3z1usMe7ve88RTXIJN1qPd92SD0IU7xSHHaG8mztbyhMKODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14a80c97aee9bcf4711a61266c1d84e07436b1a45dd0bc6a0938d6c2e0eef17d","last_reissued_at":"2026-05-18T02:47:31.950459Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:31.950459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.4086","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":"2026-05-18T02:47:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X7QCesk8Dx5ErsuzGinzCDArD+WHaXMI5Ll0AaatHfkoiLvn/++Ke0eeR65AIRenVrZfJ5QeheF9lkGK8jlECg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:45:31.734819Z"},"content_sha256":"7f750b9503449f1f14e2bd1670e0991175f7d7f6982f6535ad906e25720fb60a","schema_version":"1.0","event_id":"sha256:7f750b9503449f1f14e2bd1670e0991175f7d7f6982f6535ad906e25720fb60a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CSUAZF5O5G6PI4I2METGYHME4B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dispersive estimates with loss of derivatives via the heat semigroup and the wave operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Frederic Bernicot (LMJL), Valentin Samoyeau (LMJL)","submitted_at":"2014-07-15T18:24:19Z","abstract_excerpt":"This paper aims to give a general (possibly compact or noncompact) analog of Strichartz inequalities with loss of derivatives, obtained by Burq, G\\'erard, and Tzvetkov [19] and Staffilani and Tataru [51]. Moreover we present a new approach, relying only on the heat semigroup in order to understand the analytic connexion between the heat semigroup and the unitary Schr\\\"odinger group (both related to a same self-adjoint operator). One of the novelty is to forget the endpoint $L^1-L^\\infty$ dispersive estimates and to look for a weaker $H^1-BMO$ estimates (Hardy and BMO spaces both adapted to the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4086","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":"2026-05-18T02:47:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qcYggBH0LqRbwS58sTSK5r1hn14HPW088FrODOkyj0rqKuKw8hvRpDvf8cvrFDc4/M1MxBQD8EI7B8KcmkEXBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:45:31.735179Z"},"content_sha256":"eb4204fd7d5fa054dee3f4d93f7f2d3340c78d3839018a902bc4a2ffb4548b21","schema_version":"1.0","event_id":"sha256:eb4204fd7d5fa054dee3f4d93f7f2d3340c78d3839018a902bc4a2ffb4548b21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CSUAZF5O5G6PI4I2METGYHME4B/bundle.json","state_url":"https://pith.science/pith/CSUAZF5O5G6PI4I2METGYHME4B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CSUAZF5O5G6PI4I2METGYHME4B/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":"2026-06-27T04:45:31Z","links":{"resolver":"https://pith.science/pith/CSUAZF5O5G6PI4I2METGYHME4B","bundle":"https://pith.science/pith/CSUAZF5O5G6PI4I2METGYHME4B/bundle.json","state":"https://pith.science/pith/CSUAZF5O5G6PI4I2METGYHME4B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CSUAZF5O5G6PI4I2METGYHME4B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CSUAZF5O5G6PI4I2METGYHME4B","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":"a0763e92ea83c56f9c13dd87afccac9775d2c3bb1291f78813076afe2480a008","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-07-15T18:24:19Z","title_canon_sha256":"bcf02e15dea8085b0b463a46b849e6c499962526981336733c943909226cfbe4"},"schema_version":"1.0","source":{"id":"1407.4086","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4086","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4086v1","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4086","created_at":"2026-05-18T02:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"CSUAZF5O5G6P","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CSUAZF5O5G6PI4I2","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CSUAZF5O","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:eb4204fd7d5fa054dee3f4d93f7f2d3340c78d3839018a902bc4a2ffb4548b21","target":"graph","created_at":"2026-05-18T02:47:31Z","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":"This paper aims to give a general (possibly compact or noncompact) analog of Strichartz inequalities with loss of derivatives, obtained by Burq, G\\'erard, and Tzvetkov [19] and Staffilani and Tataru [51]. Moreover we present a new approach, relying only on the heat semigroup in order to understand the analytic connexion between the heat semigroup and the unitary Schr\\\"odinger group (both related to a same self-adjoint operator). One of the novelty is to forget the endpoint $L^1-L^\\infty$ dispersive estimates and to look for a weaker $H^1-BMO$ estimates (Hardy and BMO spaces both adapted to the","authors_text":"Frederic Bernicot (LMJL), Valentin Samoyeau (LMJL)","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-07-15T18:24:19Z","title":"Dispersive estimates with loss of derivatives via the heat semigroup and the wave operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4086","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":"sha256:7f750b9503449f1f14e2bd1670e0991175f7d7f6982f6535ad906e25720fb60a","target":"record","created_at":"2026-05-18T02:47:31Z","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":"a0763e92ea83c56f9c13dd87afccac9775d2c3bb1291f78813076afe2480a008","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-07-15T18:24:19Z","title_canon_sha256":"bcf02e15dea8085b0b463a46b849e6c499962526981336733c943909226cfbe4"},"schema_version":"1.0","source":{"id":"1407.4086","kind":"arxiv","version":1}},"canonical_sha256":"14a80c97aee9bcf4711a61266c1d84e07436b1a45dd0bc6a0938d6c2e0eef17d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14a80c97aee9bcf4711a61266c1d84e07436b1a45dd0bc6a0938d6c2e0eef17d","first_computed_at":"2026-05-18T02:47:31.950459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:31.950459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L/X5ifvJ3h4bR7eZyNNl55z+XiQdOHrkjBFjeE3z1usMe7ve88RTXIJN1qPd92SD0IU7xSHHaG8mztbyhMKODw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:31.951094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4086","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f750b9503449f1f14e2bd1670e0991175f7d7f6982f6535ad906e25720fb60a","sha256:eb4204fd7d5fa054dee3f4d93f7f2d3340c78d3839018a902bc4a2ffb4548b21"],"state_sha256":"47a7b4c4a73cf95b5703ed70f0a3b2bc61c5956b2913c64b27e28e9ca877034f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nnkDANUxdhGSWbI80HoCep4LS5Y4y6pHTrTbJ8uVbzYRCEW0j+nu3BOJM0poH11fAxJ9bwrIF6mDiSwgHG5NBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T04:45:31.737083Z","bundle_sha256":"bec11b3fb6dbde9ee546d31eb17334aeaf3b156529ec644939400aaebb5339a1"}}