{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:667M6AWGBEY577JNT4G4UVTCOB","short_pith_number":"pith:667M6AWG","canonical_record":{"source":{"id":"1606.00873","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-02T20:55:43Z","cross_cats_sorted":[],"title_canon_sha256":"c722c6030fe1a1e3031a9b320ad1a14d48b91a134c8c111a623b2afae57e9344","abstract_canon_sha256":"a2b2e861a50b7638cf640aa1bc88ffc515b85b33eeb6715323675d2608c5fc38"},"schema_version":"1.0"},"canonical_sha256":"f7becf02c60931dffd2d9f0dca5662705730979afb93f29dc37d1433aa42aae5","source":{"kind":"arxiv","id":"1606.00873","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00873","created_at":"2026-05-18T01:07:48Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00873v2","created_at":"2026-05-18T01:07:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00873","created_at":"2026-05-18T01:07:48Z"},{"alias_kind":"pith_short_12","alias_value":"667M6AWGBEY5","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"667M6AWGBEY577JN","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"667M6AWG","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:667M6AWGBEY577JNT4G4UVTCOB","target":"record","payload":{"canonical_record":{"source":{"id":"1606.00873","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-02T20:55:43Z","cross_cats_sorted":[],"title_canon_sha256":"c722c6030fe1a1e3031a9b320ad1a14d48b91a134c8c111a623b2afae57e9344","abstract_canon_sha256":"a2b2e861a50b7638cf640aa1bc88ffc515b85b33eeb6715323675d2608c5fc38"},"schema_version":"1.0"},"canonical_sha256":"f7becf02c60931dffd2d9f0dca5662705730979afb93f29dc37d1433aa42aae5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:48.894899Z","signature_b64":"rd+aft1UwYWfFFfIcwvO9RBmpKZXOiqUFfA5gjx6RRdefcH2LZzjE+sLhl32myXgf+FM0IzIq5quZrRWBtjwDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7becf02c60931dffd2d9f0dca5662705730979afb93f29dc37d1433aa42aae5","last_reissued_at":"2026-05-18T01:07:48.894473Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:48.894473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.00873","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:07:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tTNKB1mDV6ZzI0vHWI1aG670ehecZ8fFDU4nXcWwkzE4HbsAGb4Jim2PEWpayEc/R5Zlibkk/qw8GgY+OY5UCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:33:57.145958Z"},"content_sha256":"d0eadfb3c94b2da10385cd6df2b38a9d370a53823af3be054b52dc23b9c268a6","schema_version":"1.0","event_id":"sha256:d0eadfb3c94b2da10385cd6df2b38a9d370a53823af3be054b52dc23b9c268a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:667M6AWGBEY577JNT4G4UVTCOB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Existence and Uniqueness Theory for the Fractional Heat Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juan Luis Vazquez, Matteo Bonforte, Yannick Sire","submitted_at":"2016-06-02T20:55:43Z","abstract_excerpt":"We construct a theory of existence, uniqueness and regularity of solutions for the fractional heat equation $\\partial_t u +(-\\Delta)^s u=0$, $0<s<1$, posed in the whole space $\\mathbb{R}^N$ with data in a class of locally bounded Radon measures that are allowed to grow at infinity with an optimal growth rate. We consider a class of nonnegative weak solutions and prove that there is an equivalence between nonnegative data and solutions, which is given in one direction by the representation formula, in the other one by the initial trace. We review many of the typical properties of the solutions,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00873","kind":"arxiv","version":2},"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":"2026-05-18T01:07:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PMbqRIGVxL5dGaTx+3guV4WOI+JZIZQ5GuYRrP90bZ/aIUJITI+PuWGc1eMZjblYLbJjb3s/WgjG2Aduo17FBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:33:57.146323Z"},"content_sha256":"a63ea7264963b7b510138ff177c43f16cd6721d28ba06709568e8321fc960371","schema_version":"1.0","event_id":"sha256:a63ea7264963b7b510138ff177c43f16cd6721d28ba06709568e8321fc960371"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/667M6AWGBEY577JNT4G4UVTCOB/bundle.json","state_url":"https://pith.science/pith/667M6AWGBEY577JNT4G4UVTCOB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/667M6AWGBEY577JNT4G4UVTCOB/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":"2026-05-28T01:33:57Z","links":{"resolver":"https://pith.science/pith/667M6AWGBEY577JNT4G4UVTCOB","bundle":"https://pith.science/pith/667M6AWGBEY577JNT4G4UVTCOB/bundle.json","state":"https://pith.science/pith/667M6AWGBEY577JNT4G4UVTCOB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/667M6AWGBEY577JNT4G4UVTCOB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:667M6AWGBEY577JNT4G4UVTCOB","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":"a2b2e861a50b7638cf640aa1bc88ffc515b85b33eeb6715323675d2608c5fc38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-02T20:55:43Z","title_canon_sha256":"c722c6030fe1a1e3031a9b320ad1a14d48b91a134c8c111a623b2afae57e9344"},"schema_version":"1.0","source":{"id":"1606.00873","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00873","created_at":"2026-05-18T01:07:48Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00873v2","created_at":"2026-05-18T01:07:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00873","created_at":"2026-05-18T01:07:48Z"},{"alias_kind":"pith_short_12","alias_value":"667M6AWGBEY5","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"667M6AWGBEY577JN","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"667M6AWG","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:a63ea7264963b7b510138ff177c43f16cd6721d28ba06709568e8321fc960371","target":"graph","created_at":"2026-05-18T01:07:48Z","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 construct a theory of existence, uniqueness and regularity of solutions for the fractional heat equation $\\partial_t u +(-\\Delta)^s u=0$, $0<s<1$, posed in the whole space $\\mathbb{R}^N$ with data in a class of locally bounded Radon measures that are allowed to grow at infinity with an optimal growth rate. We consider a class of nonnegative weak solutions and prove that there is an equivalence between nonnegative data and solutions, which is given in one direction by the representation formula, in the other one by the initial trace. We review many of the typical properties of the solutions,","authors_text":"Juan Luis Vazquez, Matteo Bonforte, Yannick Sire","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-02T20:55:43Z","title":"Optimal Existence and Uniqueness Theory for the Fractional Heat Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00873","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:d0eadfb3c94b2da10385cd6df2b38a9d370a53823af3be054b52dc23b9c268a6","target":"record","created_at":"2026-05-18T01:07:48Z","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":"a2b2e861a50b7638cf640aa1bc88ffc515b85b33eeb6715323675d2608c5fc38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-02T20:55:43Z","title_canon_sha256":"c722c6030fe1a1e3031a9b320ad1a14d48b91a134c8c111a623b2afae57e9344"},"schema_version":"1.0","source":{"id":"1606.00873","kind":"arxiv","version":2}},"canonical_sha256":"f7becf02c60931dffd2d9f0dca5662705730979afb93f29dc37d1433aa42aae5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7becf02c60931dffd2d9f0dca5662705730979afb93f29dc37d1433aa42aae5","first_computed_at":"2026-05-18T01:07:48.894473Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:48.894473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rd+aft1UwYWfFFfIcwvO9RBmpKZXOiqUFfA5gjx6RRdefcH2LZzjE+sLhl32myXgf+FM0IzIq5quZrRWBtjwDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:48.894899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.00873","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0eadfb3c94b2da10385cd6df2b38a9d370a53823af3be054b52dc23b9c268a6","sha256:a63ea7264963b7b510138ff177c43f16cd6721d28ba06709568e8321fc960371"],"state_sha256":"eefd8437feb27976b7b5786a731e838b03599f9b679f54d47c202ec064bd11e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ueAbYuqI87VKBR1GulaAe5Q36SFtcuQL4LLKfTpKwYsMcTAJkyT2fZcjIKEriO2FIMT4+ry6+RvTj+wWn/KmBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:33:57.148553Z","bundle_sha256":"d203050c3ef15d2a090067befe1692b8e1f3bc22fd644088f65de8f2fe0553b9"}}