{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SUDQCP276U3NIYK4AYX3L4YOXY","short_pith_number":"pith:SUDQCP27","canonical_record":{"source":{"id":"1611.09597","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-29T12:34:41Z","cross_cats_sorted":[],"title_canon_sha256":"d97dfd09607dea2de89faca1d8cfe04d2127bfe957cfb8655ee844ebaddafa57","abstract_canon_sha256":"143b49e888332700a53bac2dcb1f48a58d8356ea1e668c2ced43e392ca031b13"},"schema_version":"1.0"},"canonical_sha256":"9507013f5ff536d4615c062fb5f30ebe1d80e0257fed6fe0b4e73fe00a92ffa8","source":{"kind":"arxiv","id":"1611.09597","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09597","created_at":"2026-05-18T00:56:17Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09597v1","created_at":"2026-05-18T00:56:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09597","created_at":"2026-05-18T00:56:17Z"},{"alias_kind":"pith_short_12","alias_value":"SUDQCP276U3N","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SUDQCP276U3NIYK4","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SUDQCP27","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SUDQCP276U3NIYK4AYX3L4YOXY","target":"record","payload":{"canonical_record":{"source":{"id":"1611.09597","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-29T12:34:41Z","cross_cats_sorted":[],"title_canon_sha256":"d97dfd09607dea2de89faca1d8cfe04d2127bfe957cfb8655ee844ebaddafa57","abstract_canon_sha256":"143b49e888332700a53bac2dcb1f48a58d8356ea1e668c2ced43e392ca031b13"},"schema_version":"1.0"},"canonical_sha256":"9507013f5ff536d4615c062fb5f30ebe1d80e0257fed6fe0b4e73fe00a92ffa8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:17.968950Z","signature_b64":"+YRmKrZQDKXjvaFnaC60IqzzWzo+UWic06Dha/z6cPlxVCoy4XGGJpcaNAjcZqGqocWmpG44kNfERXviuObDBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9507013f5ff536d4615c062fb5f30ebe1d80e0257fed6fe0b4e73fe00a92ffa8","last_reissued_at":"2026-05-18T00:56:17.968293Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:17.968293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.09597","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":"2026-05-18T00:56:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tig4+Nu+SGgTYpWWYFTvnIg/ngpruHr2oO2Zz2cVyF2hCPaBUMhOw7qr2+F+eUbV47b6kszUb0s2ce08+hZPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:02:51.682339Z"},"content_sha256":"ddf27e98d832579b3255ba724bf646a9ccc63cafcf01d6b0ed131bd8bb24c57b","schema_version":"1.0","event_id":"sha256:ddf27e98d832579b3255ba724bf646a9ccc63cafcf01d6b0ed131bd8bb24c57b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SUDQCP276U3NIYK4AYX3L4YOXY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Flows and functional inequalities for fractional operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"An Zhang (CEREMADE), Jean Dolbeault (CEREMADE)","submitted_at":"2016-11-29T12:34:41Z","abstract_excerpt":"This paper collects results concerning global rates and large time asymptotics of a fractional fast diffusion on the Euclidean space, which is deeply related with a family of fractional Gagliardo-Nirenberg-Sobolev inequalities. Generically, self-similar solutions are not optimal for the Gagliardo-Nirenberg-Sobolev inequalities, in strong contrast with usual standard fast diffusion equations based on non-fractional operators. Various aspects of the stability of the self-similar solutions and of the entropy methods like carr{\\'e} du champ and R{\\'e}nyi entropy powers methods are investigated and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09597","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":"2026-05-18T00:56:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ofSiECF9Lr/QUsgMGMumJOiaIDPn5SomYjljDersOu7O6zycBCBqxcOszTpFerFnnYTyvhRaXFQtoC1iP1LyBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:02:51.683058Z"},"content_sha256":"15ba5575f836707e60db229956e2782fafdc046328768e75356a3957de1589b2","schema_version":"1.0","event_id":"sha256:15ba5575f836707e60db229956e2782fafdc046328768e75356a3957de1589b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SUDQCP276U3NIYK4AYX3L4YOXY/bundle.json","state_url":"https://pith.science/pith/SUDQCP276U3NIYK4AYX3L4YOXY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SUDQCP276U3NIYK4AYX3L4YOXY/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":"2026-06-09T16:02:51Z","links":{"resolver":"https://pith.science/pith/SUDQCP276U3NIYK4AYX3L4YOXY","bundle":"https://pith.science/pith/SUDQCP276U3NIYK4AYX3L4YOXY/bundle.json","state":"https://pith.science/pith/SUDQCP276U3NIYK4AYX3L4YOXY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SUDQCP276U3NIYK4AYX3L4YOXY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SUDQCP276U3NIYK4AYX3L4YOXY","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":"143b49e888332700a53bac2dcb1f48a58d8356ea1e668c2ced43e392ca031b13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-29T12:34:41Z","title_canon_sha256":"d97dfd09607dea2de89faca1d8cfe04d2127bfe957cfb8655ee844ebaddafa57"},"schema_version":"1.0","source":{"id":"1611.09597","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09597","created_at":"2026-05-18T00:56:17Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09597v1","created_at":"2026-05-18T00:56:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09597","created_at":"2026-05-18T00:56:17Z"},{"alias_kind":"pith_short_12","alias_value":"SUDQCP276U3N","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SUDQCP276U3NIYK4","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SUDQCP27","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:15ba5575f836707e60db229956e2782fafdc046328768e75356a3957de1589b2","target":"graph","created_at":"2026-05-18T00:56:17Z","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 collects results concerning global rates and large time asymptotics of a fractional fast diffusion on the Euclidean space, which is deeply related with a family of fractional Gagliardo-Nirenberg-Sobolev inequalities. Generically, self-similar solutions are not optimal for the Gagliardo-Nirenberg-Sobolev inequalities, in strong contrast with usual standard fast diffusion equations based on non-fractional operators. Various aspects of the stability of the self-similar solutions and of the entropy methods like carr{\\'e} du champ and R{\\'e}nyi entropy powers methods are investigated and","authors_text":"An Zhang (CEREMADE), Jean Dolbeault (CEREMADE)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-29T12:34:41Z","title":"Flows and functional inequalities for fractional operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09597","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:ddf27e98d832579b3255ba724bf646a9ccc63cafcf01d6b0ed131bd8bb24c57b","target":"record","created_at":"2026-05-18T00:56:17Z","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":"143b49e888332700a53bac2dcb1f48a58d8356ea1e668c2ced43e392ca031b13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-29T12:34:41Z","title_canon_sha256":"d97dfd09607dea2de89faca1d8cfe04d2127bfe957cfb8655ee844ebaddafa57"},"schema_version":"1.0","source":{"id":"1611.09597","kind":"arxiv","version":1}},"canonical_sha256":"9507013f5ff536d4615c062fb5f30ebe1d80e0257fed6fe0b4e73fe00a92ffa8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9507013f5ff536d4615c062fb5f30ebe1d80e0257fed6fe0b4e73fe00a92ffa8","first_computed_at":"2026-05-18T00:56:17.968293Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:17.968293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+YRmKrZQDKXjvaFnaC60IqzzWzo+UWic06Dha/z6cPlxVCoy4XGGJpcaNAjcZqGqocWmpG44kNfERXviuObDBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:17.968950Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.09597","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddf27e98d832579b3255ba724bf646a9ccc63cafcf01d6b0ed131bd8bb24c57b","sha256:15ba5575f836707e60db229956e2782fafdc046328768e75356a3957de1589b2"],"state_sha256":"a0c9929cf19e30d632495ae6cf386d6563893a46b2e7b0fffb3a52a52d1c14ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gtjQahVsnt4oFxk2VZ/K9YzQY8HFyWDnUAreDnEdvPTrA2WT17ORKc0P1m8NxgzfGO/g1xQAuwOt9692Dcy9Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T16:02:51.687284Z","bundle_sha256":"8c4d3e5fe66c432229ddef1a4d15533b166f9349251ac042cc6fe7e18b330114"}}