{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2FS7EY3XZUWQU2JOVU4PTBIV2K","short_pith_number":"pith:2FS7EY3X","canonical_record":{"source":{"id":"1810.00562","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-01T07:37:12Z","cross_cats_sorted":["cs.IT","math-ph","math.IT","math.MP"],"title_canon_sha256":"24340ff16cf69e5e76272d9d4528af7da17cf224e8a9c4de27904768e1e7a117","abstract_canon_sha256":"1e8333c8b6856e4eaae0ac0ab70f560f65a5c7a704581c377d480902a061fcc7"},"schema_version":"1.0"},"canonical_sha256":"d165f26377cd2d0a692ead38f98515d29bb0deb9100168bc70ea9929c7dd948d","source":{"kind":"arxiv","id":"1810.00562","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00562","created_at":"2026-05-18T00:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00562v1","created_at":"2026-05-18T00:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00562","created_at":"2026-05-18T00:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"2FS7EY3XZUWQ","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2FS7EY3XZUWQU2JO","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2FS7EY3X","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2FS7EY3XZUWQU2JOVU4PTBIV2K","target":"record","payload":{"canonical_record":{"source":{"id":"1810.00562","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-01T07:37:12Z","cross_cats_sorted":["cs.IT","math-ph","math.IT","math.MP"],"title_canon_sha256":"24340ff16cf69e5e76272d9d4528af7da17cf224e8a9c4de27904768e1e7a117","abstract_canon_sha256":"1e8333c8b6856e4eaae0ac0ab70f560f65a5c7a704581c377d480902a061fcc7"},"schema_version":"1.0"},"canonical_sha256":"d165f26377cd2d0a692ead38f98515d29bb0deb9100168bc70ea9929c7dd948d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:25.409239Z","signature_b64":"p/EXEXWYpquSuobnYww64NJfTfH1Sx5E5gi+xDRwGhkDZ97UNWVDMCIp2BMfXXwFpWi7adAOB16/et+PeEkeBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d165f26377cd2d0a692ead38f98515d29bb0deb9100168bc70ea9929c7dd948d","last_reissued_at":"2026-05-18T00:04:25.408688Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:25.408688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.00562","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":"2026-05-18T00:04:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iAzoDYwKhKOU7q9FyLlN9apLQL51skEG2bosq6kUDtF/z4JGWwIkE7nUdyMzOl7lZzE0rER36E+uAmfschn9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:37:34.172117Z"},"content_sha256":"083e8b2a6a225083a7de14e2e3e7ac4b0ae101b48f8f1588fd0f2ae03b918aa0","schema_version":"1.0","event_id":"sha256:083e8b2a6a225083a7de14e2e3e7ac4b0ae101b48f8f1588fd0f2ae03b918aa0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2FS7EY3XZUWQU2JOVU4PTBIV2K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The information-theoretic meaning of Gagliardo--Nirenberg type inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math-ph","math.IT","math.MP"],"primary_cat":"math.FA","authors_text":"Giuseppe Toscani","submitted_at":"2018-10-01T07:37:12Z","abstract_excerpt":"Gagliardo--Nirenberg inequalities are interpolation inequalities which were proved independently by Gagliardo and Nirenberg in the late fifties. In recent years, their connections with theoretic aspects of information theory and nonlinear diffusion equations allowed to obtain some of them in optimal form, by recovering both the sharp constants and the explicit form of the optimizers. In this note, at the light of these recent researches, we review the main connections between Shannon-type entropies, diffusion equations and a class of these inequalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00562","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":"2026-05-18T00:04:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mflxFjyEalQiGV2j4OMjVYnvdZZAlmf8yXBlN6lPDI7CLmPg1Tn7Af05ukyYdMmDa9V46RHE3QblWwfyctR1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:37:34.172478Z"},"content_sha256":"8f5a7452cdbc084efd880fc5adb7e7d359726edda7e7b01463679b9e084830c2","schema_version":"1.0","event_id":"sha256:8f5a7452cdbc084efd880fc5adb7e7d359726edda7e7b01463679b9e084830c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2FS7EY3XZUWQU2JOVU4PTBIV2K/bundle.json","state_url":"https://pith.science/pith/2FS7EY3XZUWQU2JOVU4PTBIV2K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2FS7EY3XZUWQU2JOVU4PTBIV2K/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":"2026-06-20T22:37:34Z","links":{"resolver":"https://pith.science/pith/2FS7EY3XZUWQU2JOVU4PTBIV2K","bundle":"https://pith.science/pith/2FS7EY3XZUWQU2JOVU4PTBIV2K/bundle.json","state":"https://pith.science/pith/2FS7EY3XZUWQU2JOVU4PTBIV2K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2FS7EY3XZUWQU2JOVU4PTBIV2K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2FS7EY3XZUWQU2JOVU4PTBIV2K","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":"1e8333c8b6856e4eaae0ac0ab70f560f65a5c7a704581c377d480902a061fcc7","cross_cats_sorted":["cs.IT","math-ph","math.IT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-01T07:37:12Z","title_canon_sha256":"24340ff16cf69e5e76272d9d4528af7da17cf224e8a9c4de27904768e1e7a117"},"schema_version":"1.0","source":{"id":"1810.00562","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00562","created_at":"2026-05-18T00:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00562v1","created_at":"2026-05-18T00:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00562","created_at":"2026-05-18T00:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"2FS7EY3XZUWQ","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2FS7EY3XZUWQU2JO","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2FS7EY3X","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:8f5a7452cdbc084efd880fc5adb7e7d359726edda7e7b01463679b9e084830c2","target":"graph","created_at":"2026-05-18T00:04:25Z","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":"Gagliardo--Nirenberg inequalities are interpolation inequalities which were proved independently by Gagliardo and Nirenberg in the late fifties. In recent years, their connections with theoretic aspects of information theory and nonlinear diffusion equations allowed to obtain some of them in optimal form, by recovering both the sharp constants and the explicit form of the optimizers. In this note, at the light of these recent researches, we review the main connections between Shannon-type entropies, diffusion equations and a class of these inequalities.","authors_text":"Giuseppe Toscani","cross_cats":["cs.IT","math-ph","math.IT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-01T07:37:12Z","title":"The information-theoretic meaning of Gagliardo--Nirenberg type inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00562","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":"sha256:083e8b2a6a225083a7de14e2e3e7ac4b0ae101b48f8f1588fd0f2ae03b918aa0","target":"record","created_at":"2026-05-18T00:04:25Z","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":"1e8333c8b6856e4eaae0ac0ab70f560f65a5c7a704581c377d480902a061fcc7","cross_cats_sorted":["cs.IT","math-ph","math.IT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-01T07:37:12Z","title_canon_sha256":"24340ff16cf69e5e76272d9d4528af7da17cf224e8a9c4de27904768e1e7a117"},"schema_version":"1.0","source":{"id":"1810.00562","kind":"arxiv","version":1}},"canonical_sha256":"d165f26377cd2d0a692ead38f98515d29bb0deb9100168bc70ea9929c7dd948d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d165f26377cd2d0a692ead38f98515d29bb0deb9100168bc70ea9929c7dd948d","first_computed_at":"2026-05-18T00:04:25.408688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:25.408688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p/EXEXWYpquSuobnYww64NJfTfH1Sx5E5gi+xDRwGhkDZ97UNWVDMCIp2BMfXXwFpWi7adAOB16/et+PeEkeBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:25.409239Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.00562","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:083e8b2a6a225083a7de14e2e3e7ac4b0ae101b48f8f1588fd0f2ae03b918aa0","sha256:8f5a7452cdbc084efd880fc5adb7e7d359726edda7e7b01463679b9e084830c2"],"state_sha256":"18b25619700a6c7c9b40fdddf5fb39b8b6b7c6b43c7aa5bd03bbab1745f65dd7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X7sT7VWEibUCQOKbdXR1FD9atAMM8DoGoiXAn1lcLugs+OJxgxLrE1fbOcMKuVax8Og/+TciN0v8AroPEofyCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T22:37:34.174421Z","bundle_sha256":"e1aed85229a4e55db201001b017a21a4abe99889b53fcddfd7faca05ac3fc272"}}