{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:K253QBE4MOP347P3G34PWXPVBT","short_pith_number":"pith:K253QBE4","canonical_record":{"source":{"id":"1906.06510","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-15T09:49:45Z","cross_cats_sorted":[],"title_canon_sha256":"1043011178870bf3c72ca1b4f0fce1878c61eddb9f2ae5aa4b67274fbf115885","abstract_canon_sha256":"9ec75ace8a587a1763916d035055b928087b9e33a70ff7280b58505ce5a85cbf"},"schema_version":"1.0"},"canonical_sha256":"56bbb8049c639fbe7dfb36f8fb5df50cea76ce8fb47159f7f4288271f4749dd5","source":{"kind":"arxiv","id":"1906.06510","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.06510","created_at":"2026-05-17T23:43:13Z"},{"alias_kind":"arxiv_version","alias_value":"1906.06510v1","created_at":"2026-05-17T23:43:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.06510","created_at":"2026-05-17T23:43:13Z"},{"alias_kind":"pith_short_12","alias_value":"K253QBE4MOP3","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"K253QBE4MOP347P3","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"K253QBE4","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:K253QBE4MOP347P3G34PWXPVBT","target":"record","payload":{"canonical_record":{"source":{"id":"1906.06510","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-15T09:49:45Z","cross_cats_sorted":[],"title_canon_sha256":"1043011178870bf3c72ca1b4f0fce1878c61eddb9f2ae5aa4b67274fbf115885","abstract_canon_sha256":"9ec75ace8a587a1763916d035055b928087b9e33a70ff7280b58505ce5a85cbf"},"schema_version":"1.0"},"canonical_sha256":"56bbb8049c639fbe7dfb36f8fb5df50cea76ce8fb47159f7f4288271f4749dd5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:13.492099Z","signature_b64":"pwab9D3i9333QoNZnuteJ3H7CR/uLDZlHtyj22KieT272LQavgbZKQn10+uoyl1kdncezLKoyqjvKd5mus1xAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56bbb8049c639fbe7dfb36f8fb5df50cea76ce8fb47159f7f4288271f4749dd5","last_reissued_at":"2026-05-17T23:43:13.491634Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:13.491634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.06510","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":"2026-05-17T23:43:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JRWzcArWu2j8mu+sH7IglBGw+36GKVEZPG9U1eVucvB/npMPlbgaGRcTf7ovRFbqIQs+ODQ3u7Qs9knbx1KFBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T17:29:13.665346Z"},"content_sha256":"675ed826e5c6a0aaf17b1c014a97486ed81b2339ad05b063825d762439bcd52f","schema_version":"1.0","event_id":"sha256:675ed826e5c6a0aaf17b1c014a97486ed81b2339ad05b063825d762439bcd52f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:K253QBE4MOP347P3G34PWXPVBT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the upper semicontinuity of a quasiconcave functional","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Denis Serre, Luigi De Rosa, Riccardo Tione","submitted_at":"2019-06-15T09:49:45Z","abstract_excerpt":"In the recent paper \\cite{SER}, the second author proved a divergence-quasiconcavity inequality for the following functional $ \\mathbb{D}(A)=\\int_{\\mathbb{T}^n} det(A(x))^{\\frac{1}{n-1}}\\,dx$ defined on the space of $p$-summable positive definite matrices with zero divergence. We prove that this implies the weak upper semicontinuity of the functional $\\mathbb{D}(\\cdot)$ if and only if $p>\\frac{n}{n-1}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.06510","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":"2026-05-17T23:43:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OKVF8vLFdztxuhxMfEFBOVfWsHUHlA+EeFWyklFF/NAMOzx37cZ03cgbV7MzoipNCGw1X66Z4sA8ybLxoQ2aAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T17:29:13.665911Z"},"content_sha256":"82aca5c8a0850f1b63dbb4a755cca6f0d8de7b02c4cda89bfff86e0a6d05aba4","schema_version":"1.0","event_id":"sha256:82aca5c8a0850f1b63dbb4a755cca6f0d8de7b02c4cda89bfff86e0a6d05aba4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K253QBE4MOP347P3G34PWXPVBT/bundle.json","state_url":"https://pith.science/pith/K253QBE4MOP347P3G34PWXPVBT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K253QBE4MOP347P3G34PWXPVBT/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":"2026-05-22T17:29:13Z","links":{"resolver":"https://pith.science/pith/K253QBE4MOP347P3G34PWXPVBT","bundle":"https://pith.science/pith/K253QBE4MOP347P3G34PWXPVBT/bundle.json","state":"https://pith.science/pith/K253QBE4MOP347P3G34PWXPVBT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K253QBE4MOP347P3G34PWXPVBT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:K253QBE4MOP347P3G34PWXPVBT","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":"9ec75ace8a587a1763916d035055b928087b9e33a70ff7280b58505ce5a85cbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-15T09:49:45Z","title_canon_sha256":"1043011178870bf3c72ca1b4f0fce1878c61eddb9f2ae5aa4b67274fbf115885"},"schema_version":"1.0","source":{"id":"1906.06510","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.06510","created_at":"2026-05-17T23:43:13Z"},{"alias_kind":"arxiv_version","alias_value":"1906.06510v1","created_at":"2026-05-17T23:43:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.06510","created_at":"2026-05-17T23:43:13Z"},{"alias_kind":"pith_short_12","alias_value":"K253QBE4MOP3","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"K253QBE4MOP347P3","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"K253QBE4","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:82aca5c8a0850f1b63dbb4a755cca6f0d8de7b02c4cda89bfff86e0a6d05aba4","target":"graph","created_at":"2026-05-17T23:43:13Z","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":"In the recent paper \\cite{SER}, the second author proved a divergence-quasiconcavity inequality for the following functional $ \\mathbb{D}(A)=\\int_{\\mathbb{T}^n} det(A(x))^{\\frac{1}{n-1}}\\,dx$ defined on the space of $p$-summable positive definite matrices with zero divergence. We prove that this implies the weak upper semicontinuity of the functional $\\mathbb{D}(\\cdot)$ if and only if $p>\\frac{n}{n-1}$.","authors_text":"Denis Serre, Luigi De Rosa, Riccardo Tione","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-15T09:49:45Z","title":"On the upper semicontinuity of a quasiconcave functional"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.06510","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":"sha256:675ed826e5c6a0aaf17b1c014a97486ed81b2339ad05b063825d762439bcd52f","target":"record","created_at":"2026-05-17T23:43:13Z","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":"9ec75ace8a587a1763916d035055b928087b9e33a70ff7280b58505ce5a85cbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-15T09:49:45Z","title_canon_sha256":"1043011178870bf3c72ca1b4f0fce1878c61eddb9f2ae5aa4b67274fbf115885"},"schema_version":"1.0","source":{"id":"1906.06510","kind":"arxiv","version":1}},"canonical_sha256":"56bbb8049c639fbe7dfb36f8fb5df50cea76ce8fb47159f7f4288271f4749dd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56bbb8049c639fbe7dfb36f8fb5df50cea76ce8fb47159f7f4288271f4749dd5","first_computed_at":"2026-05-17T23:43:13.491634Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:13.491634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pwab9D3i9333QoNZnuteJ3H7CR/uLDZlHtyj22KieT272LQavgbZKQn10+uoyl1kdncezLKoyqjvKd5mus1xAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:13.492099Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.06510","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:675ed826e5c6a0aaf17b1c014a97486ed81b2339ad05b063825d762439bcd52f","sha256:82aca5c8a0850f1b63dbb4a755cca6f0d8de7b02c4cda89bfff86e0a6d05aba4"],"state_sha256":"6103da425d8b2f0fbfc94bb1f542a0abd3a021cc6c35c94a1421eac77af2e7fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5b5FBEUuVV4iMbhaDC4i9HDjoLN2iz0Ee3jpyoRY2iJ064K7EVmI90qt+bnddRgtfrgTkLOKJxU/FSQxIcgKAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T17:29:13.669196Z","bundle_sha256":"b514d9012041d9f3c69130d4d215df965548dce645315dc56b2814f2f4b43aa6"}}