{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:OX34FFQ56K665HXULANJ3T34QV","short_pith_number":"pith:OX34FFQ5","canonical_record":{"source":{"id":"2608.06367","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-06T17:57:45Z","cross_cats_sorted":[],"title_canon_sha256":"d2ce4d9b89ffdf906dd12e2dd053f5d3ee3712ac729aa485b32781efb94899cd","abstract_canon_sha256":"e5daf20a185829b838ca4303ff4cdcc3f90c63393a80471d7ff16d5888d34a33"},"schema_version":"1.0"},"canonical_sha256":"75f7c2961df2bdee9ef4581a9dcf7c854288b7cc39d99d25097d15b47db27954","source":{"kind":"arxiv","id":"2608.06367","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.06367","created_at":"2026-08-07T01:41:29Z"},{"alias_kind":"arxiv_version","alias_value":"2608.06367v1","created_at":"2026-08-07T01:41:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06367","created_at":"2026-08-07T01:41:29Z"},{"alias_kind":"pith_short_12","alias_value":"OX34FFQ56K66","created_at":"2026-08-07T01:41:29Z"},{"alias_kind":"pith_short_16","alias_value":"OX34FFQ56K665HXU","created_at":"2026-08-07T01:41:29Z"},{"alias_kind":"pith_short_8","alias_value":"OX34FFQ5","created_at":"2026-08-07T01:41:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:OX34FFQ56K665HXULANJ3T34QV","target":"record","payload":{"canonical_record":{"source":{"id":"2608.06367","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-06T17:57:45Z","cross_cats_sorted":[],"title_canon_sha256":"d2ce4d9b89ffdf906dd12e2dd053f5d3ee3712ac729aa485b32781efb94899cd","abstract_canon_sha256":"e5daf20a185829b838ca4303ff4cdcc3f90c63393a80471d7ff16d5888d34a33"},"schema_version":"1.0"},"canonical_sha256":"75f7c2961df2bdee9ef4581a9dcf7c854288b7cc39d99d25097d15b47db27954","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-07T01:41:29.635056Z","signature_b64":"3ROkqJrSpp8XukXeb/zMnbWtE4ttppR8pkh50Sil219wrfPwbb8uFAWlRKtOoIo5HGFZcKfLtcplF8qTvE70Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75f7c2961df2bdee9ef4581a9dcf7c854288b7cc39d99d25097d15b47db27954","last_reissued_at":"2026-08-07T01:41:29.633526Z","signature_status":"signed_v1","first_computed_at":"2026-08-07T01:41:29.633526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.06367","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":"2026-08-07T01:41:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uCYe233PAsb+88miIuOdmNrbiWcoi6DixGwnEpgIMwDoLjRXINIOjydHVKMxwcU7k+18Kqddg+YOztAd5YQFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T12:41:35.152762Z"},"content_sha256":"ea02d449f8a556a727ed89293e1b761ca6daec3afbeef0ba706f8c6a4c05b59e","schema_version":"1.0","event_id":"sha256:ea02d449f8a556a727ed89293e1b761ca6daec3afbeef0ba706f8c6a4c05b59e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:OX34FFQ56K665HXULANJ3T34QV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasiconvexity for the Dacorogna--Marcellini Energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Federico Pasqualotto, Giuseppe Bruno","submitted_at":"2026-08-06T17:57:45Z","abstract_excerpt":"We prove that the planar Dacorogna--Marcellini energy $f_\\gamma(A)=|A|^4-2\\gamma|A|^2\\det A$ is quasiconvex exactly when it is rank-one convex, i.e. if and only if $|\\gamma|\\leq\\frac{2}{\\sqrt3}$. The proof uses a monotonicity property of the energy functional along the componentwise heat flow. As a corollary of our method, we show that for homogeneous quartic polynomials on $2 \\times 2$ matrices invariant by left and right rotation, quasiconvexity is equivalent to rank one convexity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06367","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.06367/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-08-07T01:41:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3kgYDO3YDb0siysNPvhhHECn9Udc5GH7QfjunQ0ij4LewhlJPx/c+14vwUSXfx3CTHlBkABMzFdnBPWjs78yAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T12:41:35.153239Z"},"content_sha256":"7b4d038192f63ff5d7247f4184e0cf83a09fa4d982166b3a176c13be0e12e5f5","schema_version":"1.0","event_id":"sha256:7b4d038192f63ff5d7247f4184e0cf83a09fa4d982166b3a176c13be0e12e5f5"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:OX34FFQ56K665HXULANJ3T34QV","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/s11511-008-0028-1) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"D. Faraco and L. Székelyhidi, Jr., Tartar’s conjecture and localization of the quasi- convex hull inR2×2,Acta Math.200(2008), no. 2, 279–305, doi:10.1007/s11511-008- 0028-1","arxiv_id":"2608.06367","detector":"doi_compliance","evidence":{"ref_index":11,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"10.1007/s11511-008-","reconstructed_doi":"10.1007/s11511-008-0028-1"},"severity":"advisory","ref_index":11,"audited_at":"2026-08-07T04:38:14.553491Z","event_type":"pith.integrity.v1","detected_doi":"10.1007/s11511-008-0028-1","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"22e9c7b8cc6c8f401fa1965f9c681b975dd00686a6ff13a34707197c92dc0e88","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":18446,"payload_sha256":"a42aaca69a8670dd075c244effe61e11e11b0f6213a180cf22607a2532b28145","signature_b64":"5SeY1rWntPgt18Pq77RxJlN2Zxlfkva5RPYvOlKm+2lam7QhZzEDIPM5DyZyNZ2y3FiCQ/9iyULGCiaqKXyICA==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-07T04:38:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M8NpqGRnjkwDPFY0ee7oEqOjj9sPf8xK7p3PCcROVww7PF5fSyJhKlDwqoNc8zTGVCD/zHeFrTTmWTwN3mW+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T12:41:35.156938Z"},"content_sha256":"d586700ac1ede7083310bc5d27fc08f210b521c2a06f34856d233bc508b33883","schema_version":"1.0","event_id":"sha256:d586700ac1ede7083310bc5d27fc08f210b521c2a06f34856d233bc508b33883"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:OX34FFQ56K665HXULANJ3T34QV","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/978-0-387-55249-1) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"B. Dacorogna,Direct Methods in the Calculus of Variations, second ed., Applied Mathematical Sciences, vol. 78, Springer, New York, 2008, doi:10.1007/978-0-387- 55249-1","arxiv_id":"2608.06367","detector":"doi_compliance","evidence":{"ref_index":5,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"10.1007/978-0-387-","reconstructed_doi":"10.1007/978-0-387-55249-1"},"severity":"advisory","ref_index":5,"audited_at":"2026-08-07T04:38:14.553491Z","event_type":"pith.integrity.v1","detected_doi":"10.1007/978-0-387-55249-1","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"cf25639e7f0f638cae93bd508dd5865a9f20eecff9957c50eb687f5ca88b54ad","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":18445,"payload_sha256":"452e8250cb5bab8f4fd2fa67b65463c9b91d12fdbb3141ca5639d87157664e8a","signature_b64":"tKbccD6sPqgps0s3UZFISuuHobKFhpAwkzbWgY45qFSDJpcTvuL1OJTOBHEWPGXrvDD7M2/umjwFv+8F0uxVBA==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-07T04:38:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yKtJdLyrs4erRzGNVqj4MjL0S1Z7tboK3W6GBhrEpiR+gIKqNt1oHSpHOrf2Z72m/sfjatBDQbMZ1PNU+UA0Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T12:41:35.157298Z"},"content_sha256":"7d426d5ef0cae5e8c9e0ede69354d94256d817800ddfa167278ecdca1d23dc94","schema_version":"1.0","event_id":"sha256:7d426d5ef0cae5e8c9e0ede69354d94256d817800ddfa167278ecdca1d23dc94"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OX34FFQ56K665HXULANJ3T34QV/bundle.json","state_url":"https://pith.science/pith/OX34FFQ56K665HXULANJ3T34QV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OX34FFQ56K665HXULANJ3T34QV/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":"2026-08-14T12:41:35Z","links":{"resolver":"https://pith.science/pith/OX34FFQ56K665HXULANJ3T34QV","bundle":"https://pith.science/pith/OX34FFQ56K665HXULANJ3T34QV/bundle.json","state":"https://pith.science/pith/OX34FFQ56K665HXULANJ3T34QV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OX34FFQ56K665HXULANJ3T34QV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OX34FFQ56K665HXULANJ3T34QV","merge_version":"pith-open-graph-merge-v1","event_count":4,"valid_event_count":4,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e5daf20a185829b838ca4303ff4cdcc3f90c63393a80471d7ff16d5888d34a33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-06T17:57:45Z","title_canon_sha256":"d2ce4d9b89ffdf906dd12e2dd053f5d3ee3712ac729aa485b32781efb94899cd"},"schema_version":"1.0","source":{"id":"2608.06367","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.06367","created_at":"2026-08-07T01:41:29Z"},{"alias_kind":"arxiv_version","alias_value":"2608.06367v1","created_at":"2026-08-07T01:41:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06367","created_at":"2026-08-07T01:41:29Z"},{"alias_kind":"pith_short_12","alias_value":"OX34FFQ56K66","created_at":"2026-08-07T01:41:29Z"},{"alias_kind":"pith_short_16","alias_value":"OX34FFQ56K665HXU","created_at":"2026-08-07T01:41:29Z"},{"alias_kind":"pith_short_8","alias_value":"OX34FFQ5","created_at":"2026-08-07T01:41:29Z"}],"graph_snapshots":[{"event_id":"sha256:7b4d038192f63ff5d7247f4184e0cf83a09fa4d982166b3a176c13be0e12e5f5","target":"graph","created_at":"2026-08-07T01:41:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.06367/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the planar Dacorogna--Marcellini energy $f_\\gamma(A)=|A|^4-2\\gamma|A|^2\\det A$ is quasiconvex exactly when it is rank-one convex, i.e. if and only if $|\\gamma|\\leq\\frac{2}{\\sqrt3}$. The proof uses a monotonicity property of the energy functional along the componentwise heat flow. As a corollary of our method, we show that for homogeneous quartic polynomials on $2 \\times 2$ matrices invariant by left and right rotation, quasiconvexity is equivalent to rank one convexity.","authors_text":"Federico Pasqualotto, Giuseppe Bruno","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-06T17:57:45Z","title":"Quasiconvexity for the Dacorogna--Marcellini Energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06367","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:ea02d449f8a556a727ed89293e1b761ca6daec3afbeef0ba706f8c6a4c05b59e","target":"record","created_at":"2026-08-07T01:41:29Z","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":"e5daf20a185829b838ca4303ff4cdcc3f90c63393a80471d7ff16d5888d34a33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-08-06T17:57:45Z","title_canon_sha256":"d2ce4d9b89ffdf906dd12e2dd053f5d3ee3712ac729aa485b32781efb94899cd"},"schema_version":"1.0","source":{"id":"2608.06367","kind":"arxiv","version":1}},"canonical_sha256":"75f7c2961df2bdee9ef4581a9dcf7c854288b7cc39d99d25097d15b47db27954","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75f7c2961df2bdee9ef4581a9dcf7c854288b7cc39d99d25097d15b47db27954","first_computed_at":"2026-08-07T01:41:29.633526Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-07T01:41:29.633526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3ROkqJrSpp8XukXeb/zMnbWtE4ttppR8pkh50Sil219wrfPwbb8uFAWlRKtOoIo5HGFZcKfLtcplF8qTvE70Aw==","signature_status":"signed_v1","signed_at":"2026-08-07T01:41:29.635056Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.06367","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:7d426d5ef0cae5e8c9e0ede69354d94256d817800ddfa167278ecdca1d23dc94","sha256:d586700ac1ede7083310bc5d27fc08f210b521c2a06f34856d233bc508b33883"]}],"invalid_events":[],"applied_event_ids":["sha256:ea02d449f8a556a727ed89293e1b761ca6daec3afbeef0ba706f8c6a4c05b59e","sha256:7b4d038192f63ff5d7247f4184e0cf83a09fa4d982166b3a176c13be0e12e5f5"],"state_sha256":"25578064295a04f5247c90c33f8771522fb96aa0ce1bbeeb666d88f5412f5921"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OYzkVTwugnUkW5y8WW0+sIHXLPz3Ezvvnakk8S/RfSslEYao2N7AS6Y1fCuYbJKWzQ/xkD1cvR5C5SC5X+JADA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T12:41:35.159785Z","bundle_sha256":"6dc3993cf717e79ce7e49b8f4f7d2bd5ca6a1f67b10eb9ff31281b34976fbe55"}}