{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:24TDJAFWWG5ESSXHIAJWSOEK5G","short_pith_number":"pith:24TDJAFW","canonical_record":{"source":{"id":"0707.0727","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2007-07-05T07:50:37Z","cross_cats_sorted":[],"title_canon_sha256":"dcd353130d748fab3a8a153b79a3156edf957306bdb50d922dd654e810632a1c","abstract_canon_sha256":"e1e20cb078d940e53d8f8e42c870a03fbdc0bc45db896fe63cd9e1ce85b51081"},"schema_version":"1.0"},"canonical_sha256":"d7263480b6b1ba494ae7401369388ae987a5318d4def4c3a0a3027ec916d9c8f","source":{"kind":"arxiv","id":"0707.0727","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.0727","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"arxiv_version","alias_value":"0707.0727v1","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.0727","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"pith_short_12","alias_value":"24TDJAFWWG5E","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"24TDJAFWWG5ESSXH","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"24TDJAFW","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:24TDJAFWWG5ESSXHIAJWSOEK5G","target":"record","payload":{"canonical_record":{"source":{"id":"0707.0727","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2007-07-05T07:50:37Z","cross_cats_sorted":[],"title_canon_sha256":"dcd353130d748fab3a8a153b79a3156edf957306bdb50d922dd654e810632a1c","abstract_canon_sha256":"e1e20cb078d940e53d8f8e42c870a03fbdc0bc45db896fe63cd9e1ce85b51081"},"schema_version":"1.0"},"canonical_sha256":"d7263480b6b1ba494ae7401369388ae987a5318d4def4c3a0a3027ec916d9c8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:50.588192Z","signature_b64":"yBMFjwT7Z8QOeXjRUfnzztFG/IWQIjZqwOc8rCFHedR3mtiYAp9WbYcgo5Np8CpQVjnHr1rKr0eD2K/hCrLDDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7263480b6b1ba494ae7401369388ae987a5318d4def4c3a0a3027ec916d9c8f","last_reissued_at":"2026-05-18T04:36:50.587770Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:50.587770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0707.0727","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":"2026-05-18T04:36:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KDaa1ZD4IdZRYZnhSru/4/m7/UiF4RReJNVD1qgEsReISuWrvCNc1p8QmNHI4gHcd5WIJCWn4zj2CY2W+CWICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T22:11:08.680822Z"},"content_sha256":"ee3ba6e0ceabeb1371b899ec1faa6bcd13c9e6e53f01421cabb1179c65abce36","schema_version":"1.0","event_id":"sha256:ee3ba6e0ceabeb1371b899ec1faa6bcd13c9e6e53f01421cabb1179c65abce36"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:24TDJAFWWG5ESSXHIAJWSOEK5G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Beltrami operators, non--symmetric elliptic equations and quantitative Jacobian bounds","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giovanni Alessandrini, Vincenzo Nesi","submitted_at":"2007-07-05T07:50:37Z","abstract_excerpt":"In recent studies on the G-convergence of Beltrami operators, a number of issues arouse concerning injectivity properties of families of quasiconformal mappings. Bojarski, D'Onofrio, Iwaniec and Sbordone formulated a conjecture based on the existence of a so-called primary pair. Very recently, Bojarski proved the existence of one such pair. We provide a general, constructive, procedure for obtaining a new rich class of such primary pairs. This proof is obtained as a slight adaptation of previous work by the authors concerning the nonvanishing of the Jacobian of pairs of solutions of elliptic e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.0727","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":"2026-05-18T04:36:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k7rVpF3e36frOlmZhK2iXoO/cmTfQEaMHnXynmeEGKY56xiXJp0fwCADYpwJ4pxEC8kXwlgrbrDhAqcAuw17Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T22:11:08.681168Z"},"content_sha256":"8c947a619f4c86d7eedcd5bacab346dc57a84b633a9625e60c96974c4b061c7f","schema_version":"1.0","event_id":"sha256:8c947a619f4c86d7eedcd5bacab346dc57a84b633a9625e60c96974c4b061c7f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/24TDJAFWWG5ESSXHIAJWSOEK5G/bundle.json","state_url":"https://pith.science/pith/24TDJAFWWG5ESSXHIAJWSOEK5G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/24TDJAFWWG5ESSXHIAJWSOEK5G/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":"2026-07-01T22:11:08Z","links":{"resolver":"https://pith.science/pith/24TDJAFWWG5ESSXHIAJWSOEK5G","bundle":"https://pith.science/pith/24TDJAFWWG5ESSXHIAJWSOEK5G/bundle.json","state":"https://pith.science/pith/24TDJAFWWG5ESSXHIAJWSOEK5G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/24TDJAFWWG5ESSXHIAJWSOEK5G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:24TDJAFWWG5ESSXHIAJWSOEK5G","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":"e1e20cb078d940e53d8f8e42c870a03fbdc0bc45db896fe63cd9e1ce85b51081","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2007-07-05T07:50:37Z","title_canon_sha256":"dcd353130d748fab3a8a153b79a3156edf957306bdb50d922dd654e810632a1c"},"schema_version":"1.0","source":{"id":"0707.0727","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.0727","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"arxiv_version","alias_value":"0707.0727v1","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.0727","created_at":"2026-05-18T04:36:50Z"},{"alias_kind":"pith_short_12","alias_value":"24TDJAFWWG5E","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"24TDJAFWWG5ESSXH","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"24TDJAFW","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:8c947a619f4c86d7eedcd5bacab346dc57a84b633a9625e60c96974c4b061c7f","target":"graph","created_at":"2026-05-18T04:36:50Z","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 recent studies on the G-convergence of Beltrami operators, a number of issues arouse concerning injectivity properties of families of quasiconformal mappings. Bojarski, D'Onofrio, Iwaniec and Sbordone formulated a conjecture based on the existence of a so-called primary pair. Very recently, Bojarski proved the existence of one such pair. We provide a general, constructive, procedure for obtaining a new rich class of such primary pairs. This proof is obtained as a slight adaptation of previous work by the authors concerning the nonvanishing of the Jacobian of pairs of solutions of elliptic e","authors_text":"Giovanni Alessandrini, Vincenzo Nesi","cross_cats":[],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2007-07-05T07:50:37Z","title":"Beltrami operators, non--symmetric elliptic equations and quantitative Jacobian bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.0727","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:ee3ba6e0ceabeb1371b899ec1faa6bcd13c9e6e53f01421cabb1179c65abce36","target":"record","created_at":"2026-05-18T04:36:50Z","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":"e1e20cb078d940e53d8f8e42c870a03fbdc0bc45db896fe63cd9e1ce85b51081","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2007-07-05T07:50:37Z","title_canon_sha256":"dcd353130d748fab3a8a153b79a3156edf957306bdb50d922dd654e810632a1c"},"schema_version":"1.0","source":{"id":"0707.0727","kind":"arxiv","version":1}},"canonical_sha256":"d7263480b6b1ba494ae7401369388ae987a5318d4def4c3a0a3027ec916d9c8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7263480b6b1ba494ae7401369388ae987a5318d4def4c3a0a3027ec916d9c8f","first_computed_at":"2026-05-18T04:36:50.587770Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:50.587770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yBMFjwT7Z8QOeXjRUfnzztFG/IWQIjZqwOc8rCFHedR3mtiYAp9WbYcgo5Np8CpQVjnHr1rKr0eD2K/hCrLDDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:50.588192Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.0727","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee3ba6e0ceabeb1371b899ec1faa6bcd13c9e6e53f01421cabb1179c65abce36","sha256:8c947a619f4c86d7eedcd5bacab346dc57a84b633a9625e60c96974c4b061c7f"],"state_sha256":"c97e7c9afbdf5736ffddfcdc91cdbaaa9d2a362868537ad4fd01cd29f9b5909e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zMViYxndQd0BbHA9SDQShJCi9vdyVEODzSCfWHER7r+xiEHJOKmLqaSZ5ESfJ02dVZy2h3gwQgjcOvXoaEUaDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T22:11:08.683108Z","bundle_sha256":"55546bd0c5d6ccf64dc03a3d4b997e019414f4676bfeb19d3faf82ab9a538ad0"}}