{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:3X4ZZ6BVB7CWBEJKUFNDHLRJKW","short_pith_number":"pith:3X4ZZ6BV","canonical_record":{"source":{"id":"1009.1277","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-07T12:58:12Z","cross_cats_sorted":[],"title_canon_sha256":"86f4f780b8fab7a03beca89e4af4f6eeebf312719aa5de37e19df3143968695d","abstract_canon_sha256":"00f2158226c7f7704717669f326db64d9c9b2d3594b162538d94a615e1e6999e"},"schema_version":"1.0"},"canonical_sha256":"ddf99cf8350fc560912aa15a33ae2955901c318b39b0514aac99047effbad73f","source":{"kind":"arxiv","id":"1009.1277","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1277","created_at":"2026-05-18T04:41:15Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1277v1","created_at":"2026-05-18T04:41:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1277","created_at":"2026-05-18T04:41:15Z"},{"alias_kind":"pith_short_12","alias_value":"3X4ZZ6BVB7CW","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3X4ZZ6BVB7CWBEJK","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3X4ZZ6BV","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:3X4ZZ6BVB7CWBEJKUFNDHLRJKW","target":"record","payload":{"canonical_record":{"source":{"id":"1009.1277","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-07T12:58:12Z","cross_cats_sorted":[],"title_canon_sha256":"86f4f780b8fab7a03beca89e4af4f6eeebf312719aa5de37e19df3143968695d","abstract_canon_sha256":"00f2158226c7f7704717669f326db64d9c9b2d3594b162538d94a615e1e6999e"},"schema_version":"1.0"},"canonical_sha256":"ddf99cf8350fc560912aa15a33ae2955901c318b39b0514aac99047effbad73f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:15.794963Z","signature_b64":"KQYWDi5u+qEVP8ArX96DRkq8UXTSnGHeZqc0ozHH9eVDxKG8y2Kl+mZ3w9bBqiV6HHdLRVV0XCaCBw0vy6MpDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddf99cf8350fc560912aa15a33ae2955901c318b39b0514aac99047effbad73f","last_reissued_at":"2026-05-18T04:41:15.794486Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:15.794486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.1277","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":"2026-05-18T04:41:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"32NHtRVaLiHjLhokZbwnj8sDiHVqARjRYQrXfkdrRdh7EUu+ISOr1QaPyBYBR6+Xpq94duKCWiaX+kkj11qnDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:19:13.174436Z"},"content_sha256":"94260604969f1393fc1362b11c5c4af9cd4baff792b52ebdd2b906ce5704ded7","schema_version":"1.0","event_id":"sha256:94260604969f1393fc1362b11c5c4af9cd4baff792b52ebdd2b906ce5704ded7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:3X4ZZ6BVB7CWBEJKUFNDHLRJKW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Bernoulli problem with non constant gradient boundary constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chiara Bianchini","submitted_at":"2010-09-07T12:58:12Z","abstract_excerpt":"We present in this paper a result about existence and convexity of solutions to a free boundary problem of Bernoulli type, with non constant gradient boundary constraint depending on the outer unit normal. In particular we prove that, in the convex case, the existence of a subsolution guarantees the existence of a classical solution, which is proved to be convex."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1277","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":"2026-05-18T04:41:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g4VWlBMkkAVIBTzUAr9Az2Yig/tDfNOb9p9IOpcbeOrCGLSHbO+yzW+/7k8ft8Ax7YBi37j7Uv50R0dWqq49DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:19:13.174782Z"},"content_sha256":"8587d86257c58a902ddb70734c47674deb9ab4470d49cef7f27db9e1098a2f96","schema_version":"1.0","event_id":"sha256:8587d86257c58a902ddb70734c47674deb9ab4470d49cef7f27db9e1098a2f96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3X4ZZ6BVB7CWBEJKUFNDHLRJKW/bundle.json","state_url":"https://pith.science/pith/3X4ZZ6BVB7CWBEJKUFNDHLRJKW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3X4ZZ6BVB7CWBEJKUFNDHLRJKW/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":"2026-06-02T02:19:13Z","links":{"resolver":"https://pith.science/pith/3X4ZZ6BVB7CWBEJKUFNDHLRJKW","bundle":"https://pith.science/pith/3X4ZZ6BVB7CWBEJKUFNDHLRJKW/bundle.json","state":"https://pith.science/pith/3X4ZZ6BVB7CWBEJKUFNDHLRJKW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3X4ZZ6BVB7CWBEJKUFNDHLRJKW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3X4ZZ6BVB7CWBEJKUFNDHLRJKW","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":"00f2158226c7f7704717669f326db64d9c9b2d3594b162538d94a615e1e6999e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-07T12:58:12Z","title_canon_sha256":"86f4f780b8fab7a03beca89e4af4f6eeebf312719aa5de37e19df3143968695d"},"schema_version":"1.0","source":{"id":"1009.1277","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1277","created_at":"2026-05-18T04:41:15Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1277v1","created_at":"2026-05-18T04:41:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1277","created_at":"2026-05-18T04:41:15Z"},{"alias_kind":"pith_short_12","alias_value":"3X4ZZ6BVB7CW","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3X4ZZ6BVB7CWBEJK","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3X4ZZ6BV","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:8587d86257c58a902ddb70734c47674deb9ab4470d49cef7f27db9e1098a2f96","target":"graph","created_at":"2026-05-18T04:41:15Z","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":"We present in this paper a result about existence and convexity of solutions to a free boundary problem of Bernoulli type, with non constant gradient boundary constraint depending on the outer unit normal. In particular we prove that, in the convex case, the existence of a subsolution guarantees the existence of a classical solution, which is proved to be convex.","authors_text":"Chiara Bianchini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-07T12:58:12Z","title":"A Bernoulli problem with non constant gradient boundary constraint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1277","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":"sha256:94260604969f1393fc1362b11c5c4af9cd4baff792b52ebdd2b906ce5704ded7","target":"record","created_at":"2026-05-18T04:41:15Z","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":"00f2158226c7f7704717669f326db64d9c9b2d3594b162538d94a615e1e6999e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-07T12:58:12Z","title_canon_sha256":"86f4f780b8fab7a03beca89e4af4f6eeebf312719aa5de37e19df3143968695d"},"schema_version":"1.0","source":{"id":"1009.1277","kind":"arxiv","version":1}},"canonical_sha256":"ddf99cf8350fc560912aa15a33ae2955901c318b39b0514aac99047effbad73f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ddf99cf8350fc560912aa15a33ae2955901c318b39b0514aac99047effbad73f","first_computed_at":"2026-05-18T04:41:15.794486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:15.794486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KQYWDi5u+qEVP8ArX96DRkq8UXTSnGHeZqc0ozHH9eVDxKG8y2Kl+mZ3w9bBqiV6HHdLRVV0XCaCBw0vy6MpDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:15.794963Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.1277","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94260604969f1393fc1362b11c5c4af9cd4baff792b52ebdd2b906ce5704ded7","sha256:8587d86257c58a902ddb70734c47674deb9ab4470d49cef7f27db9e1098a2f96"],"state_sha256":"a2c08fbdb6f006a2da4ffdd4a18c93380865564c57aa2e5f224987bdfe4bff07"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eGbvDxqwVCLJf0OgnyIy1HcDwEwev4HHUQ1UrQzJXW8ZhYFCjaHtcFQjKqwXYWy+2FJURhu5+1Q9CYn5I7awDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:19:13.176833Z","bundle_sha256":"33ec3f96c209e7d37f110797f1d9ab6d446eb4e9bb9a446ecb448469f5d53efb"}}