{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:FR3VWLVMWAMQOHR4XUFGKYIDEB","short_pith_number":"pith:FR3VWLVM","canonical_record":{"source":{"id":"1911.02165","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-06T02:13:42Z","cross_cats_sorted":[],"title_canon_sha256":"f03ad0bb4799b61b829fc30c2378397d670d3bd63a1d6d4f6865b5452c0fbb63","abstract_canon_sha256":"0a79d83973a3703a901e6966f7c910e759e67a297a0ae1bbdd9ecf6d5e090298"},"schema_version":"1.0"},"canonical_sha256":"2c775b2eacb019071e3cbd0a6561032059d1ca3dccd7f11d9451c55dc9d77be9","source":{"kind":"arxiv","id":"1911.02165","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.02165","created_at":"2026-07-05T00:19:11Z"},{"alias_kind":"arxiv_version","alias_value":"1911.02165v2","created_at":"2026-07-05T00:19:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.02165","created_at":"2026-07-05T00:19:11Z"},{"alias_kind":"pith_short_12","alias_value":"FR3VWLVMWAMQ","created_at":"2026-07-05T00:19:11Z"},{"alias_kind":"pith_short_16","alias_value":"FR3VWLVMWAMQOHR4","created_at":"2026-07-05T00:19:11Z"},{"alias_kind":"pith_short_8","alias_value":"FR3VWLVM","created_at":"2026-07-05T00:19:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:FR3VWLVMWAMQOHR4XUFGKYIDEB","target":"record","payload":{"canonical_record":{"source":{"id":"1911.02165","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-06T02:13:42Z","cross_cats_sorted":[],"title_canon_sha256":"f03ad0bb4799b61b829fc30c2378397d670d3bd63a1d6d4f6865b5452c0fbb63","abstract_canon_sha256":"0a79d83973a3703a901e6966f7c910e759e67a297a0ae1bbdd9ecf6d5e090298"},"schema_version":"1.0"},"canonical_sha256":"2c775b2eacb019071e3cbd0a6561032059d1ca3dccd7f11d9451c55dc9d77be9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:19:11.278351Z","signature_b64":"kKUelOF1tt5kjNdZy5umZYv3AGZvNJDiCo84f1TiX2GLDmLSB5gKMrApS3wbNx3tZ1f3ysWFQsT5GrAP5LPoDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c775b2eacb019071e3cbd0a6561032059d1ca3dccd7f11d9451c55dc9d77be9","last_reissued_at":"2026-07-05T00:19:11.277878Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:19:11.277878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1911.02165","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:19:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e6kn3RTUx3CK5gzOFdtzDdusZiuwNgt21Q6XTg41+yVUde2ul/U3Bz0jzuf7QOlcbK/bA1BTAPt8lq4NrlhaAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T13:56:00.125494Z"},"content_sha256":"049a12cacc6696ede81e7d93ca0bd2d5d666d6cb7476c3b223a821e3afc70605","schema_version":"1.0","event_id":"sha256:049a12cacc6696ede81e7d93ca0bd2d5d666d6cb7476c3b223a821e3afc70605"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:FR3VWLVMWAMQOHR4XUFGKYIDEB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity of the free boundary for the two-phase Bernoulli problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bozhidar Velichkov, Guido De Philippis, Luca Spolaor","submitted_at":"2019-11-06T02:13:42Z","abstract_excerpt":"We prove a regularity theorem for the free boundary of minimizers of the two-phase Bernoulli problem, completing the analysis started by Alt, Caffarelli and Friedman in the 80s. As a consequence, we also show regularity of minimizers of the multiphase spectral optimization problem for the principal eigenvalue of the Dirichlet Laplacian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.02165","kind":"arxiv","version":2},"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/1911.02165/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":"2026-07-05T00:19:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EVFe0WJSR6Z/BlB7xypbjDk32qAWW0VDJxHuagyDia/hS8YQdDvcFlg/k+dWaSkPMSF1wcygYYBef7F+JiqRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T13:56:00.125835Z"},"content_sha256":"a98663f1c1cd68c7ca55aac244eb2dd769b9a552885bb165e8ba6cfab2867ad3","schema_version":"1.0","event_id":"sha256:a98663f1c1cd68c7ca55aac244eb2dd769b9a552885bb165e8ba6cfab2867ad3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FR3VWLVMWAMQOHR4XUFGKYIDEB/bundle.json","state_url":"https://pith.science/pith/FR3VWLVMWAMQOHR4XUFGKYIDEB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FR3VWLVMWAMQOHR4XUFGKYIDEB/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":"2026-08-06T13:56:00Z","links":{"resolver":"https://pith.science/pith/FR3VWLVMWAMQOHR4XUFGKYIDEB","bundle":"https://pith.science/pith/FR3VWLVMWAMQOHR4XUFGKYIDEB/bundle.json","state":"https://pith.science/pith/FR3VWLVMWAMQOHR4XUFGKYIDEB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FR3VWLVMWAMQOHR4XUFGKYIDEB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FR3VWLVMWAMQOHR4XUFGKYIDEB","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":"0a79d83973a3703a901e6966f7c910e759e67a297a0ae1bbdd9ecf6d5e090298","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-06T02:13:42Z","title_canon_sha256":"f03ad0bb4799b61b829fc30c2378397d670d3bd63a1d6d4f6865b5452c0fbb63"},"schema_version":"1.0","source":{"id":"1911.02165","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.02165","created_at":"2026-07-05T00:19:11Z"},{"alias_kind":"arxiv_version","alias_value":"1911.02165v2","created_at":"2026-07-05T00:19:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.02165","created_at":"2026-07-05T00:19:11Z"},{"alias_kind":"pith_short_12","alias_value":"FR3VWLVMWAMQ","created_at":"2026-07-05T00:19:11Z"},{"alias_kind":"pith_short_16","alias_value":"FR3VWLVMWAMQOHR4","created_at":"2026-07-05T00:19:11Z"},{"alias_kind":"pith_short_8","alias_value":"FR3VWLVM","created_at":"2026-07-05T00:19:11Z"}],"graph_snapshots":[{"event_id":"sha256:a98663f1c1cd68c7ca55aac244eb2dd769b9a552885bb165e8ba6cfab2867ad3","target":"graph","created_at":"2026-07-05T00:19:11Z","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/1911.02165/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a regularity theorem for the free boundary of minimizers of the two-phase Bernoulli problem, completing the analysis started by Alt, Caffarelli and Friedman in the 80s. As a consequence, we also show regularity of minimizers of the multiphase spectral optimization problem for the principal eigenvalue of the Dirichlet Laplacian.","authors_text":"Bozhidar Velichkov, Guido De Philippis, Luca Spolaor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-06T02:13:42Z","title":"Regularity of the free boundary for the two-phase Bernoulli problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.02165","kind":"arxiv","version":2},"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":"sha256:049a12cacc6696ede81e7d93ca0bd2d5d666d6cb7476c3b223a821e3afc70605","target":"record","created_at":"2026-07-05T00:19:11Z","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":"0a79d83973a3703a901e6966f7c910e759e67a297a0ae1bbdd9ecf6d5e090298","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-06T02:13:42Z","title_canon_sha256":"f03ad0bb4799b61b829fc30c2378397d670d3bd63a1d6d4f6865b5452c0fbb63"},"schema_version":"1.0","source":{"id":"1911.02165","kind":"arxiv","version":2}},"canonical_sha256":"2c775b2eacb019071e3cbd0a6561032059d1ca3dccd7f11d9451c55dc9d77be9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c775b2eacb019071e3cbd0a6561032059d1ca3dccd7f11d9451c55dc9d77be9","first_computed_at":"2026-07-05T00:19:11.277878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:19:11.277878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kKUelOF1tt5kjNdZy5umZYv3AGZvNJDiCo84f1TiX2GLDmLSB5gKMrApS3wbNx3tZ1f3ysWFQsT5GrAP5LPoDw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:19:11.278351Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.02165","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:049a12cacc6696ede81e7d93ca0bd2d5d666d6cb7476c3b223a821e3afc70605","sha256:a98663f1c1cd68c7ca55aac244eb2dd769b9a552885bb165e8ba6cfab2867ad3"],"state_sha256":"108815c647f79896634f9376c9a15c783e70b6fcb777197b93b8d80728a9ba3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uUwSnCaBUMl/x1tRH8seo0WoJCOf/QXFlmwdvp1GcCySuRwvVzBQbbrXxEasNH8o4wIlfZlwt2wKWcirsCYDDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T13:56:00.129356Z","bundle_sha256":"9c0d77fd86a0fe4c0b6a673c5a58e669a137da1d7f3b765658832766e2d70c1d"}}