{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:U65TLHGY24S43ISEQ6FWW6GWDV","short_pith_number":"pith:U65TLHGY","canonical_record":{"source":{"id":"1905.10139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-24T10:44:47Z","cross_cats_sorted":[],"title_canon_sha256":"b969bf4aa0c51a9a06fb8180f818f750325b3253ae3ad2648b178ea12a2ef00c","abstract_canon_sha256":"97439c924c98c34788c35c3bf1258528b2530aab9328ea62e3b711bf8a377850"},"schema_version":"1.0"},"canonical_sha256":"a7bb359cd8d725cda244878b6b78d61d7544aa9b73500d88bce783e4675cf710","source":{"kind":"arxiv","id":"1905.10139","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.10139","created_at":"2026-05-17T23:45:11Z"},{"alias_kind":"arxiv_version","alias_value":"1905.10139v1","created_at":"2026-05-17T23:45:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.10139","created_at":"2026-05-17T23:45:11Z"},{"alias_kind":"pith_short_12","alias_value":"U65TLHGY24S4","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"U65TLHGY24S43ISE","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"U65TLHGY","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:U65TLHGY24S43ISEQ6FWW6GWDV","target":"record","payload":{"canonical_record":{"source":{"id":"1905.10139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-24T10:44:47Z","cross_cats_sorted":[],"title_canon_sha256":"b969bf4aa0c51a9a06fb8180f818f750325b3253ae3ad2648b178ea12a2ef00c","abstract_canon_sha256":"97439c924c98c34788c35c3bf1258528b2530aab9328ea62e3b711bf8a377850"},"schema_version":"1.0"},"canonical_sha256":"a7bb359cd8d725cda244878b6b78d61d7544aa9b73500d88bce783e4675cf710","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:11.258587Z","signature_b64":"wVEtrwT2mjKYcl2rkdWdNP5qboescdmeiL5SC2m0/E8AvispBtovLbYJg+V35HNY5TnbRjWUPAnk/QZdZNLYCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7bb359cd8d725cda244878b6b78d61d7544aa9b73500d88bce783e4675cf710","last_reissued_at":"2026-05-17T23:45:11.257942Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:11.257942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.10139","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":"2026-05-17T23:45:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9oRWoqHBgSRLzhXuPvMcxZCd+lYxi+9Xy3+CAE1Y33/MwJ88Ms2nb+Xt8cOwq9F7VgfSC4zg+wcC2LvIJRNDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:44:53.781099Z"},"content_sha256":"e760083dfa71855a0c90916e8e752081924d5feaa9f746d9e3d86eb33e750b07","schema_version":"1.0","event_id":"sha256:e760083dfa71855a0c90916e8e752081924d5feaa9f746d9e3d86eb33e750b07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:U65TLHGY24S43ISEQ6FWW6GWDV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isoperimetric cones and minimal solutions of partial overdetermined problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filomena Pacella, Giulio Tralli","submitted_at":"2019-05-24T10:44:47Z","abstract_excerpt":"In this paper we consider a partial overdetermined mixed boundary value problem in domains inside a cone as in [18]. We show that in cones having an isoperimetric property the only domains which admit a solution and which minimize a torsional energy functional are spherical sectors centered at the vertex of the cone. We also show that cones close in the $C^{1,1}$-metric to an isoperimetric one are also isoperimetric, generalizing so a result of [1]. This is achieved by using a characterization of constant mean curvature polar graphs in cones which improves a result of [18]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10139","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":"2026-05-17T23:45:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DFZkeXVuaoOO/S6I8L6y4cnDqDrdoNyQ7x6hzfRFfUMMxu0cgWxyd97VRuHfMMH2k+MMZUovz1XJcUrv7ztDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:44:53.781837Z"},"content_sha256":"82f9b9fbf1feabf375555d62aafc5c7f1e939244a380a1f2b4a87afab3ad87ab","schema_version":"1.0","event_id":"sha256:82f9b9fbf1feabf375555d62aafc5c7f1e939244a380a1f2b4a87afab3ad87ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U65TLHGY24S43ISEQ6FWW6GWDV/bundle.json","state_url":"https://pith.science/pith/U65TLHGY24S43ISEQ6FWW6GWDV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U65TLHGY24S43ISEQ6FWW6GWDV/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":"2026-05-25T15:44:53Z","links":{"resolver":"https://pith.science/pith/U65TLHGY24S43ISEQ6FWW6GWDV","bundle":"https://pith.science/pith/U65TLHGY24S43ISEQ6FWW6GWDV/bundle.json","state":"https://pith.science/pith/U65TLHGY24S43ISEQ6FWW6GWDV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U65TLHGY24S43ISEQ6FWW6GWDV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:U65TLHGY24S43ISEQ6FWW6GWDV","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":"97439c924c98c34788c35c3bf1258528b2530aab9328ea62e3b711bf8a377850","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-24T10:44:47Z","title_canon_sha256":"b969bf4aa0c51a9a06fb8180f818f750325b3253ae3ad2648b178ea12a2ef00c"},"schema_version":"1.0","source":{"id":"1905.10139","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.10139","created_at":"2026-05-17T23:45:11Z"},{"alias_kind":"arxiv_version","alias_value":"1905.10139v1","created_at":"2026-05-17T23:45:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.10139","created_at":"2026-05-17T23:45:11Z"},{"alias_kind":"pith_short_12","alias_value":"U65TLHGY24S4","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"U65TLHGY24S43ISE","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"U65TLHGY","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:82f9b9fbf1feabf375555d62aafc5c7f1e939244a380a1f2b4a87afab3ad87ab","target":"graph","created_at":"2026-05-17T23:45:11Z","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"},"paper":{"abstract_excerpt":"In this paper we consider a partial overdetermined mixed boundary value problem in domains inside a cone as in [18]. We show that in cones having an isoperimetric property the only domains which admit a solution and which minimize a torsional energy functional are spherical sectors centered at the vertex of the cone. We also show that cones close in the $C^{1,1}$-metric to an isoperimetric one are also isoperimetric, generalizing so a result of [1]. This is achieved by using a characterization of constant mean curvature polar graphs in cones which improves a result of [18].","authors_text":"Filomena Pacella, Giulio Tralli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-24T10:44:47Z","title":"Isoperimetric cones and minimal solutions of partial overdetermined problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10139","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:e760083dfa71855a0c90916e8e752081924d5feaa9f746d9e3d86eb33e750b07","target":"record","created_at":"2026-05-17T23:45:11Z","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":"97439c924c98c34788c35c3bf1258528b2530aab9328ea62e3b711bf8a377850","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-24T10:44:47Z","title_canon_sha256":"b969bf4aa0c51a9a06fb8180f818f750325b3253ae3ad2648b178ea12a2ef00c"},"schema_version":"1.0","source":{"id":"1905.10139","kind":"arxiv","version":1}},"canonical_sha256":"a7bb359cd8d725cda244878b6b78d61d7544aa9b73500d88bce783e4675cf710","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7bb359cd8d725cda244878b6b78d61d7544aa9b73500d88bce783e4675cf710","first_computed_at":"2026-05-17T23:45:11.257942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:11.257942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wVEtrwT2mjKYcl2rkdWdNP5qboescdmeiL5SC2m0/E8AvispBtovLbYJg+V35HNY5TnbRjWUPAnk/QZdZNLYCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:11.258587Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.10139","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e760083dfa71855a0c90916e8e752081924d5feaa9f746d9e3d86eb33e750b07","sha256:82f9b9fbf1feabf375555d62aafc5c7f1e939244a380a1f2b4a87afab3ad87ab"],"state_sha256":"a313a4b0a8114efcbebf767b44a3f2cc7008686e7f7717700f32103b03bd6c75"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QlMo4msQWVzqfxuAfrAcWogdzZ9V2+N00Cn0BHO7s9XtKVOIi1k8bQscuxjRH78Qc6XNX9kzIbOqpJufoCS0Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T15:44:53.785502Z","bundle_sha256":"bba993728833d1b2aa979f0743daed2f846fa60bcab44b86597dbc25e03aa725"}}