{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:74PEVXR5CT7TT3AKWS2Y3L5W6Q","short_pith_number":"pith:74PEVXR5","canonical_record":{"source":{"id":"1810.03578","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-08T16:58:52Z","cross_cats_sorted":[],"title_canon_sha256":"8c6c9664e61445648b95bf23847a448c218007fb4ccf6ccfb59aff2dde045e09","abstract_canon_sha256":"a0bf36311349a7e5a2326f235df46ff1a639ad320baf40a6a0875edf82115b5a"},"schema_version":"1.0"},"canonical_sha256":"ff1e4ade3d14ff39ec0ab4b58dafb6f433f6458b66fc38f0ef00343a8c47e0c5","source":{"kind":"arxiv","id":"1810.03578","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03578","created_at":"2026-05-17T23:43:04Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03578v1","created_at":"2026-05-17T23:43:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03578","created_at":"2026-05-17T23:43:04Z"},{"alias_kind":"pith_short_12","alias_value":"74PEVXR5CT7T","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"74PEVXR5CT7TT3AK","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"74PEVXR5","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:74PEVXR5CT7TT3AKWS2Y3L5W6Q","target":"record","payload":{"canonical_record":{"source":{"id":"1810.03578","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-08T16:58:52Z","cross_cats_sorted":[],"title_canon_sha256":"8c6c9664e61445648b95bf23847a448c218007fb4ccf6ccfb59aff2dde045e09","abstract_canon_sha256":"a0bf36311349a7e5a2326f235df46ff1a639ad320baf40a6a0875edf82115b5a"},"schema_version":"1.0"},"canonical_sha256":"ff1e4ade3d14ff39ec0ab4b58dafb6f433f6458b66fc38f0ef00343a8c47e0c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:04.517965Z","signature_b64":"KrDgf5RYdd7ADMZd258rpWfeW9gDjdwoi/5tYpzYzYTuBA5Ew3rsbt6Y350pj1LPqFCmEKTDjSqj+2tjHX6+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff1e4ade3d14ff39ec0ab4b58dafb6f433f6458b66fc38f0ef00343a8c47e0c5","last_reissued_at":"2026-05-17T23:43:04.517330Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:04.517330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.03578","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":"2026-05-17T23:43:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c23BbvrildYRUN3l52bamBnBRTywf8Bee0fTRCScYf8GfETEY/7wwgXvu5oWGYc87rRSwOwTPbYu5ytKkF7KCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:55:24.263829Z"},"content_sha256":"7da3e41c33263e00cf3f4bfcea6f1f26727c2582cb79c90642e97210e50b8f81","schema_version":"1.0","event_id":"sha256:7da3e41c33263e00cf3f4bfcea6f1f26727c2582cb79c90642e97210e50b8f81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:74PEVXR5CT7TT3AKWS2Y3L5W6Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The halfspace theorem for minimal hypersurfaces in regions bounded by minimal cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Marcos Petr\\'ucio Cavalcante, Wagner Oliveira Costa-Filho","submitted_at":"2018-10-08T16:58:52Z","abstract_excerpt":"We prove that there are no minimal hypersurfaces properly immersed in any region of the Euclidean space bounded by unstable minimal cones. We also prove the analogous result for $r$-minimal hypersurfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03578","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":"2026-05-17T23:43:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ztR2/e1Kxj2+1RJptDuE49lC3LxxyC/cpH3TX0/pjBCvRYaX2NUSvPR2P250ShHoausf/EYhQJviXLyasQIFAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:55:24.264169Z"},"content_sha256":"37cd3dc2d0cb88a04d83b52f84c8226f70b32131fcad156ff96a21863d9abd3c","schema_version":"1.0","event_id":"sha256:37cd3dc2d0cb88a04d83b52f84c8226f70b32131fcad156ff96a21863d9abd3c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/74PEVXR5CT7TT3AKWS2Y3L5W6Q/bundle.json","state_url":"https://pith.science/pith/74PEVXR5CT7TT3AKWS2Y3L5W6Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/74PEVXR5CT7TT3AKWS2Y3L5W6Q/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":"2026-06-25T18:55:24Z","links":{"resolver":"https://pith.science/pith/74PEVXR5CT7TT3AKWS2Y3L5W6Q","bundle":"https://pith.science/pith/74PEVXR5CT7TT3AKWS2Y3L5W6Q/bundle.json","state":"https://pith.science/pith/74PEVXR5CT7TT3AKWS2Y3L5W6Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/74PEVXR5CT7TT3AKWS2Y3L5W6Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:74PEVXR5CT7TT3AKWS2Y3L5W6Q","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":"a0bf36311349a7e5a2326f235df46ff1a639ad320baf40a6a0875edf82115b5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-08T16:58:52Z","title_canon_sha256":"8c6c9664e61445648b95bf23847a448c218007fb4ccf6ccfb59aff2dde045e09"},"schema_version":"1.0","source":{"id":"1810.03578","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03578","created_at":"2026-05-17T23:43:04Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03578v1","created_at":"2026-05-17T23:43:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03578","created_at":"2026-05-17T23:43:04Z"},{"alias_kind":"pith_short_12","alias_value":"74PEVXR5CT7T","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"74PEVXR5CT7TT3AK","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"74PEVXR5","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:37cd3dc2d0cb88a04d83b52f84c8226f70b32131fcad156ff96a21863d9abd3c","target":"graph","created_at":"2026-05-17T23:43:04Z","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 prove that there are no minimal hypersurfaces properly immersed in any region of the Euclidean space bounded by unstable minimal cones. We also prove the analogous result for $r$-minimal hypersurfaces.","authors_text":"Marcos Petr\\'ucio Cavalcante, Wagner Oliveira Costa-Filho","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-08T16:58:52Z","title":"The halfspace theorem for minimal hypersurfaces in regions bounded by minimal cones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03578","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":"sha256:7da3e41c33263e00cf3f4bfcea6f1f26727c2582cb79c90642e97210e50b8f81","target":"record","created_at":"2026-05-17T23:43:04Z","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":"a0bf36311349a7e5a2326f235df46ff1a639ad320baf40a6a0875edf82115b5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-08T16:58:52Z","title_canon_sha256":"8c6c9664e61445648b95bf23847a448c218007fb4ccf6ccfb59aff2dde045e09"},"schema_version":"1.0","source":{"id":"1810.03578","kind":"arxiv","version":1}},"canonical_sha256":"ff1e4ade3d14ff39ec0ab4b58dafb6f433f6458b66fc38f0ef00343a8c47e0c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff1e4ade3d14ff39ec0ab4b58dafb6f433f6458b66fc38f0ef00343a8c47e0c5","first_computed_at":"2026-05-17T23:43:04.517330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:04.517330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KrDgf5RYdd7ADMZd258rpWfeW9gDjdwoi/5tYpzYzYTuBA5Ew3rsbt6Y350pj1LPqFCmEKTDjSqj+2tjHX6+BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:04.517965Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.03578","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7da3e41c33263e00cf3f4bfcea6f1f26727c2582cb79c90642e97210e50b8f81","sha256:37cd3dc2d0cb88a04d83b52f84c8226f70b32131fcad156ff96a21863d9abd3c"],"state_sha256":"21eca6c82b9277f64878ea473d797e6319c758ac4341d61717eecd271d62527a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UTsrgrqAfuxr4BWEOgxQvLIX9D0Go07nDaeP4D+M81hXx8c6CCvRl9Z2vkF3Zxp1NPBLzHt1OkZliRKm9irPCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T18:55:24.266146Z","bundle_sha256":"1c3c8920c06782c7eeb88fb815be2f79c71a1eded76e048486781f9228535148"}}