{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:GEVFBLC7MTFU7UX5MFGRTPDSG6","short_pith_number":"pith:GEVFBLC7","canonical_record":{"source":{"id":"2012.02065","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2020-12-03T16:52:17Z","cross_cats_sorted":[],"title_canon_sha256":"58cca0d463b05c6396d552a34bd67c6fae9ebb8ebe7abf14bd5356e4b6f9abf3","abstract_canon_sha256":"933fe76302d3e82561f728cf42274a7ed2c20d4c9006f2d33fb49c9d5fb14b30"},"schema_version":"1.0"},"canonical_sha256":"312a50ac5f64cb4fd2fd614d19bc723787d8438b4c3b98dd775fea0641107f21","source":{"kind":"arxiv","id":"2012.02065","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.02065","created_at":"2026-07-05T01:56:52Z"},{"alias_kind":"arxiv_version","alias_value":"2012.02065v1","created_at":"2026-07-05T01:56:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.02065","created_at":"2026-07-05T01:56:52Z"},{"alias_kind":"pith_short_12","alias_value":"GEVFBLC7MTFU","created_at":"2026-07-05T01:56:52Z"},{"alias_kind":"pith_short_16","alias_value":"GEVFBLC7MTFU7UX5","created_at":"2026-07-05T01:56:52Z"},{"alias_kind":"pith_short_8","alias_value":"GEVFBLC7","created_at":"2026-07-05T01:56:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:GEVFBLC7MTFU7UX5MFGRTPDSG6","target":"record","payload":{"canonical_record":{"source":{"id":"2012.02065","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2020-12-03T16:52:17Z","cross_cats_sorted":[],"title_canon_sha256":"58cca0d463b05c6396d552a34bd67c6fae9ebb8ebe7abf14bd5356e4b6f9abf3","abstract_canon_sha256":"933fe76302d3e82561f728cf42274a7ed2c20d4c9006f2d33fb49c9d5fb14b30"},"schema_version":"1.0"},"canonical_sha256":"312a50ac5f64cb4fd2fd614d19bc723787d8438b4c3b98dd775fea0641107f21","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:56:52.851612Z","signature_b64":"yjEVdqlGmKq6zGCZTfU0mtkTKieG0Hhd24SoZxrpdkC3XOyw9mciwllErvvWZ/TdBxE2YAE53OXZrA3J8Gf4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"312a50ac5f64cb4fd2fd614d19bc723787d8438b4c3b98dd775fea0641107f21","last_reissued_at":"2026-07-05T01:56:52.851249Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:56:52.851249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2012.02065","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":"2026-07-05T01:56:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u48PDWaZFYm3LHZFXmVvDhJwKRvHH2LVn4Dcto//0wAUNq+P5ob9mS3DirUArjwDvMV4bFQsoautL/WdRWZLCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T21:07:31.393244Z"},"content_sha256":"1215cd14f0de5e7ae0e7d278c19788c07320dd96ed358a4071f6abb919fd5610","schema_version":"1.0","event_id":"sha256:1215cd14f0de5e7ae0e7d278c19788c07320dd96ed358a4071f6abb919fd5610"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:GEVFBLC7MTFU7UX5MFGRTPDSG6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniqueness of certain cylindrical tangent cones","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"G\\'abor Sz\\'ekelyhidi","submitted_at":"2020-12-03T16:52:17Z","abstract_excerpt":"We show that the cylindrical tangent cone $C\\times \\mathbf{R}$ for an area-minimizing hypersurface is unique, where $C$ is the Simons cone $C_S= C(S^3\\times S^3)$. Previously Simon proved a uniqueness result for cylindrical tangent cones that applies to a large class of cones $C$, however not to the Simons cone. The main new difficulty is that the cylindrical cone $C_S\\times \\mathbf{R}$ is not integrable, and we need to develop a suitable replacement for Simon's infinite dimensional Lojasiewicz inequality in the setting of tangent cones with non-isolated singularities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.02065","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.02065/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":"2026-07-05T01:56:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r3XqHsMq3C2LwPtDbOJVuBw057QC/4UU+ErrNABgMXs4zQ+ueSVhQDw4FsZ8rwWkWRmDzj92dN+rfrRZB7qwBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T21:07:31.393640Z"},"content_sha256":"dbbd689fef5b67041afc5d0ca4fae14d0495ddb8fa0f6e6d33a4d40f135b11c8","schema_version":"1.0","event_id":"sha256:dbbd689fef5b67041afc5d0ca4fae14d0495ddb8fa0f6e6d33a4d40f135b11c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GEVFBLC7MTFU7UX5MFGRTPDSG6/bundle.json","state_url":"https://pith.science/pith/GEVFBLC7MTFU7UX5MFGRTPDSG6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GEVFBLC7MTFU7UX5MFGRTPDSG6/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":"2026-08-11T21:07:31Z","links":{"resolver":"https://pith.science/pith/GEVFBLC7MTFU7UX5MFGRTPDSG6","bundle":"https://pith.science/pith/GEVFBLC7MTFU7UX5MFGRTPDSG6/bundle.json","state":"https://pith.science/pith/GEVFBLC7MTFU7UX5MFGRTPDSG6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GEVFBLC7MTFU7UX5MFGRTPDSG6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:GEVFBLC7MTFU7UX5MFGRTPDSG6","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":"933fe76302d3e82561f728cf42274a7ed2c20d4c9006f2d33fb49c9d5fb14b30","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2020-12-03T16:52:17Z","title_canon_sha256":"58cca0d463b05c6396d552a34bd67c6fae9ebb8ebe7abf14bd5356e4b6f9abf3"},"schema_version":"1.0","source":{"id":"2012.02065","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.02065","created_at":"2026-07-05T01:56:52Z"},{"alias_kind":"arxiv_version","alias_value":"2012.02065v1","created_at":"2026-07-05T01:56:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.02065","created_at":"2026-07-05T01:56:52Z"},{"alias_kind":"pith_short_12","alias_value":"GEVFBLC7MTFU","created_at":"2026-07-05T01:56:52Z"},{"alias_kind":"pith_short_16","alias_value":"GEVFBLC7MTFU7UX5","created_at":"2026-07-05T01:56:52Z"},{"alias_kind":"pith_short_8","alias_value":"GEVFBLC7","created_at":"2026-07-05T01:56:52Z"}],"graph_snapshots":[{"event_id":"sha256:dbbd689fef5b67041afc5d0ca4fae14d0495ddb8fa0f6e6d33a4d40f135b11c8","target":"graph","created_at":"2026-07-05T01:56:52Z","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/2012.02065/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the cylindrical tangent cone $C\\times \\mathbf{R}$ for an area-minimizing hypersurface is unique, where $C$ is the Simons cone $C_S= C(S^3\\times S^3)$. Previously Simon proved a uniqueness result for cylindrical tangent cones that applies to a large class of cones $C$, however not to the Simons cone. The main new difficulty is that the cylindrical cone $C_S\\times \\mathbf{R}$ is not integrable, and we need to develop a suitable replacement for Simon's infinite dimensional Lojasiewicz inequality in the setting of tangent cones with non-isolated singularities.","authors_text":"G\\'abor Sz\\'ekelyhidi","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2020-12-03T16:52:17Z","title":"Uniqueness of certain cylindrical tangent cones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.02065","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":"sha256:1215cd14f0de5e7ae0e7d278c19788c07320dd96ed358a4071f6abb919fd5610","target":"record","created_at":"2026-07-05T01:56:52Z","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":"933fe76302d3e82561f728cf42274a7ed2c20d4c9006f2d33fb49c9d5fb14b30","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2020-12-03T16:52:17Z","title_canon_sha256":"58cca0d463b05c6396d552a34bd67c6fae9ebb8ebe7abf14bd5356e4b6f9abf3"},"schema_version":"1.0","source":{"id":"2012.02065","kind":"arxiv","version":1}},"canonical_sha256":"312a50ac5f64cb4fd2fd614d19bc723787d8438b4c3b98dd775fea0641107f21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"312a50ac5f64cb4fd2fd614d19bc723787d8438b4c3b98dd775fea0641107f21","first_computed_at":"2026-07-05T01:56:52.851249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:56:52.851249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yjEVdqlGmKq6zGCZTfU0mtkTKieG0Hhd24SoZxrpdkC3XOyw9mciwllErvvWZ/TdBxE2YAE53OXZrA3J8Gf4DA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:56:52.851612Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.02065","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1215cd14f0de5e7ae0e7d278c19788c07320dd96ed358a4071f6abb919fd5610","sha256:dbbd689fef5b67041afc5d0ca4fae14d0495ddb8fa0f6e6d33a4d40f135b11c8"],"state_sha256":"8c157d48ebd7a3189068e34001967d1748267abeb7fdcfa0514feb1b5054d9c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/EupR4g1OrdaFEP16O+Qxcf9XXC6Euw8i9Ec7B78sXb6dn+xXNfFELquApPZXbDDCM27DIY6aXaReudgj5G0AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T21:07:31.396770Z","bundle_sha256":"62aec770f2834b1aada5d1685c6390284903e4f3fcbc29b0ae15fd6e8ab059d8"}}