{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QF37WCFTT3VW6M7XWRIUWMSKBR","short_pith_number":"pith:QF37WCFT","canonical_record":{"source":{"id":"1706.08135","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-25T16:34:56Z","cross_cats_sorted":["math.GN","math.GT","math.MG"],"title_canon_sha256":"4d307aa1c2b2c7b712293de591c78495673d73f697e3a60b16f7d119578273a9","abstract_canon_sha256":"23aa491e639bf62921569d11af4cdf7268005c10ffa2b0564cb8831416fa5f4e"},"schema_version":"1.0"},"canonical_sha256":"8177fb08b39eeb6f33f7b4514b324a0c53b45605567a90a80ca67f40acd4b3c8","source":{"kind":"arxiv","id":"1706.08135","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08135","created_at":"2026-05-17T23:40:43Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08135v3","created_at":"2026-05-17T23:40:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08135","created_at":"2026-05-17T23:40:43Z"},{"alias_kind":"pith_short_12","alias_value":"QF37WCFTT3VW","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QF37WCFTT3VW6M7X","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QF37WCFT","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QF37WCFTT3VW6M7XWRIUWMSKBR","target":"record","payload":{"canonical_record":{"source":{"id":"1706.08135","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-25T16:34:56Z","cross_cats_sorted":["math.GN","math.GT","math.MG"],"title_canon_sha256":"4d307aa1c2b2c7b712293de591c78495673d73f697e3a60b16f7d119578273a9","abstract_canon_sha256":"23aa491e639bf62921569d11af4cdf7268005c10ffa2b0564cb8831416fa5f4e"},"schema_version":"1.0"},"canonical_sha256":"8177fb08b39eeb6f33f7b4514b324a0c53b45605567a90a80ca67f40acd4b3c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:43.916870Z","signature_b64":"dY5/+xTUqi/zP+qdxrjhd2LqEWSjYxvIJ0NnHm7FAllTNWB0A3GnEQNF3vriaOp3vixHIQUn7RdY4QT9/qavDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8177fb08b39eeb6f33f7b4514b324a0c53b45605567a90a80ca67f40acd4b3c8","last_reissued_at":"2026-05-17T23:40:43.916122Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:43.916122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.08135","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zrW9q7BBPeTcWAfSZOQABEEVUlDO7vVLXPrpBwq6NKKKj58QvVDCFFgfU4vgD75GUvw2AI6y/8hE5mttaGN7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:21:47.837725Z"},"content_sha256":"cce67b164636bcebd5026d5fbeab9d9656f42e2e0575148bda37a6e61d7d5ed5","schema_version":"1.0","event_id":"sha256:cce67b164636bcebd5026d5fbeab9d9656f42e2e0575148bda37a6e61d7d5ed5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QF37WCFTT3VW6M7XWRIUWMSKBR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Centers of disks in Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.GT","math.MG"],"primary_cat":"math.DG","authors_text":"Igor Belegradek, Mohammad Ghomi","submitted_at":"2017-06-25T16:34:56Z","abstract_excerpt":"We prove the existence of a center, or continuous selection of a point, in the relative interior of $C^1$ embedded $k$-disks in Riemannian $n$-manifolds. If $k\\le 3$ the center can be made equivariant with respect to the isometries of the manifold, and under mild assumptions the same holds for $k=4=n$. By contrast, for every $n\\ge k\\ge 6$ there are examples where an equivariant center does not exist. The center can be chosen to agree with any of the classical centers defined on the set of convex compacta in the Euclidean space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08135","kind":"arxiv","version":3},"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":"2026-05-17T23:40:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rlUueYyPmCiqut2XqycX8FyA+7DiK56uxVnkuUNPwv347Lt8hJf/IU3RvlpLoOBl6LdPjSKEJQ7uxjZ2n18iCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:21:47.838073Z"},"content_sha256":"0cfd9ce3e5af5d9f568bf512ffdfd52f48f71c8308ae2800c8c0f63addb72881","schema_version":"1.0","event_id":"sha256:0cfd9ce3e5af5d9f568bf512ffdfd52f48f71c8308ae2800c8c0f63addb72881"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QF37WCFTT3VW6M7XWRIUWMSKBR/bundle.json","state_url":"https://pith.science/pith/QF37WCFTT3VW6M7XWRIUWMSKBR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QF37WCFTT3VW6M7XWRIUWMSKBR/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":"2026-06-26T08:21:47Z","links":{"resolver":"https://pith.science/pith/QF37WCFTT3VW6M7XWRIUWMSKBR","bundle":"https://pith.science/pith/QF37WCFTT3VW6M7XWRIUWMSKBR/bundle.json","state":"https://pith.science/pith/QF37WCFTT3VW6M7XWRIUWMSKBR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QF37WCFTT3VW6M7XWRIUWMSKBR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QF37WCFTT3VW6M7XWRIUWMSKBR","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":"23aa491e639bf62921569d11af4cdf7268005c10ffa2b0564cb8831416fa5f4e","cross_cats_sorted":["math.GN","math.GT","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-25T16:34:56Z","title_canon_sha256":"4d307aa1c2b2c7b712293de591c78495673d73f697e3a60b16f7d119578273a9"},"schema_version":"1.0","source":{"id":"1706.08135","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08135","created_at":"2026-05-17T23:40:43Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08135v3","created_at":"2026-05-17T23:40:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08135","created_at":"2026-05-17T23:40:43Z"},{"alias_kind":"pith_short_12","alias_value":"QF37WCFTT3VW","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QF37WCFTT3VW6M7X","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QF37WCFT","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:0cfd9ce3e5af5d9f568bf512ffdfd52f48f71c8308ae2800c8c0f63addb72881","target":"graph","created_at":"2026-05-17T23:40:43Z","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 the existence of a center, or continuous selection of a point, in the relative interior of $C^1$ embedded $k$-disks in Riemannian $n$-manifolds. If $k\\le 3$ the center can be made equivariant with respect to the isometries of the manifold, and under mild assumptions the same holds for $k=4=n$. By contrast, for every $n\\ge k\\ge 6$ there are examples where an equivariant center does not exist. The center can be chosen to agree with any of the classical centers defined on the set of convex compacta in the Euclidean space.","authors_text":"Igor Belegradek, Mohammad Ghomi","cross_cats":["math.GN","math.GT","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-25T16:34:56Z","title":"Centers of disks in Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08135","kind":"arxiv","version":3},"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:cce67b164636bcebd5026d5fbeab9d9656f42e2e0575148bda37a6e61d7d5ed5","target":"record","created_at":"2026-05-17T23:40:43Z","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":"23aa491e639bf62921569d11af4cdf7268005c10ffa2b0564cb8831416fa5f4e","cross_cats_sorted":["math.GN","math.GT","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-25T16:34:56Z","title_canon_sha256":"4d307aa1c2b2c7b712293de591c78495673d73f697e3a60b16f7d119578273a9"},"schema_version":"1.0","source":{"id":"1706.08135","kind":"arxiv","version":3}},"canonical_sha256":"8177fb08b39eeb6f33f7b4514b324a0c53b45605567a90a80ca67f40acd4b3c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8177fb08b39eeb6f33f7b4514b324a0c53b45605567a90a80ca67f40acd4b3c8","first_computed_at":"2026-05-17T23:40:43.916122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:43.916122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dY5/+xTUqi/zP+qdxrjhd2LqEWSjYxvIJ0NnHm7FAllTNWB0A3GnEQNF3vriaOp3vixHIQUn7RdY4QT9/qavDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:43.916870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.08135","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cce67b164636bcebd5026d5fbeab9d9656f42e2e0575148bda37a6e61d7d5ed5","sha256:0cfd9ce3e5af5d9f568bf512ffdfd52f48f71c8308ae2800c8c0f63addb72881"],"state_sha256":"8878a19d63cf9f48bdff36de510715b7268146be088c1b0869a4aa02ffef586f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wpX465TMwEsCLW9H40dPDo40pzCXWVQAaVxNvntCyKSfcPdmzr+OyoVgZMprwURyeyvlvO6tEa6nsxzIuSGtBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T08:21:47.840074Z","bundle_sha256":"9d1627a767c0709a0be710906f87decf631c49405d622d033366e731b279f0da"}}