{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YAWXEIYTNDOT3U2OPQZLX7EX5R","short_pith_number":"pith:YAWXEIYT","canonical_record":{"source":{"id":"1412.0341","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-01T04:05:50Z","cross_cats_sorted":[],"title_canon_sha256":"f36a2f108241b7dc53431c5b32a6fc471826c19b4e96cc1d148bf209188501c4","abstract_canon_sha256":"79e23d037a0dc6da9e1fd3667e4ff4c3ff922efdb16af0df86abc953d0e59259"},"schema_version":"1.0"},"canonical_sha256":"c02d72231368dd3dd34e7c32bbfc97ec4088571fbbf05daf6fca2a8dc6efc4ce","source":{"kind":"arxiv","id":"1412.0341","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0341","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0341v3","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0341","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"pith_short_12","alias_value":"YAWXEIYTNDOT","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YAWXEIYTNDOT3U2O","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YAWXEIYT","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YAWXEIYTNDOT3U2OPQZLX7EX5R","target":"record","payload":{"canonical_record":{"source":{"id":"1412.0341","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-01T04:05:50Z","cross_cats_sorted":[],"title_canon_sha256":"f36a2f108241b7dc53431c5b32a6fc471826c19b4e96cc1d148bf209188501c4","abstract_canon_sha256":"79e23d037a0dc6da9e1fd3667e4ff4c3ff922efdb16af0df86abc953d0e59259"},"schema_version":"1.0"},"canonical_sha256":"c02d72231368dd3dd34e7c32bbfc97ec4088571fbbf05daf6fca2a8dc6efc4ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:20.845458Z","signature_b64":"fKh0P5Sc1nUijPfBzfGGmRPftec/X/BusG0Y6CyW9UbwRiBAs70w8JUz7FA/JcGzIcPyGb44/nEhUDhCmNQSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c02d72231368dd3dd34e7c32bbfc97ec4088571fbbf05daf6fca2a8dc6efc4ce","last_reissued_at":"2026-05-18T00:48:20.844675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:20.844675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.0341","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":"2026-05-18T00:48:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3M9zkk34u/E3GeF4zWVnLMH/aWErqt1LO7eIkHuAnc5ZCe+FV55+lZ3S5g1t4c6B4IhWj+EriULZqlvb5UVhCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T00:36:51.941329Z"},"content_sha256":"5a92b46017eb9d329bda896887c1966f6f3bbcab938e2c5ae8b153db5eed670c","schema_version":"1.0","event_id":"sha256:5a92b46017eb9d329bda896887c1966f6f3bbcab938e2c5ae8b153db5eed670c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YAWXEIYTNDOT3U2OPQZLX7EX5R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The convexity radius of a Riemannian manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"James Dibble","submitted_at":"2014-12-01T04:05:50Z","abstract_excerpt":"The ratio of convexity radius over injectivity radius may be made arbitrarily small within the class of compact Riemannian manifolds of any fixed dimension at least two. This is proved using Gulliver's method of constructing manifolds with focal points but no conjugate points. The approach is suggested by a characterization of the convexity radius that resembles a classical result of Klingenberg about the injectivity radius."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0341","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":"2026-05-18T00:48:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"41jH1j8Qn+ixCfRc7ZKsWfkZaFyRgszPYd8KNqYQ+JLJWpOJtvtR74Qr5AtVQ8l+TjlG0dig1tm3FYQjrBLeDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T00:36:51.941980Z"},"content_sha256":"e544ce33708595e424063284a31f3f4548a9dcda93ad45f72c3261a57fa19c4a","schema_version":"1.0","event_id":"sha256:e544ce33708595e424063284a31f3f4548a9dcda93ad45f72c3261a57fa19c4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YAWXEIYTNDOT3U2OPQZLX7EX5R/bundle.json","state_url":"https://pith.science/pith/YAWXEIYTNDOT3U2OPQZLX7EX5R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YAWXEIYTNDOT3U2OPQZLX7EX5R/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":"2026-06-29T00:36:51Z","links":{"resolver":"https://pith.science/pith/YAWXEIYTNDOT3U2OPQZLX7EX5R","bundle":"https://pith.science/pith/YAWXEIYTNDOT3U2OPQZLX7EX5R/bundle.json","state":"https://pith.science/pith/YAWXEIYTNDOT3U2OPQZLX7EX5R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YAWXEIYTNDOT3U2OPQZLX7EX5R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YAWXEIYTNDOT3U2OPQZLX7EX5R","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":"79e23d037a0dc6da9e1fd3667e4ff4c3ff922efdb16af0df86abc953d0e59259","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-01T04:05:50Z","title_canon_sha256":"f36a2f108241b7dc53431c5b32a6fc471826c19b4e96cc1d148bf209188501c4"},"schema_version":"1.0","source":{"id":"1412.0341","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0341","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0341v3","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0341","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"pith_short_12","alias_value":"YAWXEIYTNDOT","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YAWXEIYTNDOT3U2O","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YAWXEIYT","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:e544ce33708595e424063284a31f3f4548a9dcda93ad45f72c3261a57fa19c4a","target":"graph","created_at":"2026-05-18T00:48:20Z","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":"The ratio of convexity radius over injectivity radius may be made arbitrarily small within the class of compact Riemannian manifolds of any fixed dimension at least two. This is proved using Gulliver's method of constructing manifolds with focal points but no conjugate points. The approach is suggested by a characterization of the convexity radius that resembles a classical result of Klingenberg about the injectivity radius.","authors_text":"James Dibble","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-01T04:05:50Z","title":"The convexity radius of a Riemannian manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0341","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":"sha256:5a92b46017eb9d329bda896887c1966f6f3bbcab938e2c5ae8b153db5eed670c","target":"record","created_at":"2026-05-18T00:48:20Z","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":"79e23d037a0dc6da9e1fd3667e4ff4c3ff922efdb16af0df86abc953d0e59259","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-01T04:05:50Z","title_canon_sha256":"f36a2f108241b7dc53431c5b32a6fc471826c19b4e96cc1d148bf209188501c4"},"schema_version":"1.0","source":{"id":"1412.0341","kind":"arxiv","version":3}},"canonical_sha256":"c02d72231368dd3dd34e7c32bbfc97ec4088571fbbf05daf6fca2a8dc6efc4ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c02d72231368dd3dd34e7c32bbfc97ec4088571fbbf05daf6fca2a8dc6efc4ce","first_computed_at":"2026-05-18T00:48:20.844675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:20.844675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fKh0P5Sc1nUijPfBzfGGmRPftec/X/BusG0Y6CyW9UbwRiBAs70w8JUz7FA/JcGzIcPyGb44/nEhUDhCmNQSBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:20.845458Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.0341","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a92b46017eb9d329bda896887c1966f6f3bbcab938e2c5ae8b153db5eed670c","sha256:e544ce33708595e424063284a31f3f4548a9dcda93ad45f72c3261a57fa19c4a"],"state_sha256":"50d7e7894459c6fd8b79ac363ffa75f3d3010ae3f4dc0c78de408b23df8c9499"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d1ELpZ7OJkC87Ca0tVmC9pr7F31l8S6JfGqsP2pO+Gi01k0f6+92VUYa0olySX2SAMzt6jU9ObPgpDT5IhpqCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T00:36:51.943840Z","bundle_sha256":"a56e20ecedbdf5cd44e224dc188e8b40c4c34e12882b1183093f47f58c8ed853"}}