{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:E7KJZWFZX4U2L6DC3XLEVDHF2B","short_pith_number":"pith:E7KJZWFZ","canonical_record":{"source":{"id":"2103.00588","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2021-02-28T19:01:34Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"fb47e54b2527cc3987d4f104e8377b76a5e0965adb9b93a70cb60e3aed0948ac","abstract_canon_sha256":"cd910f1626f86ef514a1f9fc112d2ae1c1815e115a44e34e7fded6ca3b6e314c"},"schema_version":"1.0"},"canonical_sha256":"27d49cd8b9bf29a5f862ddd64a8ce5d05178b51f3b6061b9dd602bbf90343dad","source":{"kind":"arxiv","id":"2103.00588","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.00588","created_at":"2026-07-05T02:19:07Z"},{"alias_kind":"arxiv_version","alias_value":"2103.00588v1","created_at":"2026-07-05T02:19:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.00588","created_at":"2026-07-05T02:19:07Z"},{"alias_kind":"pith_short_12","alias_value":"E7KJZWFZX4U2","created_at":"2026-07-05T02:19:07Z"},{"alias_kind":"pith_short_16","alias_value":"E7KJZWFZX4U2L6DC","created_at":"2026-07-05T02:19:07Z"},{"alias_kind":"pith_short_8","alias_value":"E7KJZWFZ","created_at":"2026-07-05T02:19:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:E7KJZWFZX4U2L6DC3XLEVDHF2B","target":"record","payload":{"canonical_record":{"source":{"id":"2103.00588","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2021-02-28T19:01:34Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"fb47e54b2527cc3987d4f104e8377b76a5e0965adb9b93a70cb60e3aed0948ac","abstract_canon_sha256":"cd910f1626f86ef514a1f9fc112d2ae1c1815e115a44e34e7fded6ca3b6e314c"},"schema_version":"1.0"},"canonical_sha256":"27d49cd8b9bf29a5f862ddd64a8ce5d05178b51f3b6061b9dd602bbf90343dad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:19:07.172417Z","signature_b64":"/V3NvIYLY6W4wT82g5LjEK5xG0sjwN7apu3IhnLuTaCm0qfwEm5PeTOQzHk/xSpk3ZzHD94re3znfNcTeMimAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27d49cd8b9bf29a5f862ddd64a8ce5d05178b51f3b6061b9dd602bbf90343dad","last_reissued_at":"2026-07-05T02:19:07.171920Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:19:07.171920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2103.00588","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":"2026-07-05T02:19:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RolzxPaJOcz19pTPV2j31bRL8R32qiNMI3212jCT5foSjXMzq0Lgif1BnVNTDnEOrJW42lnyVZV6ZzV6MYqsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T10:31:49.129740Z"},"content_sha256":"52d6e4f2f6930493ca5807a147d9811811185312c933fa5715cd14f6f97d956a","schema_version":"1.0","event_id":"sha256:52d6e4f2f6930493ca5807a147d9811811185312c933fa5715cd14f6f97d956a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:E7KJZWFZX4U2L6DC3XLEVDHF2B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diffusion Means and Heat Kernel on Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Benjamin Eltzner, Pernille Hansen, Stefan Sommer","submitted_at":"2021-02-28T19:01:34Z","abstract_excerpt":"We introduce diffusion means as location statistics on manifold data spaces. A diffusion mean is defined as the starting point of an isotropic diffusion with a given diffusivity. They can therefore be defined on all spaces on which a Brownian motion can be defined and numerical calculation of sample diffusion means is possible on a variety of spaces using the heat kernel expansion. We present several classes of spaces, for which the heat kernel is known and sample diffusion means can therefore be calculated. As an example, we investigate a classic data set from directional statistics, for whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.00588","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/2103.00588/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":"2026-07-05T02:19:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"itGni99nXHH7tHEcJ9LtDQYSfrbZsO8ntTbD/ATkZIXsDw9w3fwOhwE3k36s5mFDJ8mlZkiW+g1iyiZc3mZEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T10:31:49.130616Z"},"content_sha256":"b2861cc5c8ac2f236ad5c877f4fadaa4ff4068453951257658ebfcefea0ace43","schema_version":"1.0","event_id":"sha256:b2861cc5c8ac2f236ad5c877f4fadaa4ff4068453951257658ebfcefea0ace43"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E7KJZWFZX4U2L6DC3XLEVDHF2B/bundle.json","state_url":"https://pith.science/pith/E7KJZWFZX4U2L6DC3XLEVDHF2B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E7KJZWFZX4U2L6DC3XLEVDHF2B/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":"2026-08-06T10:31:49Z","links":{"resolver":"https://pith.science/pith/E7KJZWFZX4U2L6DC3XLEVDHF2B","bundle":"https://pith.science/pith/E7KJZWFZX4U2L6DC3XLEVDHF2B/bundle.json","state":"https://pith.science/pith/E7KJZWFZX4U2L6DC3XLEVDHF2B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E7KJZWFZX4U2L6DC3XLEVDHF2B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:E7KJZWFZX4U2L6DC3XLEVDHF2B","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":"cd910f1626f86ef514a1f9fc112d2ae1c1815e115a44e34e7fded6ca3b6e314c","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2021-02-28T19:01:34Z","title_canon_sha256":"fb47e54b2527cc3987d4f104e8377b76a5e0965adb9b93a70cb60e3aed0948ac"},"schema_version":"1.0","source":{"id":"2103.00588","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.00588","created_at":"2026-07-05T02:19:07Z"},{"alias_kind":"arxiv_version","alias_value":"2103.00588v1","created_at":"2026-07-05T02:19:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.00588","created_at":"2026-07-05T02:19:07Z"},{"alias_kind":"pith_short_12","alias_value":"E7KJZWFZX4U2","created_at":"2026-07-05T02:19:07Z"},{"alias_kind":"pith_short_16","alias_value":"E7KJZWFZX4U2L6DC","created_at":"2026-07-05T02:19:07Z"},{"alias_kind":"pith_short_8","alias_value":"E7KJZWFZ","created_at":"2026-07-05T02:19:07Z"}],"graph_snapshots":[{"event_id":"sha256:b2861cc5c8ac2f236ad5c877f4fadaa4ff4068453951257658ebfcefea0ace43","target":"graph","created_at":"2026-07-05T02:19:07Z","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/2103.00588/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce diffusion means as location statistics on manifold data spaces. A diffusion mean is defined as the starting point of an isotropic diffusion with a given diffusivity. They can therefore be defined on all spaces on which a Brownian motion can be defined and numerical calculation of sample diffusion means is possible on a variety of spaces using the heat kernel expansion. We present several classes of spaces, for which the heat kernel is known and sample diffusion means can therefore be calculated. As an example, we investigate a classic data set from directional statistics, for whic","authors_text":"Benjamin Eltzner, Pernille Hansen, Stefan Sommer","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2021-02-28T19:01:34Z","title":"Diffusion Means and Heat Kernel on Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.00588","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":"sha256:52d6e4f2f6930493ca5807a147d9811811185312c933fa5715cd14f6f97d956a","target":"record","created_at":"2026-07-05T02:19:07Z","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":"cd910f1626f86ef514a1f9fc112d2ae1c1815e115a44e34e7fded6ca3b6e314c","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2021-02-28T19:01:34Z","title_canon_sha256":"fb47e54b2527cc3987d4f104e8377b76a5e0965adb9b93a70cb60e3aed0948ac"},"schema_version":"1.0","source":{"id":"2103.00588","kind":"arxiv","version":1}},"canonical_sha256":"27d49cd8b9bf29a5f862ddd64a8ce5d05178b51f3b6061b9dd602bbf90343dad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27d49cd8b9bf29a5f862ddd64a8ce5d05178b51f3b6061b9dd602bbf90343dad","first_computed_at":"2026-07-05T02:19:07.171920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:19:07.171920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/V3NvIYLY6W4wT82g5LjEK5xG0sjwN7apu3IhnLuTaCm0qfwEm5PeTOQzHk/xSpk3ZzHD94re3znfNcTeMimAw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:19:07.172417Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.00588","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52d6e4f2f6930493ca5807a147d9811811185312c933fa5715cd14f6f97d956a","sha256:b2861cc5c8ac2f236ad5c877f4fadaa4ff4068453951257658ebfcefea0ace43"],"state_sha256":"a66591150567d1cb039911c0d60c1e95fed7d222fb3e7a9824ac9c216c5ea6ab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MDARvrZVsA2u9VWbQ6XlfiAy8zpLYNTWLbRkqIpshCshtok5nhk6JLpfURWgFsjaldvvL4QyI1QWCm/ldo69AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T10:31:49.138006Z","bundle_sha256":"8d0d954d05e26cfb2895773a326713a0ff080440b330bfffde59bf382c4438d8"}}