{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ZZDV4UHV54NX4KO5QYNIMM3PTU","short_pith_number":"pith:ZZDV4UHV","canonical_record":{"source":{"id":"1906.01507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-06-04T15:15:14Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"13a039c808b9a6e0b5bfda2494f073021156689a99e5a0b246466976cb9544f6","abstract_canon_sha256":"4837b5015247ac9a9b06666509e7de2dbad04d902b28148db6b129757dfb2e0d"},"schema_version":"1.0"},"canonical_sha256":"ce475e50f5ef1b7e29dd861a86336f9d2adb1b87a61fbf4fad23ba278a5a91f1","source":{"kind":"arxiv","id":"1906.01507","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.01507","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"arxiv_version","alias_value":"1906.01507v1","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01507","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"pith_short_12","alias_value":"ZZDV4UHV54NX","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZZDV4UHV54NX4KO5","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZZDV4UHV","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ZZDV4UHV54NX4KO5QYNIMM3PTU","target":"record","payload":{"canonical_record":{"source":{"id":"1906.01507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-06-04T15:15:14Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"13a039c808b9a6e0b5bfda2494f073021156689a99e5a0b246466976cb9544f6","abstract_canon_sha256":"4837b5015247ac9a9b06666509e7de2dbad04d902b28148db6b129757dfb2e0d"},"schema_version":"1.0"},"canonical_sha256":"ce475e50f5ef1b7e29dd861a86336f9d2adb1b87a61fbf4fad23ba278a5a91f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:16.330793Z","signature_b64":"fzODAURRl5kxW86CgvmE9gIyomXV+MBPZb48betS3vxImY1oocHynQjtvnJh4cbItWlDypBHWPBq1lWemFnXAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce475e50f5ef1b7e29dd861a86336f9d2adb1b87a61fbf4fad23ba278a5a91f1","last_reissued_at":"2026-05-17T23:44:16.330228Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:16.330228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.01507","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":"2026-05-17T23:44:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q7TLTG/EsDWYZ5aGUyD/+r3e2Exx8ZQJMJowFOxnBrq8p05FXP3tzpapwMcPv7MsjB9rtzDfVQwiWZcZ0qysCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:44:24.986950Z"},"content_sha256":"ff6ab3bd538642eeb0beb407b9a210baafe261f5a8f24589a805fe0e91c605ad","schema_version":"1.0","event_id":"sha256:ff6ab3bd538642eeb0beb407b9a210baafe261f5a8f24589a805fe0e91c605ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ZZDV4UHV54NX4KO5QYNIMM3PTU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A numerical measure of the instability of Mapper-type algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.AT","authors_text":"Francisco Belch\\'i, Jacek Brodzki, Mahesan Niranjan, Matthew Burfitt","submitted_at":"2019-06-04T15:15:14Z","abstract_excerpt":"Mapper is an unsupervised machine learning algorithm generalising the notion of clustering to obtain a geometric description of a dataset. The procedure splits the data into possibly overlapping bins which are then clustered. The output of the algorithm is a graph where nodes represent clusters and edges represent the sharing of data points between two clusters. However, several parameters must be selected before applying Mapper and the resulting graph may vary dramatically with the choice of parameters.\n  We define an intrinsic notion of Mapper instability that measures the variability of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01507","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":"2026-05-17T23:44:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RHtHDDTz2uk9KGlKduM4lljNhQ+dzafrdeEQpGo8efp5nVbQVoELwRCId9XYXU1RiAQwztWZpaxdoHnb71UTCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:44:24.987293Z"},"content_sha256":"a4e4af0059c26e70e358a9c271bf8875a384cb68eb312c2548dce8460bafa82d","schema_version":"1.0","event_id":"sha256:a4e4af0059c26e70e358a9c271bf8875a384cb68eb312c2548dce8460bafa82d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZZDV4UHV54NX4KO5QYNIMM3PTU/bundle.json","state_url":"https://pith.science/pith/ZZDV4UHV54NX4KO5QYNIMM3PTU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZZDV4UHV54NX4KO5QYNIMM3PTU/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":"2026-06-02T14:44:24Z","links":{"resolver":"https://pith.science/pith/ZZDV4UHV54NX4KO5QYNIMM3PTU","bundle":"https://pith.science/pith/ZZDV4UHV54NX4KO5QYNIMM3PTU/bundle.json","state":"https://pith.science/pith/ZZDV4UHV54NX4KO5QYNIMM3PTU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZZDV4UHV54NX4KO5QYNIMM3PTU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZZDV4UHV54NX4KO5QYNIMM3PTU","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":"4837b5015247ac9a9b06666509e7de2dbad04d902b28148db6b129757dfb2e0d","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-06-04T15:15:14Z","title_canon_sha256":"13a039c808b9a6e0b5bfda2494f073021156689a99e5a0b246466976cb9544f6"},"schema_version":"1.0","source":{"id":"1906.01507","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.01507","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"arxiv_version","alias_value":"1906.01507v1","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01507","created_at":"2026-05-17T23:44:16Z"},{"alias_kind":"pith_short_12","alias_value":"ZZDV4UHV54NX","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZZDV4UHV54NX4KO5","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZZDV4UHV","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:a4e4af0059c26e70e358a9c271bf8875a384cb68eb312c2548dce8460bafa82d","target":"graph","created_at":"2026-05-17T23:44:16Z","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":"Mapper is an unsupervised machine learning algorithm generalising the notion of clustering to obtain a geometric description of a dataset. The procedure splits the data into possibly overlapping bins which are then clustered. The output of the algorithm is a graph where nodes represent clusters and edges represent the sharing of data points between two clusters. However, several parameters must be selected before applying Mapper and the resulting graph may vary dramatically with the choice of parameters.\n  We define an intrinsic notion of Mapper instability that measures the variability of the","authors_text":"Francisco Belch\\'i, Jacek Brodzki, Mahesan Niranjan, Matthew Burfitt","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-06-04T15:15:14Z","title":"A numerical measure of the instability of Mapper-type algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01507","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:ff6ab3bd538642eeb0beb407b9a210baafe261f5a8f24589a805fe0e91c605ad","target":"record","created_at":"2026-05-17T23:44:16Z","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":"4837b5015247ac9a9b06666509e7de2dbad04d902b28148db6b129757dfb2e0d","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-06-04T15:15:14Z","title_canon_sha256":"13a039c808b9a6e0b5bfda2494f073021156689a99e5a0b246466976cb9544f6"},"schema_version":"1.0","source":{"id":"1906.01507","kind":"arxiv","version":1}},"canonical_sha256":"ce475e50f5ef1b7e29dd861a86336f9d2adb1b87a61fbf4fad23ba278a5a91f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce475e50f5ef1b7e29dd861a86336f9d2adb1b87a61fbf4fad23ba278a5a91f1","first_computed_at":"2026-05-17T23:44:16.330228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:16.330228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fzODAURRl5kxW86CgvmE9gIyomXV+MBPZb48betS3vxImY1oocHynQjtvnJh4cbItWlDypBHWPBq1lWemFnXAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:16.330793Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.01507","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff6ab3bd538642eeb0beb407b9a210baafe261f5a8f24589a805fe0e91c605ad","sha256:a4e4af0059c26e70e358a9c271bf8875a384cb68eb312c2548dce8460bafa82d"],"state_sha256":"6140eccaf94042bab6448b07c0dbb20f629e8e48280c7653e65535e3ddd90eef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gl1t9xZnImmczSYOOUR/i1Y8ZXCL2n5dlT8J3gEpcYN4nDRd1Ku+o624jMQpTOhzYWCVs0KGNof4HzhHtNAhBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:44:24.989185Z","bundle_sha256":"75f2804851a36369fffb4b0abff859c7abba8316d0856867382f9a167f228f73"}}