{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:FOFLE5GBY6GYDN4YVFAVHJ25H6","short_pith_number":"pith:FOFLE5GB","canonical_record":{"source":{"id":"2607.20799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-22T23:55:33Z","cross_cats_sorted":["cs.IT","math.IT","stat.ME"],"title_canon_sha256":"2bd5dc3118737b027d57cc2ecce08d15a9951784f839b971b3d2c21f467e8619","abstract_canon_sha256":"7de4cb5c9c08fd1259dd33588155c858d3d36191899f3aa1ae182039445e1079"},"schema_version":"1.0"},"canonical_sha256":"2b8ab274c1c78d81b798a94153a75d3fb59026d7f174bdc127257fa04729dcc5","source":{"kind":"arxiv","id":"2607.20799","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.20799","created_at":"2026-07-24T00:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"2607.20799v1","created_at":"2026-07-24T00:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.20799","created_at":"2026-07-24T00:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"FOFLE5GBY6GY","created_at":"2026-07-24T00:23:35Z"},{"alias_kind":"pith_short_16","alias_value":"FOFLE5GBY6GYDN4Y","created_at":"2026-07-24T00:23:35Z"},{"alias_kind":"pith_short_8","alias_value":"FOFLE5GB","created_at":"2026-07-24T00:23:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:FOFLE5GBY6GYDN4YVFAVHJ25H6","target":"record","payload":{"canonical_record":{"source":{"id":"2607.20799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-22T23:55:33Z","cross_cats_sorted":["cs.IT","math.IT","stat.ME"],"title_canon_sha256":"2bd5dc3118737b027d57cc2ecce08d15a9951784f839b971b3d2c21f467e8619","abstract_canon_sha256":"7de4cb5c9c08fd1259dd33588155c858d3d36191899f3aa1ae182039445e1079"},"schema_version":"1.0"},"canonical_sha256":"2b8ab274c1c78d81b798a94153a75d3fb59026d7f174bdc127257fa04729dcc5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-24T00:23:35.356680Z","signature_b64":"2S3xnulQVJgqtfe1Qu7gTqOrywzv+HY0D/917emim6INyLEfFU4cRfGmbYeIowhLvOvwzfiMPTrGB6btIo32Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b8ab274c1c78d81b798a94153a75d3fb59026d7f174bdc127257fa04729dcc5","last_reissued_at":"2026-07-24T00:23:35.355759Z","signature_status":"signed_v1","first_computed_at":"2026-07-24T00:23:35.355759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.20799","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":"2026-07-24T00:23:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jfLD4WuZBFUWQgfMMk5c/bib8tOFaUfZH4FSgdvbM4hUl7BJKl7Pko4Y8rTOmXg9tHazZgJNYeXrXWCxMeK4DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T05:45:39.297770Z"},"content_sha256":"72775ab4ef02252d14a144f61d1daaf4a9197ffd79b7de908355f1b344448db6","schema_version":"1.0","event_id":"sha256:72775ab4ef02252d14a144f61d1daaf4a9197ffd79b7de908355f1b344448db6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:FOFLE5GBY6GYDN4YVFAVHJ25H6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"External Clustering Validation by the Homogeneity-Parsimony Trade-off","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.ME"],"primary_cat":"cs.LG","authors_text":"Andreas Tiffeau-Mayer","submitted_at":"2026-07-22T23:55:33Z","abstract_excerpt":"Scalar metrics are often used to evaluate clusterings against known classes, but they can obscure a fundamental trade-off: clusterings should be informative about class labels while avoiding unnecessary fragmentation. Here we describe normalized scores of cluster homogeneity and parsimony that quantify this trade-off. These scores build on the information bottleneck principle, modified to not reward lossy compression. We show by example and mathematical proof that our definitions of these scores have the intuitive property of varying monotonically under cluster refinement in contrast to relate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20799","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/2607.20799/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":"2026-07-24T00:23:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZA+V/dhlkpNP453UhMU62NzplHs3Pxwjl26nnr4ZPn7DI2XY3jBl78AvHDl4vHrI6LEWJHtgimb5aoTe+5n1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T05:45:39.298307Z"},"content_sha256":"ff9f858b949ff1a5310e51236a25c4960cfaf6ecf30111b0c36f76aef5f0f3f5","schema_version":"1.0","event_id":"sha256:ff9f858b949ff1a5310e51236a25c4960cfaf6ecf30111b0c36f76aef5f0f3f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FOFLE5GBY6GYDN4YVFAVHJ25H6/bundle.json","state_url":"https://pith.science/pith/FOFLE5GBY6GYDN4YVFAVHJ25H6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FOFLE5GBY6GYDN4YVFAVHJ25H6/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":"2026-08-04T05:45:39Z","links":{"resolver":"https://pith.science/pith/FOFLE5GBY6GYDN4YVFAVHJ25H6","bundle":"https://pith.science/pith/FOFLE5GBY6GYDN4YVFAVHJ25H6/bundle.json","state":"https://pith.science/pith/FOFLE5GBY6GYDN4YVFAVHJ25H6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FOFLE5GBY6GYDN4YVFAVHJ25H6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FOFLE5GBY6GYDN4YVFAVHJ25H6","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":"7de4cb5c9c08fd1259dd33588155c858d3d36191899f3aa1ae182039445e1079","cross_cats_sorted":["cs.IT","math.IT","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-22T23:55:33Z","title_canon_sha256":"2bd5dc3118737b027d57cc2ecce08d15a9951784f839b971b3d2c21f467e8619"},"schema_version":"1.0","source":{"id":"2607.20799","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.20799","created_at":"2026-07-24T00:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"2607.20799v1","created_at":"2026-07-24T00:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.20799","created_at":"2026-07-24T00:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"FOFLE5GBY6GY","created_at":"2026-07-24T00:23:35Z"},{"alias_kind":"pith_short_16","alias_value":"FOFLE5GBY6GYDN4Y","created_at":"2026-07-24T00:23:35Z"},{"alias_kind":"pith_short_8","alias_value":"FOFLE5GB","created_at":"2026-07-24T00:23:35Z"}],"graph_snapshots":[{"event_id":"sha256:ff9f858b949ff1a5310e51236a25c4960cfaf6ecf30111b0c36f76aef5f0f3f5","target":"graph","created_at":"2026-07-24T00:23:35Z","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/2607.20799/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Scalar metrics are often used to evaluate clusterings against known classes, but they can obscure a fundamental trade-off: clusterings should be informative about class labels while avoiding unnecessary fragmentation. Here we describe normalized scores of cluster homogeneity and parsimony that quantify this trade-off. These scores build on the information bottleneck principle, modified to not reward lossy compression. We show by example and mathematical proof that our definitions of these scores have the intuitive property of varying monotonically under cluster refinement in contrast to relate","authors_text":"Andreas Tiffeau-Mayer","cross_cats":["cs.IT","math.IT","stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-22T23:55:33Z","title":"External Clustering Validation by the Homogeneity-Parsimony Trade-off"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20799","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":"sha256:72775ab4ef02252d14a144f61d1daaf4a9197ffd79b7de908355f1b344448db6","target":"record","created_at":"2026-07-24T00:23:35Z","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":"7de4cb5c9c08fd1259dd33588155c858d3d36191899f3aa1ae182039445e1079","cross_cats_sorted":["cs.IT","math.IT","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-22T23:55:33Z","title_canon_sha256":"2bd5dc3118737b027d57cc2ecce08d15a9951784f839b971b3d2c21f467e8619"},"schema_version":"1.0","source":{"id":"2607.20799","kind":"arxiv","version":1}},"canonical_sha256":"2b8ab274c1c78d81b798a94153a75d3fb59026d7f174bdc127257fa04729dcc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b8ab274c1c78d81b798a94153a75d3fb59026d7f174bdc127257fa04729dcc5","first_computed_at":"2026-07-24T00:23:35.355759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-24T00:23:35.355759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2S3xnulQVJgqtfe1Qu7gTqOrywzv+HY0D/917emim6INyLEfFU4cRfGmbYeIowhLvOvwzfiMPTrGB6btIo32Aw==","signature_status":"signed_v1","signed_at":"2026-07-24T00:23:35.356680Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.20799","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72775ab4ef02252d14a144f61d1daaf4a9197ffd79b7de908355f1b344448db6","sha256:ff9f858b949ff1a5310e51236a25c4960cfaf6ecf30111b0c36f76aef5f0f3f5"],"state_sha256":"f78946a31dd5eb4a97174ad79392a08eaf885dd1626dcd2e3f2ef7378160f5e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sWelLZfgV4p1E1LYJR5HZHREGEx5PdSLyxMRraNRStmKq9QHrcdpedq5sWFMlxf3SGvJYK8YgXAlpmV33ScUBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T05:45:39.303211Z","bundle_sha256":"9a97cdf0d1e32aa82e09dba472864ee01cc9cdcead4b1c7f6d3cb50b7714efd1"}}