{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:7IDOVI5LTTLYMM3YYXBCOYETHV","short_pith_number":"pith:7IDOVI5L","canonical_record":{"source":{"id":"2103.12641","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-03-23T15:51:25Z","cross_cats_sorted":[],"title_canon_sha256":"5d282149e4c428b3e84e2a7404161e036b25140b4d297e3687d233d457819d13","abstract_canon_sha256":"0d24e173673dbd1976e242dfa959d8d5545909124f33d14372fa8dd100aff6e4"},"schema_version":"1.0"},"canonical_sha256":"fa06eaa3ab9cd7863378c5c22760933d4f7d522fb5c17edfb1b214d0fae2780a","source":{"kind":"arxiv","id":"2103.12641","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.12641","created_at":"2026-07-05T02:25:48Z"},{"alias_kind":"arxiv_version","alias_value":"2103.12641v1","created_at":"2026-07-05T02:25:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.12641","created_at":"2026-07-05T02:25:48Z"},{"alias_kind":"pith_short_12","alias_value":"7IDOVI5LTTLY","created_at":"2026-07-05T02:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"7IDOVI5LTTLYMM3Y","created_at":"2026-07-05T02:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"7IDOVI5L","created_at":"2026-07-05T02:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:7IDOVI5LTTLYMM3YYXBCOYETHV","target":"record","payload":{"canonical_record":{"source":{"id":"2103.12641","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-03-23T15:51:25Z","cross_cats_sorted":[],"title_canon_sha256":"5d282149e4c428b3e84e2a7404161e036b25140b4d297e3687d233d457819d13","abstract_canon_sha256":"0d24e173673dbd1976e242dfa959d8d5545909124f33d14372fa8dd100aff6e4"},"schema_version":"1.0"},"canonical_sha256":"fa06eaa3ab9cd7863378c5c22760933d4f7d522fb5c17edfb1b214d0fae2780a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:25:48.702918Z","signature_b64":"cQsafF1iijHjw7FSlzYXEjIH+YTrrjsFJSe8D1VBLjZlwtoCVPTKAuF7a73fTXAENlI28rmq3J5Kn4WF1NiqAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa06eaa3ab9cd7863378c5c22760933d4f7d522fb5c17edfb1b214d0fae2780a","last_reissued_at":"2026-07-05T02:25:48.702525Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:25:48.702525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2103.12641","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":"2026-07-05T02:25:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GfRQ9oAmkJVltUaUnTJGN/KFmsHMlNcyzt0Tg/1FGzTf6xti+qmggmzt14oQaRCNLfnyNGnboqKK6rCheHiUAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:22:45.485157Z"},"content_sha256":"45bc4a074267c736af8b7bfc64b565a4c9933052cfe2ec7065ccbb7946042c01","schema_version":"1.0","event_id":"sha256:45bc4a074267c736af8b7bfc64b565a4c9933052cfe2ec7065ccbb7946042c01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:7IDOVI5LTTLYMM3YYXBCOYETHV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pairwise Adjusted Mutual Information","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Denys Lazarenko, Thomas Bonald","submitted_at":"2021-03-23T15:51:25Z","abstract_excerpt":"A well-known metric for quantifying the similarity between two clusterings is the adjusted mutual information. Compared to mutual information, a corrective term based on random permutations of the labels is introduced, preventing two clusterings being similar by chance. Unfortunately, this adjustment makes the metric computationally expensive. In this paper, we propose a novel adjustment based on {pairwise} label permutations instead of full label permutations. Specifically, we consider permutations where only two samples, selected uniformly at random, exchange their labels. We show that the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.12641","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/2103.12641/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":"2026-07-05T02:25:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VHSJzhThzkjbhrGpAJw4F4hZjFj1nCrfzRwaC1TqDyDbPaG2G2pFxsLUJdN80UEBFlhjq6IMuv9Oo6zoikHGBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:22:45.485650Z"},"content_sha256":"ddc7b1cac3afca68bacba49106bd6bdeb4c6c2b08d0de2c6688830183826e17b","schema_version":"1.0","event_id":"sha256:ddc7b1cac3afca68bacba49106bd6bdeb4c6c2b08d0de2c6688830183826e17b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7IDOVI5LTTLYMM3YYXBCOYETHV/bundle.json","state_url":"https://pith.science/pith/7IDOVI5LTTLYMM3YYXBCOYETHV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7IDOVI5LTTLYMM3YYXBCOYETHV/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":"2026-08-09T07:22:45Z","links":{"resolver":"https://pith.science/pith/7IDOVI5LTTLYMM3YYXBCOYETHV","bundle":"https://pith.science/pith/7IDOVI5LTTLYMM3YYXBCOYETHV/bundle.json","state":"https://pith.science/pith/7IDOVI5LTTLYMM3YYXBCOYETHV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7IDOVI5LTTLYMM3YYXBCOYETHV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:7IDOVI5LTTLYMM3YYXBCOYETHV","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":"0d24e173673dbd1976e242dfa959d8d5545909124f33d14372fa8dd100aff6e4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-03-23T15:51:25Z","title_canon_sha256":"5d282149e4c428b3e84e2a7404161e036b25140b4d297e3687d233d457819d13"},"schema_version":"1.0","source":{"id":"2103.12641","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.12641","created_at":"2026-07-05T02:25:48Z"},{"alias_kind":"arxiv_version","alias_value":"2103.12641v1","created_at":"2026-07-05T02:25:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.12641","created_at":"2026-07-05T02:25:48Z"},{"alias_kind":"pith_short_12","alias_value":"7IDOVI5LTTLY","created_at":"2026-07-05T02:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"7IDOVI5LTTLYMM3Y","created_at":"2026-07-05T02:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"7IDOVI5L","created_at":"2026-07-05T02:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:ddc7b1cac3afca68bacba49106bd6bdeb4c6c2b08d0de2c6688830183826e17b","target":"graph","created_at":"2026-07-05T02:25:48Z","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/2103.12641/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A well-known metric for quantifying the similarity between two clusterings is the adjusted mutual information. Compared to mutual information, a corrective term based on random permutations of the labels is introduced, preventing two clusterings being similar by chance. Unfortunately, this adjustment makes the metric computationally expensive. In this paper, we propose a novel adjustment based on {pairwise} label permutations instead of full label permutations. Specifically, we consider permutations where only two samples, selected uniformly at random, exchange their labels. We show that the c","authors_text":"Denys Lazarenko, Thomas Bonald","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-03-23T15:51:25Z","title":"Pairwise Adjusted Mutual Information"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.12641","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":"sha256:45bc4a074267c736af8b7bfc64b565a4c9933052cfe2ec7065ccbb7946042c01","target":"record","created_at":"2026-07-05T02:25:48Z","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":"0d24e173673dbd1976e242dfa959d8d5545909124f33d14372fa8dd100aff6e4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-03-23T15:51:25Z","title_canon_sha256":"5d282149e4c428b3e84e2a7404161e036b25140b4d297e3687d233d457819d13"},"schema_version":"1.0","source":{"id":"2103.12641","kind":"arxiv","version":1}},"canonical_sha256":"fa06eaa3ab9cd7863378c5c22760933d4f7d522fb5c17edfb1b214d0fae2780a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa06eaa3ab9cd7863378c5c22760933d4f7d522fb5c17edfb1b214d0fae2780a","first_computed_at":"2026-07-05T02:25:48.702525Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:25:48.702525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cQsafF1iijHjw7FSlzYXEjIH+YTrrjsFJSe8D1VBLjZlwtoCVPTKAuF7a73fTXAENlI28rmq3J5Kn4WF1NiqAA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:25:48.702918Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.12641","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45bc4a074267c736af8b7bfc64b565a4c9933052cfe2ec7065ccbb7946042c01","sha256:ddc7b1cac3afca68bacba49106bd6bdeb4c6c2b08d0de2c6688830183826e17b"],"state_sha256":"d50961bf2814a0690bf8c2138736e5db1a335492df01424c8506e9d6a66c0d13"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N4fmsTtbS/+52JDR4fi9hr6i5Wjsx5+2fFI/MeZuK8n4bBUdZsStEY9VH3kyy+hCRRp8SH8vy8kKa9mnUaEXCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T07:22:45.488975Z","bundle_sha256":"87bb30b414b897f505062cda95a5ac37fc41c84d656e935c471e99ea98283e97"}}