{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:NN2JHGUQUKNWO64WWF67T5MAMS","short_pith_number":"pith:NN2JHGUQ","canonical_record":{"source":{"id":"2108.06036","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-08-13T03:03:56Z","cross_cats_sorted":[],"title_canon_sha256":"d250e5cd7cf009b0d67dfa29172519ce7f262f8bb8626ed575a3333cb72e336e","abstract_canon_sha256":"d93ffa4ea678b6363aa1dc1733999c584338f0b14333ec74df75c152b105b788"},"schema_version":"1.0"},"canonical_sha256":"6b74939a90a29b677b96b17df9f58064807227df26e82da398c8c0ec2f785d23","source":{"kind":"arxiv","id":"2108.06036","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.06036","created_at":"2026-07-05T03:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"2108.06036v1","created_at":"2026-07-05T03:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.06036","created_at":"2026-07-05T03:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"NN2JHGUQUKNW","created_at":"2026-07-05T03:05:36Z"},{"alias_kind":"pith_short_16","alias_value":"NN2JHGUQUKNWO64W","created_at":"2026-07-05T03:05:36Z"},{"alias_kind":"pith_short_8","alias_value":"NN2JHGUQ","created_at":"2026-07-05T03:05:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:NN2JHGUQUKNWO64WWF67T5MAMS","target":"record","payload":{"canonical_record":{"source":{"id":"2108.06036","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-08-13T03:03:56Z","cross_cats_sorted":[],"title_canon_sha256":"d250e5cd7cf009b0d67dfa29172519ce7f262f8bb8626ed575a3333cb72e336e","abstract_canon_sha256":"d93ffa4ea678b6363aa1dc1733999c584338f0b14333ec74df75c152b105b788"},"schema_version":"1.0"},"canonical_sha256":"6b74939a90a29b677b96b17df9f58064807227df26e82da398c8c0ec2f785d23","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:05:36.900922Z","signature_b64":"0rHhWG0n094BbH7FWg0/oZAe919SPvTsWbNP7PMFLzCCrRH249UV6gRHtCjzGF1A+ydGsTK3zMsVmTOT11UyBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b74939a90a29b677b96b17df9f58064807227df26e82da398c8c0ec2f785d23","last_reissued_at":"2026-07-05T03:05:36.900544Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:05:36.900544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2108.06036","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":"2026-07-05T03:05:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JD/yvc8HbKndSEsOFjLIM0nKRE7Qe0bxrn0d3twH6ncAj5KkMYdZMoVj94zp3mxgn8Mp3vCPvZVP3tPjViIrDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T22:13:30.074876Z"},"content_sha256":"2b5e87a38328855e9a6ed60e81c7d8d419771359ca6b64efe3ece6c3314c5db7","schema_version":"1.0","event_id":"sha256:2b5e87a38328855e9a6ed60e81c7d8d419771359ca6b64efe3ece6c3314c5db7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:NN2JHGUQUKNWO64WWF67T5MAMS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Information-theoretic Perspective of Hierarchical Clustering","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Bingchen Fan, Feng Zheng, Yicheng Pan","submitted_at":"2021-08-13T03:03:56Z","abstract_excerpt":"A combinatorial cost function for hierarchical clustering was introduced by Dasgupta \\cite{dasgupta2016cost}. It has been generalized by Cohen-Addad et al. \\cite{cohen2019hierarchical} to a general form named admissible function. In this paper, we investigate hierarchical clustering from the \\emph{information-theoretic} perspective and formulate a new objective function. We also establish the relationship between these two perspectives. In algorithmic aspect, we get rid of the traditional top-down and bottom-up frameworks, and propose a new one to stratify the \\emph{sparsest} level of a cluste"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.06036","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/2108.06036/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":"2026-07-05T03:05:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p+6XkFyntlhp4VEMEUqhE5XsLxjuREbyeCNHiSAMmRHNF3Qh8sKz92vl9C1PTKjN5LPqH3+gVPTAXMjAQWcODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T22:13:30.075249Z"},"content_sha256":"97e851e5383dae6551a534c40ed5acfeb7ff7c901be1c2b325cf08f6faf69497","schema_version":"1.0","event_id":"sha256:97e851e5383dae6551a534c40ed5acfeb7ff7c901be1c2b325cf08f6faf69497"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NN2JHGUQUKNWO64WWF67T5MAMS/bundle.json","state_url":"https://pith.science/pith/NN2JHGUQUKNWO64WWF67T5MAMS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NN2JHGUQUKNWO64WWF67T5MAMS/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":"2026-08-19T22:13:30Z","links":{"resolver":"https://pith.science/pith/NN2JHGUQUKNWO64WWF67T5MAMS","bundle":"https://pith.science/pith/NN2JHGUQUKNWO64WWF67T5MAMS/bundle.json","state":"https://pith.science/pith/NN2JHGUQUKNWO64WWF67T5MAMS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NN2JHGUQUKNWO64WWF67T5MAMS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:NN2JHGUQUKNWO64WWF67T5MAMS","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":"d93ffa4ea678b6363aa1dc1733999c584338f0b14333ec74df75c152b105b788","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-08-13T03:03:56Z","title_canon_sha256":"d250e5cd7cf009b0d67dfa29172519ce7f262f8bb8626ed575a3333cb72e336e"},"schema_version":"1.0","source":{"id":"2108.06036","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.06036","created_at":"2026-07-05T03:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"2108.06036v1","created_at":"2026-07-05T03:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.06036","created_at":"2026-07-05T03:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"NN2JHGUQUKNW","created_at":"2026-07-05T03:05:36Z"},{"alias_kind":"pith_short_16","alias_value":"NN2JHGUQUKNWO64W","created_at":"2026-07-05T03:05:36Z"},{"alias_kind":"pith_short_8","alias_value":"NN2JHGUQ","created_at":"2026-07-05T03:05:36Z"}],"graph_snapshots":[{"event_id":"sha256:97e851e5383dae6551a534c40ed5acfeb7ff7c901be1c2b325cf08f6faf69497","target":"graph","created_at":"2026-07-05T03:05:36Z","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/2108.06036/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A combinatorial cost function for hierarchical clustering was introduced by Dasgupta \\cite{dasgupta2016cost}. It has been generalized by Cohen-Addad et al. \\cite{cohen2019hierarchical} to a general form named admissible function. In this paper, we investigate hierarchical clustering from the \\emph{information-theoretic} perspective and formulate a new objective function. We also establish the relationship between these two perspectives. In algorithmic aspect, we get rid of the traditional top-down and bottom-up frameworks, and propose a new one to stratify the \\emph{sparsest} level of a cluste","authors_text":"Bingchen Fan, Feng Zheng, Yicheng Pan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-08-13T03:03:56Z","title":"An Information-theoretic Perspective of Hierarchical Clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.06036","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":"sha256:2b5e87a38328855e9a6ed60e81c7d8d419771359ca6b64efe3ece6c3314c5db7","target":"record","created_at":"2026-07-05T03:05:36Z","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":"d93ffa4ea678b6363aa1dc1733999c584338f0b14333ec74df75c152b105b788","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-08-13T03:03:56Z","title_canon_sha256":"d250e5cd7cf009b0d67dfa29172519ce7f262f8bb8626ed575a3333cb72e336e"},"schema_version":"1.0","source":{"id":"2108.06036","kind":"arxiv","version":1}},"canonical_sha256":"6b74939a90a29b677b96b17df9f58064807227df26e82da398c8c0ec2f785d23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b74939a90a29b677b96b17df9f58064807227df26e82da398c8c0ec2f785d23","first_computed_at":"2026-07-05T03:05:36.900544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:05:36.900544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0rHhWG0n094BbH7FWg0/oZAe919SPvTsWbNP7PMFLzCCrRH249UV6gRHtCjzGF1A+ydGsTK3zMsVmTOT11UyBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:05:36.900922Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.06036","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b5e87a38328855e9a6ed60e81c7d8d419771359ca6b64efe3ece6c3314c5db7","sha256:97e851e5383dae6551a534c40ed5acfeb7ff7c901be1c2b325cf08f6faf69497"],"state_sha256":"db3a9a5f25d631784d7aa10c98e277f7a425ed04507ec2598328105d1de65f26"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ABZIuYwmEc7HnQHfCI/Vw0VkqfesnoVEo5+H/uheTu1sRRqBcYastQjlOiUN6R5TrQUPAr6UqWhRGXowX3IfDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T22:13:30.077592Z","bundle_sha256":"d6558477aa99efce19df061e3a81115e48139a31940d82973ca71885c99c6b36"}}