{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ACNOM45ZKM2FXUE7A274BQ75ZO","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":"fab9bbdb4a306497c5c0af1dac952fad0d03867fedca077b822d9f65254dd969","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.OT","submitted_at":"2018-11-17T16:37:49Z","title_canon_sha256":"c3a5d4fd514448929fac2faff8e037c87804dc6d70771d2cdc2fda5eb275857e"},"schema_version":"1.0","source":{"id":"1811.06980","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.06980","created_at":"2026-05-17T23:49:56Z"},{"alias_kind":"arxiv_version","alias_value":"1811.06980v3","created_at":"2026-05-17T23:49:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.06980","created_at":"2026-05-17T23:49:56Z"},{"alias_kind":"pith_short_12","alias_value":"ACNOM45ZKM2F","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"ACNOM45ZKM2FXUE7","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"ACNOM45Z","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:646468468f6d0111dd2286d310d8bdd64a58c8c06ac23619dc73932919f1e415","target":"graph","created_at":"2026-05-17T23:49:56Z","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":"The paper deals with a Batch Self Organizing Map algorithm (DBSOM) for data described by distributional-valued variables. This kind of variables is characterized to take as values one-dimensional probability or frequency distributions on a numeric support. The objective function optimized in the algorithm depends on the choice of the distance measure. According to the nature of the date, the $L_2$ Wasserstein distance is proposed as one of the most suitable metrics to compare distributions. It is widely used in several contexts of analysis of distributional data. Conventional batch SOM algorit","authors_text":"Antonio Balzanella, Antonio Irpino, Francisco De Carvalho, Rosanna Verde","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.OT","submitted_at":"2018-11-17T16:37:49Z","title":"Batch Self Organizing maps for distributional data using adaptive distances"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06980","kind":"arxiv","version":3},"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":"sha256:5b25e9ff7e8691c5e499e51c396aa4bad5224974fcdbfaabff63b766f0800055","target":"record","created_at":"2026-05-17T23:49:56Z","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":"fab9bbdb4a306497c5c0af1dac952fad0d03867fedca077b822d9f65254dd969","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.OT","submitted_at":"2018-11-17T16:37:49Z","title_canon_sha256":"c3a5d4fd514448929fac2faff8e037c87804dc6d70771d2cdc2fda5eb275857e"},"schema_version":"1.0","source":{"id":"1811.06980","kind":"arxiv","version":3}},"canonical_sha256":"009ae673b953345bd09f06bfc0c3fdcb85deb69d6794b873941c65ce82b4f74b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"009ae673b953345bd09f06bfc0c3fdcb85deb69d6794b873941c65ce82b4f74b","first_computed_at":"2026-05-17T23:49:56.874748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:56.874748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J159Vm4En7PS+L4813DuhK55a+waLLBmRvzb2KoI/TbyVvsuQdqbXK1595sR+KPwVQ86uKxMehwZ9yq9oodSDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:56.875266Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.06980","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b25e9ff7e8691c5e499e51c396aa4bad5224974fcdbfaabff63b766f0800055","sha256:646468468f6d0111dd2286d310d8bdd64a58c8c06ac23619dc73932919f1e415"],"state_sha256":"6c00862f32671036e806143fe4f956a8256a0fc24a37b0c642eb9bbf48627f1b"}