{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4AEIEQPL722X7YK6HHAUAWI5NP","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":"aea636c14c1d77179f4a0fe3b7576ab0ca49f664af26179147008442270874ad","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-06T14:19:40Z","title_canon_sha256":"60899db37d3f77ef13d24c2399ddc85c70c0383a86ebe3c308074a8b08e0223c"},"schema_version":"1.0","source":{"id":"2606.08188","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08188","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08188v1","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08188","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"pith_short_12","alias_value":"4AEIEQPL722X","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"pith_short_16","alias_value":"4AEIEQPL722X7YK6","created_at":"2026-06-09T01:05:29Z"},{"alias_kind":"pith_short_8","alias_value":"4AEIEQPL","created_at":"2026-06-09T01:05:29Z"}],"graph_snapshots":[{"event_id":"sha256:9ef8b5616e5045d7592adfa0a3e03454efed4cc3c35d945c2f80902404c1d9ed","target":"graph","created_at":"2026-06-09T01:05:29Z","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/2606.08188/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Matrix completion has been extensively studied for real-valued data, but existing methods are often limited in handling categorical variables. We propose LCMC, a double-loop optimization framework for categorical matrix completion via latent factorization based on a binary tensor representation. In this setting, each categorical entry is encoded as a one-hot vector along a third tensor mode, thereby preserving its discrete, non-ordinal nature. The outer loop adaptively estimates the latent dimension by iteratively updating it with feedback from the inner loop, while the inner loop reconstructs","authors_text":"Meixia Lin, Qian Zhang","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-06T14:19:40Z","title":"Latent Structural Categorical Matrix Completion with Application to Quasispecies Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08188","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":"sha256:756dfcb637bb760cc9cd4897273c1f9aa83705b96430c6646cf95ae21d4908a3","target":"record","created_at":"2026-06-09T01:05:29Z","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":"aea636c14c1d77179f4a0fe3b7576ab0ca49f664af26179147008442270874ad","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-06T14:19:40Z","title_canon_sha256":"60899db37d3f77ef13d24c2399ddc85c70c0383a86ebe3c308074a8b08e0223c"},"schema_version":"1.0","source":{"id":"2606.08188","kind":"arxiv","version":1}},"canonical_sha256":"e0088241ebfeb57fe15e39c140591d6bc8811caad454484362e7d0bdb83a705a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0088241ebfeb57fe15e39c140591d6bc8811caad454484362e7d0bdb83a705a","first_computed_at":"2026-06-09T01:05:29.471350Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:29.471350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WHNk1IEY035RzbAlN3EI26hAlN9Y0WHP8tmeu8N8ynvbS0vuMby17nsPm7DmxmLtQj8euRwn/H3S8IYKIFxmAg==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:29.471834Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.08188","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:756dfcb637bb760cc9cd4897273c1f9aa83705b96430c6646cf95ae21d4908a3","sha256:9ef8b5616e5045d7592adfa0a3e03454efed4cc3c35d945c2f80902404c1d9ed"],"state_sha256":"f38743af5e85d2a1b9028e5e782ca9b252944481d8fccfeb72fd000220b70799"}