{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:KLRE25RWV3JJ5TVWURLG34E3W6","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":"b7e3546a994821f47c6a597b453ce1b03c86bb483064459ae42ad313c13b8a8a","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2008-07-11T11:28:30Z","title_canon_sha256":"447e575b6acfa170bdd1d6ef4463ba5b151df7131031f50edb0063f318963ddd"},"schema_version":"1.0","source":{"id":"0807.1826","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.1826","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"arxiv_version","alias_value":"0807.1826v2","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.1826","created_at":"2026-05-18T02:58:11Z"},{"alias_kind":"pith_short_12","alias_value":"KLRE25RWV3JJ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"KLRE25RWV3JJ5TVW","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"KLRE25RW","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:0842a96f2e29483e929fd82567604af4eb3629d14afb4fa519c02b5752db2d86","target":"graph","created_at":"2026-05-18T02:58:11Z","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":"We introduce the notion of quantum duplicates of an (associative, unital) algebra, motivated by the problem of constructing toy-models for quantizations of certain configuration spaces in quantum mechanics. The proposed (algebraic) model relies on the classification of factorization structures with a two-dimensional factor. In the present paper, main properties of this particular kind of structures are determined, and we present a complete description of quantum duplicates of finite set algebras. As an application, we obtain a classification (up to isomorphism) of all the algebras of dimension","authors_text":"Gabriel Navarro, Javier L\\'opez Pe\\~na, \\'Oscar Cortadellas","cross_cats":["math.RA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2008-07-11T11:28:30Z","title":"Factorization structures with a 2-dimensional factor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.1826","kind":"arxiv","version":2},"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":"sha256:2e1cf5b100a84e704c4aa07f9399680d85a13cbce19c97e685927c3591a2af81","target":"record","created_at":"2026-05-18T02:58:11Z","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":"b7e3546a994821f47c6a597b453ce1b03c86bb483064459ae42ad313c13b8a8a","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2008-07-11T11:28:30Z","title_canon_sha256":"447e575b6acfa170bdd1d6ef4463ba5b151df7131031f50edb0063f318963ddd"},"schema_version":"1.0","source":{"id":"0807.1826","kind":"arxiv","version":2}},"canonical_sha256":"52e24d7636aed29eceb6a4566df09bb7bb73d8918129e19bde86bd0a7db157bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52e24d7636aed29eceb6a4566df09bb7bb73d8918129e19bde86bd0a7db157bd","first_computed_at":"2026-05-18T02:58:11.366182Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:11.366182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wJQKEztX1StJ7DeY+WSJNgm4JnI/lMfu4j2SohlgP5k57L5Lf9fmlAwSnnYxawcIs2/+l8/mhmfukPvnWhgIBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:11.366760Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.1826","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e1cf5b100a84e704c4aa07f9399680d85a13cbce19c97e685927c3591a2af81","sha256:0842a96f2e29483e929fd82567604af4eb3629d14afb4fa519c02b5752db2d86"],"state_sha256":"870d59364cbcca6299566e90945e35ac583b0212e42a375c467da803eeca1485"}