{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:MTM3PMQGAWSYCUF4SQ75H2WXOV","short_pith_number":"pith:MTM3PMQG","schema_version":"1.0","canonical_sha256":"64d9b7b20605a58150bc943fd3ead7757219cac84a947d92b3cfb6c775d016f1","source":{"kind":"arxiv","id":"1612.07145","version":2},"attestation_state":"computed","paper":{"title":"The Partition Formalism and New Entropic-Information Inequalities for Real Numbers on an Example of Clebsch-Gordan Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"V. I. Manko, Z. Seilov","submitted_at":"2016-12-21T14:35:03Z","abstract_excerpt":"We discuss the procedure of different partitions in the finite set of $N$ integer numbers and construct generic formulas for a bijective map of real numbers $s_y$, where $y=1,2,\\ldots,N$, $N=\\prod \\limits_{k=1}^{n} X_k$, and $X_k$ are positive integers, onto the set of numbers $s(y(x_1,x_2,\\ldots,x_n))$. We give the functions used to present the bijective map, namely, $y(x_1,x_2,...,x_n)$ and $x_k(y)$ in an explicit form and call them the functions detecting the hidden correlations in the system. The idea to introduce and employ the notion of \"hidden gates\" for a single qudit is proposed. We o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1612.07145","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-12-21T14:35:03Z","cross_cats_sorted":[],"title_canon_sha256":"62083aa62233ce67f8cec27a5cebb71fbff240617877af23097c0f69041bbd72","abstract_canon_sha256":"a873dda2e36ac8044f6575e1a4963c16af75ae44de55daf66e90973ec4bb6e2e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:50.822818Z","signature_b64":"J+d/JXtOrbrQD3sT8FOh7EzjxQTpEMlKgfGhwR5WUXzfj7vXSg3oTGanwqwW44Pj29OdeJH9gji8oQp0S3H0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64d9b7b20605a58150bc943fd3ead7757219cac84a947d92b3cfb6c775d016f1","last_reissued_at":"2026-05-18T00:49:50.822274Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:50.822274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Partition Formalism and New Entropic-Information Inequalities for Real Numbers on an Example of Clebsch-Gordan Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"V. I. Manko, Z. Seilov","submitted_at":"2016-12-21T14:35:03Z","abstract_excerpt":"We discuss the procedure of different partitions in the finite set of $N$ integer numbers and construct generic formulas for a bijective map of real numbers $s_y$, where $y=1,2,\\ldots,N$, $N=\\prod \\limits_{k=1}^{n} X_k$, and $X_k$ are positive integers, onto the set of numbers $s(y(x_1,x_2,\\ldots,x_n))$. We give the functions used to present the bijective map, namely, $y(x_1,x_2,...,x_n)$ and $x_k(y)$ in an explicit form and call them the functions detecting the hidden correlations in the system. The idea to introduce and employ the notion of \"hidden gates\" for a single qudit is proposed. We o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07145","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1612.07145","created_at":"2026-05-18T00:49:50.822355+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.07145v2","created_at":"2026-05-18T00:49:50.822355+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07145","created_at":"2026-05-18T00:49:50.822355+00:00"},{"alias_kind":"pith_short_12","alias_value":"MTM3PMQGAWSY","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"MTM3PMQGAWSYCUF4","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"MTM3PMQG","created_at":"2026-05-18T12:30:32.724797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MTM3PMQGAWSYCUF4SQ75H2WXOV","json":"https://pith.science/pith/MTM3PMQGAWSYCUF4SQ75H2WXOV.json","graph_json":"https://pith.science/api/pith-number/MTM3PMQGAWSYCUF4SQ75H2WXOV/graph.json","events_json":"https://pith.science/api/pith-number/MTM3PMQGAWSYCUF4SQ75H2WXOV/events.json","paper":"https://pith.science/paper/MTM3PMQG"},"agent_actions":{"view_html":"https://pith.science/pith/MTM3PMQGAWSYCUF4SQ75H2WXOV","download_json":"https://pith.science/pith/MTM3PMQGAWSYCUF4SQ75H2WXOV.json","view_paper":"https://pith.science/paper/MTM3PMQG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.07145&json=true","fetch_graph":"https://pith.science/api/pith-number/MTM3PMQGAWSYCUF4SQ75H2WXOV/graph.json","fetch_events":"https://pith.science/api/pith-number/MTM3PMQGAWSYCUF4SQ75H2WXOV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MTM3PMQGAWSYCUF4SQ75H2WXOV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MTM3PMQGAWSYCUF4SQ75H2WXOV/action/storage_attestation","attest_author":"https://pith.science/pith/MTM3PMQGAWSYCUF4SQ75H2WXOV/action/author_attestation","sign_citation":"https://pith.science/pith/MTM3PMQGAWSYCUF4SQ75H2WXOV/action/citation_signature","submit_replication":"https://pith.science/pith/MTM3PMQGAWSYCUF4SQ75H2WXOV/action/replication_record"}},"created_at":"2026-05-18T00:49:50.822355+00:00","updated_at":"2026-05-18T00:49:50.822355+00:00"}