{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MTM3PMQGAWSYCUF4SQ75H2WXOV","short_pith_number":"pith:MTM3PMQG","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"},"canonical_sha256":"64d9b7b20605a58150bc943fd3ead7757219cac84a947d92b3cfb6c775d016f1","source":{"kind":"arxiv","id":"1612.07145","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07145","created_at":"2026-05-18T00:49:50Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07145v2","created_at":"2026-05-18T00:49:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07145","created_at":"2026-05-18T00:49:50Z"},{"alias_kind":"pith_short_12","alias_value":"MTM3PMQGAWSY","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MTM3PMQGAWSYCUF4","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MTM3PMQG","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MTM3PMQGAWSYCUF4SQ75H2WXOV","target":"record","payload":{"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"},"canonical_sha256":"64d9b7b20605a58150bc943fd3ead7757219cac84a947d92b3cfb6c775d016f1","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"},"source_kind":"arxiv","source_id":"1612.07145","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:49:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"93JgqN8Lp3iMMkozEBUmMhZ7uYhN5qZ56fVQd1crRol1j5nDkApaU2t6nklwOWMvbjCebHyzjOaCVT8LabxRBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:31:11.058682Z"},"content_sha256":"357a0d27b95a026aeaa8dd8159d188bd9ad17a99dce55e7ca80b3cef5775114a","schema_version":"1.0","event_id":"sha256:357a0d27b95a026aeaa8dd8159d188bd9ad17a99dce55e7ca80b3cef5775114a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MTM3PMQGAWSYCUF4SQ75H2WXOV","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:49:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ld65VcvLps9Ns0rO96zDtV9+YzbI3lkDSaBIzZAfzAVs7BUhlBuT9+m1fiF26e9aGM7FtxkQpbqqx6prNytaDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:31:11.059067Z"},"content_sha256":"a26778e02ce3c61badc0b542bcadf3761bd9554bd7b0c79bfb01e6f21ed4f216","schema_version":"1.0","event_id":"sha256:a26778e02ce3c61badc0b542bcadf3761bd9554bd7b0c79bfb01e6f21ed4f216"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MTM3PMQGAWSYCUF4SQ75H2WXOV/bundle.json","state_url":"https://pith.science/pith/MTM3PMQGAWSYCUF4SQ75H2WXOV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MTM3PMQGAWSYCUF4SQ75H2WXOV/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":"2026-06-05T08:31:11Z","links":{"resolver":"https://pith.science/pith/MTM3PMQGAWSYCUF4SQ75H2WXOV","bundle":"https://pith.science/pith/MTM3PMQGAWSYCUF4SQ75H2WXOV/bundle.json","state":"https://pith.science/pith/MTM3PMQGAWSYCUF4SQ75H2WXOV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MTM3PMQGAWSYCUF4SQ75H2WXOV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MTM3PMQGAWSYCUF4SQ75H2WXOV","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":"a873dda2e36ac8044f6575e1a4963c16af75ae44de55daf66e90973ec4bb6e2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-12-21T14:35:03Z","title_canon_sha256":"62083aa62233ce67f8cec27a5cebb71fbff240617877af23097c0f69041bbd72"},"schema_version":"1.0","source":{"id":"1612.07145","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07145","created_at":"2026-05-18T00:49:50Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07145v2","created_at":"2026-05-18T00:49:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07145","created_at":"2026-05-18T00:49:50Z"},{"alias_kind":"pith_short_12","alias_value":"MTM3PMQGAWSY","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MTM3PMQGAWSYCUF4","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MTM3PMQG","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:a26778e02ce3c61badc0b542bcadf3761bd9554bd7b0c79bfb01e6f21ed4f216","target":"graph","created_at":"2026-05-18T00:49:50Z","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 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","authors_text":"V. I. Manko, Z. Seilov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-12-21T14:35:03Z","title":"The Partition Formalism and New Entropic-Information Inequalities for Real Numbers on an Example of Clebsch-Gordan Coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07145","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":"sha256:357a0d27b95a026aeaa8dd8159d188bd9ad17a99dce55e7ca80b3cef5775114a","target":"record","created_at":"2026-05-18T00:49:50Z","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":"a873dda2e36ac8044f6575e1a4963c16af75ae44de55daf66e90973ec4bb6e2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-12-21T14:35:03Z","title_canon_sha256":"62083aa62233ce67f8cec27a5cebb71fbff240617877af23097c0f69041bbd72"},"schema_version":"1.0","source":{"id":"1612.07145","kind":"arxiv","version":2}},"canonical_sha256":"64d9b7b20605a58150bc943fd3ead7757219cac84a947d92b3cfb6c775d016f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64d9b7b20605a58150bc943fd3ead7757219cac84a947d92b3cfb6c775d016f1","first_computed_at":"2026-05-18T00:49:50.822274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:50.822274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J+d/JXtOrbrQD3sT8FOh7EzjxQTpEMlKgfGhwR5WUXzfj7vXSg3oTGanwqwW44Pj29OdeJH9gji8oQp0S3H0Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:50.822818Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.07145","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:357a0d27b95a026aeaa8dd8159d188bd9ad17a99dce55e7ca80b3cef5775114a","sha256:a26778e02ce3c61badc0b542bcadf3761bd9554bd7b0c79bfb01e6f21ed4f216"],"state_sha256":"d016cc58fe63bd9400240d5c4f6fd2f6cb6225c666eca14fe7c7c67f21339364"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1GrbgTo9tNeTqigciUp4ZHJIWdUbkB+gY4ZgUwRT6JJLIvWjSstpXUBqdWEnUtYqwTAtvt92RqX/l0Vtn8dnAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T08:31:11.061196Z","bundle_sha256":"6adc163756a4414f1e9d897d8ff2cc3d5edf29fed3207c6302cab1b481c7c4c0"}}