{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UUENE5LK7365PLUKZH44XQSB5G","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":"88a2ef7670dcf3935eef43672c8f0e7dd29b695c393fe13dbf8625d10d31c650","cross_cats_sorted":["math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-08-08T21:34:15Z","title_canon_sha256":"257f3f63ae61a85f6c84e37cbc2b9e3a9594183effe65a60504e3bd973921aad"},"schema_version":"1.0","source":{"id":"1508.01957","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01957","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01957v1","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01957","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"pith_short_12","alias_value":"UUENE5LK7365","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UUENE5LK7365PLUK","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UUENE5LK","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:578cb477094fd25b611e88593c14052b5678dd2e333a9f1ddef6f2c6c7e5482f","target":"graph","created_at":"2026-05-18T00:40:01Z","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":"In hypercube approach to correlation functions in Chern-Simons theory (knot polynomials) the central role is played by the numbers of cycles, in which the link diagram is decomposed under different resolutions. Certain functions of these numbers are further interpreted as dimensions of graded spaces, associated with hypercube vertices. Finding these functions is, however, a somewhat non-trivial problem. In arXiv:1506.07516 it was suggested to solve it with the help of the matrix model technique, in the spirit of AMM/EO topological recursion. In this paper we further elaborate on this idea and ","authors_text":"A.Morozov, An.Morozov, A.Popolitov","cross_cats":["math-ph","math.GT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-08-08T21:34:15Z","title":"Matrix model and dimensions at hypercube vertices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01957","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":"sha256:04a2cd1f0158b202ab4fddaf4f99fdbdae03acf5b84a2938d146d18d973aad1a","target":"record","created_at":"2026-05-18T00:40:01Z","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":"88a2ef7670dcf3935eef43672c8f0e7dd29b695c393fe13dbf8625d10d31c650","cross_cats_sorted":["math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-08-08T21:34:15Z","title_canon_sha256":"257f3f63ae61a85f6c84e37cbc2b9e3a9594183effe65a60504e3bd973921aad"},"schema_version":"1.0","source":{"id":"1508.01957","kind":"arxiv","version":1}},"canonical_sha256":"a508d2756afefdd7ae8ac9f9cbc241e99380f85d4bf6515fe8df10c5a5dac0ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a508d2756afefdd7ae8ac9f9cbc241e99380f85d4bf6515fe8df10c5a5dac0ff","first_computed_at":"2026-05-18T00:40:01.414128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:01.414128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/cMQ3J/5MmlXKKRyTuwgUzaDcSLSae0BIcTv8+/0vQuIs5Du0gnNZ0MXxAC9L7LsaKdntWMOTuApHSsTf8qXAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:01.414680Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01957","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04a2cd1f0158b202ab4fddaf4f99fdbdae03acf5b84a2938d146d18d973aad1a","sha256:578cb477094fd25b611e88593c14052b5678dd2e333a9f1ddef6f2c6c7e5482f"],"state_sha256":"bb723072d5b1d4646abe6e30b84a1e09dd2029ad49d6001c76b427bd2b0158bb"}