{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SZPE2RH6J4V7KTWCI3UZYNX5TM","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":"f9e8a51a89ff388cc7802afda10c60bac1888d4c6ee4aa09b397414868e44593","cross_cats_sorted":["cond-mat.str-el"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-11-12T16:21:52Z","title_canon_sha256":"394b023c93dd4c0979328776a72105cc261275b28eeeafc9219b18a494b18ab1"},"schema_version":"1.0","source":{"id":"1811.04831","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.04831","created_at":"2026-05-17T23:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"1811.04831v4","created_at":"2026-05-17T23:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04831","created_at":"2026-05-17T23:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"SZPE2RH6J4V7","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SZPE2RH6J4V7KTWC","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SZPE2RH6","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:7dd80122148d43af65401bb008183783a26721035b760cd9562a38f8c91ec2ee","target":"graph","created_at":"2026-05-17T23:40:11Z","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 study the SYK model in the large $N$ limit beyond the replica-diagonal approximation. First we show that there are exact replica-nondiagonal solutions of the saddle point equations for $q=2$ for any finite replica number $M$. In the interacting $q=4$ case we are able to construct the numerical solutions, which are in one-to-one correspondence to the analytic solutions of the quadratic model. These solutions are singular in the $M \\to 0$ limit in both quadratic and quartic interaction cases. The calculations of the on-shell action at finite integer $M$ show that the nondiagonal replica-symme","authors_text":"Igor Volovich, Irina Aref'eva, Maria Tikhanovskaya, Mikhail Khramtsov","cross_cats":["cond-mat.str-el"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-11-12T16:21:52Z","title":"Replica-nondiagonal solutions in the SYK model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04831","kind":"arxiv","version":4},"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:b588622790ab7cdf58bc192235732f00a99da7b2401cee71478c4cef4e231af5","target":"record","created_at":"2026-05-17T23:40:11Z","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":"f9e8a51a89ff388cc7802afda10c60bac1888d4c6ee4aa09b397414868e44593","cross_cats_sorted":["cond-mat.str-el"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-11-12T16:21:52Z","title_canon_sha256":"394b023c93dd4c0979328776a72105cc261275b28eeeafc9219b18a494b18ab1"},"schema_version":"1.0","source":{"id":"1811.04831","kind":"arxiv","version":4}},"canonical_sha256":"965e4d44fe4f2bf54ec246e99c36fd9b3ca9e6b31b30b68f2f882553723ae737","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"965e4d44fe4f2bf54ec246e99c36fd9b3ca9e6b31b30b68f2f882553723ae737","first_computed_at":"2026-05-17T23:40:11.458667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:11.458667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ercv/8sF/1kSrBIiu9au5FfXZPaF6+Wy9AKgO31gfZVi5FM2LM02msc6fokWNjq4OlallsZA1LLk63WhvIBBCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:11.459556Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.04831","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b588622790ab7cdf58bc192235732f00a99da7b2401cee71478c4cef4e231af5","sha256:7dd80122148d43af65401bb008183783a26721035b760cd9562a38f8c91ec2ee"],"state_sha256":"22caea15af016f4acc3a8cb1780bdddf73f7f777f09b6674991fc58725d3d679"}