{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:I7KSNQG33FR7K6BVQKMQ2KFYAB","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":"d27ca67ae635f09eda17bf15e900197316fcb1df2ad555724c98894e2042104b","cross_cats_sorted":["cond-mat.str-el"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-09-28T20:53:10Z","title_canon_sha256":"a8cbea9e3bf1a43321a3add922f54bf4a71aa8aac5e5026bebe7319ed919f5b8"},"schema_version":"1.0","source":{"id":"1609.09113","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.09113","created_at":"2026-05-18T00:39:40Z"},{"alias_kind":"arxiv_version","alias_value":"1609.09113v2","created_at":"2026-05-18T00:39:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.09113","created_at":"2026-05-18T00:39:40Z"},{"alias_kind":"pith_short_12","alias_value":"I7KSNQG33FR7","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I7KSNQG33FR7K6BV","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I7KSNQG3","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:3926be8cda0bc6c0653c6301cc37ec527f864f90bb4d6b3d69504851fd1eea79","target":"graph","created_at":"2026-05-18T00:39:40Z","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 propose formulas for the $1/N$ correction to the sphere free energy of theories with 4-fermion interactions, which are conformal for $d>2$. We also propose a formula for the scalar $O(N)$ model. Expanding these formulas in small $\\epsilon$ near various integer dimensions we find a perfect agreement with results obtained using $\\epsilon$-expansion technique. In $d=3$, the large $N$ results with the $1/N$ correction included are in good agreement with the Pade resummed $\\epsilon$-expansion.","authors_text":"Grigory Tarnopolsky","cross_cats":["cond-mat.str-el"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-09-28T20:53:10Z","title":"On Large N Expansion of the Sphere Free Energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09113","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":"sha256:455258b6adb7a1889ae4b0ca124cdca19bd8996a9d73b2fe71f9ab8b9eb7f3fc","target":"record","created_at":"2026-05-18T00:39:40Z","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":"d27ca67ae635f09eda17bf15e900197316fcb1df2ad555724c98894e2042104b","cross_cats_sorted":["cond-mat.str-el"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-09-28T20:53:10Z","title_canon_sha256":"a8cbea9e3bf1a43321a3add922f54bf4a71aa8aac5e5026bebe7319ed919f5b8"},"schema_version":"1.0","source":{"id":"1609.09113","kind":"arxiv","version":2}},"canonical_sha256":"47d526c0dbd963f5783582990d28b8004767aa3f9d47ecac24e511a79a6da874","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47d526c0dbd963f5783582990d28b8004767aa3f9d47ecac24e511a79a6da874","first_computed_at":"2026-05-18T00:39:40.147682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:40.147682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ci+QAMaTOIqPquQkR0E2LxMaK/l6JCSFgGaRFQ+biCEm07N+N4S8Fs+6RWfsMmErkhF43NIOlXt+dpYfPg7PAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:40.148481Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.09113","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:455258b6adb7a1889ae4b0ca124cdca19bd8996a9d73b2fe71f9ab8b9eb7f3fc","sha256:3926be8cda0bc6c0653c6301cc37ec527f864f90bb4d6b3d69504851fd1eea79"],"state_sha256":"883f7564a71c67eec5d8f5ab58f04ae528d0aad26c60ea7108b233c2534c2965"}