{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3RAIW4TOUAE5D5WVZ27YQO5PHZ","short_pith_number":"pith:3RAIW4TO","canonical_record":{"source":{"id":"1510.07770","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-10-27T04:59:40Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"e25fef1aee0833ec3c5b6b8928d4e7f5b0acd53e7de9edba43d35d7dab3a2a59","abstract_canon_sha256":"4bbbbf6dbffbc28e18cad19e7facb43809b6926b19d5dcb4e03f252ed569a692"},"schema_version":"1.0"},"canonical_sha256":"dc408b726ea009d1f6d5cebf883baf3e5e44e6b7d8e24e1e101d46a7df32187c","source":{"kind":"arxiv","id":"1510.07770","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07770","created_at":"2026-05-18T01:02:21Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07770v2","created_at":"2026-05-18T01:02:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07770","created_at":"2026-05-18T01:02:21Z"},{"alias_kind":"pith_short_12","alias_value":"3RAIW4TOUAE5","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3RAIW4TOUAE5D5WV","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3RAIW4TO","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3RAIW4TOUAE5D5WVZ27YQO5PHZ","target":"record","payload":{"canonical_record":{"source":{"id":"1510.07770","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-10-27T04:59:40Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"e25fef1aee0833ec3c5b6b8928d4e7f5b0acd53e7de9edba43d35d7dab3a2a59","abstract_canon_sha256":"4bbbbf6dbffbc28e18cad19e7facb43809b6926b19d5dcb4e03f252ed569a692"},"schema_version":"1.0"},"canonical_sha256":"dc408b726ea009d1f6d5cebf883baf3e5e44e6b7d8e24e1e101d46a7df32187c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:21.165561Z","signature_b64":"TPKuZj0wZ3rtMDalOs7RN19mRo2paDrrBQ+1BHARN6hIl/dDQhiCYqyPO6Rfc28syDJTU+/y0ou0/xurAH/eBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc408b726ea009d1f6d5cebf883baf3e5e44e6b7d8e24e1e101d46a7df32187c","last_reissued_at":"2026-05-18T01:02:21.164974Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:21.164974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.07770","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":"2026-05-18T01:02:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jGNulnNNoRbc84R+7kE06qSnOLh14V4AirMBb3xqVeSdT4hdmkOhiv4kME6jYjWWYTa4Mhjb/Rsst1HkUY47Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T17:56:54.485696Z"},"content_sha256":"e7aa3ad8a85a1331c85d516ac54662bfc856fcdeebc1034a8e86e7bee8b8fce9","schema_version":"1.0","event_id":"sha256:e7aa3ad8a85a1331c85d516ac54662bfc856fcdeebc1034a8e86e7bee8b8fce9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3RAIW4TOUAE5D5WVZ27YQO5PHZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On critical exponents without Feynman diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"hep-th","authors_text":"Aninda Sinha, Kallol Sen","submitted_at":"2015-10-27T04:59:40Z","abstract_excerpt":"In order to achieve a better analytic handle on the modern conformal bootstrap program, we re-examine and extend the pioneering 1974 work of Polyakov's, which was based on consistency between the operator product expansion and unitarity. As in the bootstrap approach, this method does not depend on evaluating Feynman diagrams. We show how this approach can be used to compute the anomalous dimensions of certain operators in the $O(n)$ model at the Wilson-Fisher fixed point in $4-\\epsilon$ dimensions up to $O(\\epsilon^2)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07770","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":"2026-05-18T01:02:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bmFGhTUtki7NFO2P762YDiKQx3/M9JIHf5cCER5ZkgnxJ2j1wkzDvbUuDLLvxqjhunHKM5Nq1hhTYNU25f/XAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T17:56:54.486167Z"},"content_sha256":"f8916b2bf3997a350c733cf762e8e88a9181a29341b763ad81920f08b3149b90","schema_version":"1.0","event_id":"sha256:f8916b2bf3997a350c733cf762e8e88a9181a29341b763ad81920f08b3149b90"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3RAIW4TOUAE5D5WVZ27YQO5PHZ/bundle.json","state_url":"https://pith.science/pith/3RAIW4TOUAE5D5WVZ27YQO5PHZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3RAIW4TOUAE5D5WVZ27YQO5PHZ/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":"2026-08-15T17:56:54Z","links":{"resolver":"https://pith.science/pith/3RAIW4TOUAE5D5WVZ27YQO5PHZ","bundle":"https://pith.science/pith/3RAIW4TOUAE5D5WVZ27YQO5PHZ/bundle.json","state":"https://pith.science/pith/3RAIW4TOUAE5D5WVZ27YQO5PHZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3RAIW4TOUAE5D5WVZ27YQO5PHZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3RAIW4TOUAE5D5WVZ27YQO5PHZ","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":"4bbbbf6dbffbc28e18cad19e7facb43809b6926b19d5dcb4e03f252ed569a692","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-10-27T04:59:40Z","title_canon_sha256":"e25fef1aee0833ec3c5b6b8928d4e7f5b0acd53e7de9edba43d35d7dab3a2a59"},"schema_version":"1.0","source":{"id":"1510.07770","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07770","created_at":"2026-05-18T01:02:21Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07770v2","created_at":"2026-05-18T01:02:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07770","created_at":"2026-05-18T01:02:21Z"},{"alias_kind":"pith_short_12","alias_value":"3RAIW4TOUAE5","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3RAIW4TOUAE5D5WV","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3RAIW4TO","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:f8916b2bf3997a350c733cf762e8e88a9181a29341b763ad81920f08b3149b90","target":"graph","created_at":"2026-05-18T01:02:21Z","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 order to achieve a better analytic handle on the modern conformal bootstrap program, we re-examine and extend the pioneering 1974 work of Polyakov's, which was based on consistency between the operator product expansion and unitarity. As in the bootstrap approach, this method does not depend on evaluating Feynman diagrams. We show how this approach can be used to compute the anomalous dimensions of certain operators in the $O(n)$ model at the Wilson-Fisher fixed point in $4-\\epsilon$ dimensions up to $O(\\epsilon^2)$.","authors_text":"Aninda Sinha, Kallol Sen","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-10-27T04:59:40Z","title":"On critical exponents without Feynman diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07770","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:e7aa3ad8a85a1331c85d516ac54662bfc856fcdeebc1034a8e86e7bee8b8fce9","target":"record","created_at":"2026-05-18T01:02:21Z","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":"4bbbbf6dbffbc28e18cad19e7facb43809b6926b19d5dcb4e03f252ed569a692","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-10-27T04:59:40Z","title_canon_sha256":"e25fef1aee0833ec3c5b6b8928d4e7f5b0acd53e7de9edba43d35d7dab3a2a59"},"schema_version":"1.0","source":{"id":"1510.07770","kind":"arxiv","version":2}},"canonical_sha256":"dc408b726ea009d1f6d5cebf883baf3e5e44e6b7d8e24e1e101d46a7df32187c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc408b726ea009d1f6d5cebf883baf3e5e44e6b7d8e24e1e101d46a7df32187c","first_computed_at":"2026-05-18T01:02:21.164974Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:21.164974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TPKuZj0wZ3rtMDalOs7RN19mRo2paDrrBQ+1BHARN6hIl/dDQhiCYqyPO6Rfc28syDJTU+/y0ou0/xurAH/eBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:21.165561Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.07770","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7aa3ad8a85a1331c85d516ac54662bfc856fcdeebc1034a8e86e7bee8b8fce9","sha256:f8916b2bf3997a350c733cf762e8e88a9181a29341b763ad81920f08b3149b90"],"state_sha256":"a4c0ee424936b7755bbd233dbce216e9d69ceda654756888bf66d6dc60e63456"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k1JcDzR8C9IEi1YZUTGo6arkIyvlQuCSAaBGbab+eoBSML2MAVHUG3Uwu+rxrFKkoJFnTz0QDRd0LUshFFNpCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T17:56:54.490259Z","bundle_sha256":"72bad54f9d772125b61cd0a3585d8f4dc33916dcc31eedc6762994e5ba530f4a"}}