{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:4NGSIYWEFI6A2BHQICEZROVZHS","short_pith_number":"pith:4NGSIYWE","canonical_record":{"source":{"id":"hep-lat/0007044","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-lat","submitted_at":"2000-07-28T09:57:57Z","cross_cats_sorted":[],"title_canon_sha256":"656286daca3a494a58c582feafd23dc6b2c1742e7eb0ddf3e959c8c7582fba50","abstract_canon_sha256":"b66be3f951b4ef174fc0a5c3762dc9c387602d186238842d2aacfe74f03fa171"},"schema_version":"1.0"},"canonical_sha256":"e34d2462c42a3c0d04f0408998bab93c8bc1d0ab3d6274fb59dc5f25f0feae28","source":{"kind":"arxiv","id":"hep-lat/0007044","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-lat/0007044","created_at":"2026-05-18T02:37:20Z"},{"alias_kind":"arxiv_version","alias_value":"hep-lat/0007044v1","created_at":"2026-05-18T02:37:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-lat/0007044","created_at":"2026-05-18T02:37:20Z"},{"alias_kind":"pith_short_12","alias_value":"4NGSIYWEFI6A","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"4NGSIYWEFI6A2BHQ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"4NGSIYWE","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:4NGSIYWEFI6A2BHQICEZROVZHS","target":"record","payload":{"canonical_record":{"source":{"id":"hep-lat/0007044","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-lat","submitted_at":"2000-07-28T09:57:57Z","cross_cats_sorted":[],"title_canon_sha256":"656286daca3a494a58c582feafd23dc6b2c1742e7eb0ddf3e959c8c7582fba50","abstract_canon_sha256":"b66be3f951b4ef174fc0a5c3762dc9c387602d186238842d2aacfe74f03fa171"},"schema_version":"1.0"},"canonical_sha256":"e34d2462c42a3c0d04f0408998bab93c8bc1d0ab3d6274fb59dc5f25f0feae28","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:20.698469Z","signature_b64":"CLZUgWqkY9Tok+GetD63Iat/IhpyMpJ7tOcH/1LH6tdo57iJ7U2pY8tZ/lDRZ9zacbwDuIi6T6Ldi92PynRbAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e34d2462c42a3c0d04f0408998bab93c8bc1d0ab3d6274fb59dc5f25f0feae28","last_reissued_at":"2026-05-18T02:37:20.698080Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:20.698080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-lat/0007044","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:37:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j3HZkVOEXJ5D3AaQEgpffSJUqmwgzJdlSEbpxlJH/gRchOxHQLjxVzj45zZiGUuEaxg5dAu9YreVeqOhGIMKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:46:56.271470Z"},"content_sha256":"f63d8d5b22501160661f6123baf8a17ba5e9511550d45d9e8017b74357bad2f2","schema_version":"1.0","event_id":"sha256:f63d8d5b22501160661f6123baf8a17ba5e9511550d45d9e8017b74357bad2f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:4NGSIYWEFI6A2BHQICEZROVZHS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Operator Product Expansion on the Lattice: a Numerical Test in the Two-Dimensional Non-Linear Sigma-Model","license":"","headline":"","cross_cats":[],"primary_cat":"hep-lat","authors_text":"Andrea Montanari, Andrea Pelissetto, Sergio Caracciolo","submitted_at":"2000-07-28T09:57:57Z","abstract_excerpt":"We consider the short-distance behaviour of the product of the Noether O(N) currents in the lattice nonlinear sigma-model. We compare the numerical results with the predictions of the operator product expansion, using one-loop perturbative renormalization-group improved Wilson coefficients. We find that, even on quite small lattices (m a \\approx 1/6), the perturbative operator product expansion describes that data with an error of 5-10% in a large window 2a \\ltapprox x \\ltapprox m^{-1}. We present a detailed discussion of the possible systematic errors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-lat/0007044","kind":"arxiv","version":1},"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":"2026-05-18T02:37:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AWzxmxGPcuah771hjDhPbeRnvRUWzUkuka1ilLpDFWpEYotDB6dGQmuxjTZRD8uR7Vb6WLAXseaF5TKD1mwnCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:46:56.271815Z"},"content_sha256":"0f9f45e3f6075cc9564abe96576b5d42309608edd01bec254d3e4e8b91697654","schema_version":"1.0","event_id":"sha256:0f9f45e3f6075cc9564abe96576b5d42309608edd01bec254d3e4e8b91697654"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4NGSIYWEFI6A2BHQICEZROVZHS/bundle.json","state_url":"https://pith.science/pith/4NGSIYWEFI6A2BHQICEZROVZHS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4NGSIYWEFI6A2BHQICEZROVZHS/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":"2026-06-04T10:46:56Z","links":{"resolver":"https://pith.science/pith/4NGSIYWEFI6A2BHQICEZROVZHS","bundle":"https://pith.science/pith/4NGSIYWEFI6A2BHQICEZROVZHS/bundle.json","state":"https://pith.science/pith/4NGSIYWEFI6A2BHQICEZROVZHS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4NGSIYWEFI6A2BHQICEZROVZHS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:4NGSIYWEFI6A2BHQICEZROVZHS","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":"b66be3f951b4ef174fc0a5c3762dc9c387602d186238842d2aacfe74f03fa171","cross_cats_sorted":[],"license":"","primary_cat":"hep-lat","submitted_at":"2000-07-28T09:57:57Z","title_canon_sha256":"656286daca3a494a58c582feafd23dc6b2c1742e7eb0ddf3e959c8c7582fba50"},"schema_version":"1.0","source":{"id":"hep-lat/0007044","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-lat/0007044","created_at":"2026-05-18T02:37:20Z"},{"alias_kind":"arxiv_version","alias_value":"hep-lat/0007044v1","created_at":"2026-05-18T02:37:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-lat/0007044","created_at":"2026-05-18T02:37:20Z"},{"alias_kind":"pith_short_12","alias_value":"4NGSIYWEFI6A","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"4NGSIYWEFI6A2BHQ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"4NGSIYWE","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:0f9f45e3f6075cc9564abe96576b5d42309608edd01bec254d3e4e8b91697654","target":"graph","created_at":"2026-05-18T02:37:20Z","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 consider the short-distance behaviour of the product of the Noether O(N) currents in the lattice nonlinear sigma-model. We compare the numerical results with the predictions of the operator product expansion, using one-loop perturbative renormalization-group improved Wilson coefficients. We find that, even on quite small lattices (m a \\approx 1/6), the perturbative operator product expansion describes that data with an error of 5-10% in a large window 2a \\ltapprox x \\ltapprox m^{-1}. We present a detailed discussion of the possible systematic errors.","authors_text":"Andrea Montanari, Andrea Pelissetto, Sergio Caracciolo","cross_cats":[],"headline":"","license":"","primary_cat":"hep-lat","submitted_at":"2000-07-28T09:57:57Z","title":"Operator Product Expansion on the Lattice: a Numerical Test in the Two-Dimensional Non-Linear Sigma-Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-lat/0007044","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:f63d8d5b22501160661f6123baf8a17ba5e9511550d45d9e8017b74357bad2f2","target":"record","created_at":"2026-05-18T02:37:20Z","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":"b66be3f951b4ef174fc0a5c3762dc9c387602d186238842d2aacfe74f03fa171","cross_cats_sorted":[],"license":"","primary_cat":"hep-lat","submitted_at":"2000-07-28T09:57:57Z","title_canon_sha256":"656286daca3a494a58c582feafd23dc6b2c1742e7eb0ddf3e959c8c7582fba50"},"schema_version":"1.0","source":{"id":"hep-lat/0007044","kind":"arxiv","version":1}},"canonical_sha256":"e34d2462c42a3c0d04f0408998bab93c8bc1d0ab3d6274fb59dc5f25f0feae28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e34d2462c42a3c0d04f0408998bab93c8bc1d0ab3d6274fb59dc5f25f0feae28","first_computed_at":"2026-05-18T02:37:20.698080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:20.698080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CLZUgWqkY9Tok+GetD63Iat/IhpyMpJ7tOcH/1LH6tdo57iJ7U2pY8tZ/lDRZ9zacbwDuIi6T6Ldi92PynRbAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:20.698469Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-lat/0007044","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f63d8d5b22501160661f6123baf8a17ba5e9511550d45d9e8017b74357bad2f2","sha256:0f9f45e3f6075cc9564abe96576b5d42309608edd01bec254d3e4e8b91697654"],"state_sha256":"d413f0ef41848b93b67e54ef2e834af2c14ce93afaa2e36e3c889509fb939252"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yTmzsqENPDi5+epW7Ek4y7EBBZMXhCzR1ep1QR7WZ+dEwqLUSHQ2nigfysJe2TQ5ohkp42FMJ5nbRJkbR5WCBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T10:46:56.273666Z","bundle_sha256":"66a63df860970a9812b9dec1c4d1221f8bdc7440d8d936f25eb82e2c10dd9430"}}