{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SXMPTMIXJWCADHGBMLURUWOQH5","short_pith_number":"pith:SXMPTMIX","canonical_record":{"source":{"id":"1406.6577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2014-06-25T14:07:38Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"b2b06dba3c96778b68734d80395911ece69173a41d164424b4011607ed2d10d2","abstract_canon_sha256":"497de12a533d4a1eeb80da82c055c8f29d3cffcf6634be176c73fccd4fb91a08"},"schema_version":"1.0"},"canonical_sha256":"95d8f9b1174d84019cc162e91a59d03f6122e76ff19e8bb6856adcca106cb155","source":{"kind":"arxiv","id":"1406.6577","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.6577","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"arxiv_version","alias_value":"1406.6577v1","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6577","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"pith_short_12","alias_value":"SXMPTMIXJWCA","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SXMPTMIXJWCADHGB","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SXMPTMIX","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SXMPTMIXJWCADHGBMLURUWOQH5","target":"record","payload":{"canonical_record":{"source":{"id":"1406.6577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2014-06-25T14:07:38Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"b2b06dba3c96778b68734d80395911ece69173a41d164424b4011607ed2d10d2","abstract_canon_sha256":"497de12a533d4a1eeb80da82c055c8f29d3cffcf6634be176c73fccd4fb91a08"},"schema_version":"1.0"},"canonical_sha256":"95d8f9b1174d84019cc162e91a59d03f6122e76ff19e8bb6856adcca106cb155","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:03.149211Z","signature_b64":"PZLg2iitG1NAG7p1kBCIsOc6tL7g6/ML69fp4Sz8r3a8GNGSCnKIjsL6wYyBMtBkJ+hRRAUWfRDWHE7nlsldBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95d8f9b1174d84019cc162e91a59d03f6122e76ff19e8bb6856adcca106cb155","last_reissued_at":"2026-05-18T02:40:03.148762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:03.148762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.6577","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":"2026-05-18T02:40:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qlAmFhDlKnGHEmnfmry5oQ9c3pJBRXypOyMeR7mEjEp60ZjgitdnphmaLYfsXVW4Li2h/Q6d75XpXPyLa+qMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:47:53.093150Z"},"content_sha256":"e3781bffe019ae42db67fd206eb3573c517259e9293a05fbb5a90e6b91162864","schema_version":"1.0","event_id":"sha256:e3781bffe019ae42db67fd206eb3573c517259e9293a05fbb5a90e6b91162864"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SXMPTMIXJWCADHGBMLURUWOQH5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Anomalous finite size corrections in random field models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Carlo Lucibello, Federico Ricci-Tersenghi, Flaviano Morone, Giorgio Parisi, Tommaso Rizzo","submitted_at":"2014-06-25T14:07:38Z","abstract_excerpt":"The presence of a random magnetic field in ferromagnetic systems leads, in the broken phase, to an anomalous $O(\\sqrt{1/N})$ convergence of some thermodynamic quantities to their asymptotic limits. Here we show a general method, based on the replica trick, to compute analytically the $O(\\sqrt{1/N})$ finite size correction to the average free energy. We apply this method to two mean field Ising models, fully connected and random regular graphs, and compare the results to exact numerical algorithms. We argue that this behaviour is present in finite dimensional models as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6577","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":"2026-05-18T02:40:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qQnKM1xYXj0ltuyM6OGV9ymYk0Zeqlntk76+fnk4/6ohq0/D0YxnicEIiz/o+nUzPZ6mgtEMKF6M+zzoDw3iAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:47:53.093881Z"},"content_sha256":"648a8be1b909ddb6e2864bdf2582a86952146511d0d2030adbd6b39d194067ce","schema_version":"1.0","event_id":"sha256:648a8be1b909ddb6e2864bdf2582a86952146511d0d2030adbd6b39d194067ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SXMPTMIXJWCADHGBMLURUWOQH5/bundle.json","state_url":"https://pith.science/pith/SXMPTMIXJWCADHGBMLURUWOQH5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SXMPTMIXJWCADHGBMLURUWOQH5/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":"2026-05-29T17:47:53Z","links":{"resolver":"https://pith.science/pith/SXMPTMIXJWCADHGBMLURUWOQH5","bundle":"https://pith.science/pith/SXMPTMIXJWCADHGBMLURUWOQH5/bundle.json","state":"https://pith.science/pith/SXMPTMIXJWCADHGBMLURUWOQH5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SXMPTMIXJWCADHGBMLURUWOQH5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SXMPTMIXJWCADHGBMLURUWOQH5","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":"497de12a533d4a1eeb80da82c055c8f29d3cffcf6634be176c73fccd4fb91a08","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2014-06-25T14:07:38Z","title_canon_sha256":"b2b06dba3c96778b68734d80395911ece69173a41d164424b4011607ed2d10d2"},"schema_version":"1.0","source":{"id":"1406.6577","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.6577","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"arxiv_version","alias_value":"1406.6577v1","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6577","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"pith_short_12","alias_value":"SXMPTMIXJWCA","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SXMPTMIXJWCADHGB","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SXMPTMIX","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:648a8be1b909ddb6e2864bdf2582a86952146511d0d2030adbd6b39d194067ce","target":"graph","created_at":"2026-05-18T02:40:03Z","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":"The presence of a random magnetic field in ferromagnetic systems leads, in the broken phase, to an anomalous $O(\\sqrt{1/N})$ convergence of some thermodynamic quantities to their asymptotic limits. Here we show a general method, based on the replica trick, to compute analytically the $O(\\sqrt{1/N})$ finite size correction to the average free energy. We apply this method to two mean field Ising models, fully connected and random regular graphs, and compare the results to exact numerical algorithms. We argue that this behaviour is present in finite dimensional models as well.","authors_text":"Carlo Lucibello, Federico Ricci-Tersenghi, Flaviano Morone, Giorgio Parisi, Tommaso Rizzo","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2014-06-25T14:07:38Z","title":"Anomalous finite size corrections in random field models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6577","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:e3781bffe019ae42db67fd206eb3573c517259e9293a05fbb5a90e6b91162864","target":"record","created_at":"2026-05-18T02:40:03Z","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":"497de12a533d4a1eeb80da82c055c8f29d3cffcf6634be176c73fccd4fb91a08","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2014-06-25T14:07:38Z","title_canon_sha256":"b2b06dba3c96778b68734d80395911ece69173a41d164424b4011607ed2d10d2"},"schema_version":"1.0","source":{"id":"1406.6577","kind":"arxiv","version":1}},"canonical_sha256":"95d8f9b1174d84019cc162e91a59d03f6122e76ff19e8bb6856adcca106cb155","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95d8f9b1174d84019cc162e91a59d03f6122e76ff19e8bb6856adcca106cb155","first_computed_at":"2026-05-18T02:40:03.148762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:03.148762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PZLg2iitG1NAG7p1kBCIsOc6tL7g6/ML69fp4Sz8r3a8GNGSCnKIjsL6wYyBMtBkJ+hRRAUWfRDWHE7nlsldBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:03.149211Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.6577","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3781bffe019ae42db67fd206eb3573c517259e9293a05fbb5a90e6b91162864","sha256:648a8be1b909ddb6e2864bdf2582a86952146511d0d2030adbd6b39d194067ce"],"state_sha256":"b16bfa5af24438c613a557980b4cce33a485ee659083e333ad08f2169f1ca376"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YSKos8MFecSRldBPXEamVB1Zrp3i+l0VoFJW43LXJTKdcKEiEvx/YzmAbe2kJf3UbsjgPpNQXd/4CATRvBmBCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:47:53.097680Z","bundle_sha256":"5815a2c799e03ecfd1e82d32e5708a2c6ece1d4fcc9474b17245d1c1b7fa2500"}}