{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IKLS3HMWNC53CPWV2RJ4XGDCHD","short_pith_number":"pith:IKLS3HMW","canonical_record":{"source":{"id":"1509.07071","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T17:37:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8dcea84fe4a14c6d50157af84cf11e22624828ac05fb21efdf2af6d55c44db17","abstract_canon_sha256":"08c1e9cdc777d35059d0891d15e6f29b596287eb9b471f396737ede958d3d5c8"},"schema_version":"1.0"},"canonical_sha256":"42972d9d9668bbb13ed5d453cb986238d1bc8a4d9b4f8c5839076fe55096175d","source":{"kind":"arxiv","id":"1509.07071","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07071","created_at":"2026-05-18T00:42:49Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07071v2","created_at":"2026-05-18T00:42:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07071","created_at":"2026-05-18T00:42:49Z"},{"alias_kind":"pith_short_12","alias_value":"IKLS3HMWNC53","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IKLS3HMWNC53CPWV","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IKLS3HMW","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IKLS3HMWNC53CPWV2RJ4XGDCHD","target":"record","payload":{"canonical_record":{"source":{"id":"1509.07071","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T17:37:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8dcea84fe4a14c6d50157af84cf11e22624828ac05fb21efdf2af6d55c44db17","abstract_canon_sha256":"08c1e9cdc777d35059d0891d15e6f29b596287eb9b471f396737ede958d3d5c8"},"schema_version":"1.0"},"canonical_sha256":"42972d9d9668bbb13ed5d453cb986238d1bc8a4d9b4f8c5839076fe55096175d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:49.083213Z","signature_b64":"4bZrCOdldhNR+Mv8rvakF8CTX6NyzN/R/3h+Wy5XYgDvmtm5N5PIeHN3ZchyG0LIVByrxNAcywHGDmx2WlHDBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42972d9d9668bbb13ed5d453cb986238d1bc8a4d9b4f8c5839076fe55096175d","last_reissued_at":"2026-05-18T00:42:49.082444Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:49.082444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.07071","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":"2026-05-18T00:42:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6leanV4Xm5ocqhbgE/atYAYHJirmeWWLJy+OUJrCRuZJ6lrlQ49t6/6QeVYYuIbRviJ0P2O0dtQq2n0MnTV8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:25:16.928285Z"},"content_sha256":"5ec90d1ab32ad5218d90ab0edf18ad2489df1d4b31a4bf23a8db55a67c7aded2","schema_version":"1.0","event_id":"sha256:5ec90d1ab32ad5218d90ab0edf18ad2489df1d4b31a4bf23a8db55a67c7aded2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IKLS3HMWNC53CPWV2RJ4XGDCHD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fluctuations of the free energy in the mixed $p$-spin models with external field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Dmitry Panchenko, Partha Dey, Wei-Kuo Chen","submitted_at":"2015-09-23T17:37:28Z","abstract_excerpt":"We show that the free energy in the mixed $p$-spin models of spin glasses does not superconcentrate in the presence of external field, which means that its variance is of the order suggested by the Poincar\\'e inequality. This complements the result of Chatterjee who showed that the free energy superconcentrates when there is no external field. For models without odd $p$-spin interactions for $p\\geq 3$, we prove the central limit theorem for the free energy at any temperature and give an explicit formula for the limiting variance. Although we only deal with the case of Ising spins, all our resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07071","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":"2026-05-18T00:42:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6JLK8QvTRTlpNSTsNK0bS3X0jhlHn3jTQqxTjJNTsPISsajio6MhVQtbU7uE0SrMmQWePp7AybhJghLN+wbGBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:25:16.928651Z"},"content_sha256":"b3204acced7131fb2df81702371ad662df678764d51ee12a935ed1f094f42d84","schema_version":"1.0","event_id":"sha256:b3204acced7131fb2df81702371ad662df678764d51ee12a935ed1f094f42d84"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IKLS3HMWNC53CPWV2RJ4XGDCHD/bundle.json","state_url":"https://pith.science/pith/IKLS3HMWNC53CPWV2RJ4XGDCHD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IKLS3HMWNC53CPWV2RJ4XGDCHD/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":"2026-06-04T20:25:16Z","links":{"resolver":"https://pith.science/pith/IKLS3HMWNC53CPWV2RJ4XGDCHD","bundle":"https://pith.science/pith/IKLS3HMWNC53CPWV2RJ4XGDCHD/bundle.json","state":"https://pith.science/pith/IKLS3HMWNC53CPWV2RJ4XGDCHD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IKLS3HMWNC53CPWV2RJ4XGDCHD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IKLS3HMWNC53CPWV2RJ4XGDCHD","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":"08c1e9cdc777d35059d0891d15e6f29b596287eb9b471f396737ede958d3d5c8","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T17:37:28Z","title_canon_sha256":"8dcea84fe4a14c6d50157af84cf11e22624828ac05fb21efdf2af6d55c44db17"},"schema_version":"1.0","source":{"id":"1509.07071","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07071","created_at":"2026-05-18T00:42:49Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07071v2","created_at":"2026-05-18T00:42:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07071","created_at":"2026-05-18T00:42:49Z"},{"alias_kind":"pith_short_12","alias_value":"IKLS3HMWNC53","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IKLS3HMWNC53CPWV","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IKLS3HMW","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:b3204acced7131fb2df81702371ad662df678764d51ee12a935ed1f094f42d84","target":"graph","created_at":"2026-05-18T00:42:49Z","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 show that the free energy in the mixed $p$-spin models of spin glasses does not superconcentrate in the presence of external field, which means that its variance is of the order suggested by the Poincar\\'e inequality. This complements the result of Chatterjee who showed that the free energy superconcentrates when there is no external field. For models without odd $p$-spin interactions for $p\\geq 3$, we prove the central limit theorem for the free energy at any temperature and give an explicit formula for the limiting variance. Although we only deal with the case of Ising spins, all our resu","authors_text":"Dmitry Panchenko, Partha Dey, Wei-Kuo Chen","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T17:37:28Z","title":"Fluctuations of the free energy in the mixed $p$-spin models with external field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07071","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":"sha256:5ec90d1ab32ad5218d90ab0edf18ad2489df1d4b31a4bf23a8db55a67c7aded2","target":"record","created_at":"2026-05-18T00:42:49Z","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":"08c1e9cdc777d35059d0891d15e6f29b596287eb9b471f396737ede958d3d5c8","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T17:37:28Z","title_canon_sha256":"8dcea84fe4a14c6d50157af84cf11e22624828ac05fb21efdf2af6d55c44db17"},"schema_version":"1.0","source":{"id":"1509.07071","kind":"arxiv","version":2}},"canonical_sha256":"42972d9d9668bbb13ed5d453cb986238d1bc8a4d9b4f8c5839076fe55096175d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42972d9d9668bbb13ed5d453cb986238d1bc8a4d9b4f8c5839076fe55096175d","first_computed_at":"2026-05-18T00:42:49.082444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:49.082444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4bZrCOdldhNR+Mv8rvakF8CTX6NyzN/R/3h+Wy5XYgDvmtm5N5PIeHN3ZchyG0LIVByrxNAcywHGDmx2WlHDBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:49.083213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.07071","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ec90d1ab32ad5218d90ab0edf18ad2489df1d4b31a4bf23a8db55a67c7aded2","sha256:b3204acced7131fb2df81702371ad662df678764d51ee12a935ed1f094f42d84"],"state_sha256":"69a08099ca38a2cba6969bf5f9698c8ef8cf5a64f1fabe5edb48196b855044e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8T1PvnOJWic7F5Bxw0AYagVADqNaaY4aZp0r6VrzItj13dW3LxSWf3fSDXODg7gTrXYq9gCn/y4miSJ1IK+yDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T20:25:16.930808Z","bundle_sha256":"6ccd4b69cedff9957fece0bbeffbef9e3f911ea23a5e5c83fa8b433ad3898290"}}