{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:RZLZTRTQ2DKUZ775SYBZLYB5FS","short_pith_number":"pith:RZLZTRTQ","canonical_record":{"source":{"id":"cond-mat/0507633","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-07-27T10:33:26Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"85d879c9dc2b54652df514397efd8c7048168901697e9c195cf410cb4883aca5","abstract_canon_sha256":"d70aa27ea15dbaf917bc8ee517cd1323f4f12b93109d7e9661c036e6b1ba1e51"},"schema_version":"1.0"},"canonical_sha256":"8e5799c670d0d54cfffd960395e03d2c977035fcd495f2d95499ef277fea5b05","source":{"kind":"arxiv","id":"cond-mat/0507633","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0507633","created_at":"2026-05-18T01:39:50Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0507633v2","created_at":"2026-05-18T01:39:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0507633","created_at":"2026-05-18T01:39:50Z"},{"alias_kind":"pith_short_12","alias_value":"RZLZTRTQ2DKU","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"RZLZTRTQ2DKUZ775","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"RZLZTRTQ","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:RZLZTRTQ2DKUZ775SYBZLYB5FS","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0507633","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-07-27T10:33:26Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"85d879c9dc2b54652df514397efd8c7048168901697e9c195cf410cb4883aca5","abstract_canon_sha256":"d70aa27ea15dbaf917bc8ee517cd1323f4f12b93109d7e9661c036e6b1ba1e51"},"schema_version":"1.0"},"canonical_sha256":"8e5799c670d0d54cfffd960395e03d2c977035fcd495f2d95499ef277fea5b05","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:50.672097Z","signature_b64":"CDn/gwU1NrJYrYZwQYcEhsbbHt0VBXVlZXzU/l6DM+Jj1UtqiIqCCm5bHf1TsNliUk81chyUvzc8GiyRSaQDAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e5799c670d0d54cfffd960395e03d2c977035fcd495f2d95499ef277fea5b05","last_reissued_at":"2026-05-18T01:39:50.671360Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:50.671360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0507633","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":"2026-05-18T01:39:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dz8DTvnemsEtoNz7vvJsDNN6+Fq1n9kuVKkzmGj8GKETgXlY3223WKMGCMXqcVIQTIaBILcrS0HcJaR8j4NEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:34:19.478388Z"},"content_sha256":"e21d9a0bb549050da483f69b38a38695686d8631806d3c722e431d4305110ae4","schema_version":"1.0","event_id":"sha256:e21d9a0bb549050da483f69b38a38695686d8631806d3c722e431d4305110ae4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:RZLZTRTQ2DKUZ775SYBZLYB5FS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scaling laws at the critical point","license":"","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.stat-mech","authors_text":"S. Davatolhagh","submitted_at":"2005-07-27T10:33:26Z","abstract_excerpt":"There are two independent critical exponents that describe the behavior of systems near their critical point. However, at the critical point only the exponent $\\eta$, which describes the decay of the correlation function, is usually discussed. We emphasize that there is a second independent exponent $\\eta'$ that describes the decay of the fourth-order correlation function. The exponent $\\eta'$ is related to the exponents determining the behavior of thermodynamic functions near criticality via a fluctuation-response equation for the specific heat. We also discuss a scaling law for $\\eta'$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0507633","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":"2026-05-18T01:39:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nfj87ryXcwYZLp0JLpUIirp6BoJmtpN9glI0efBGmDwEllLixj8EkkFUk8YzeDIJ+Guks6gM/jgHPUV257VyBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:34:19.478961Z"},"content_sha256":"d5537e9bdb68e4fb0f53bdb27c060c01ff5bcbd85bb4929de7ccb100d430f2d5","schema_version":"1.0","event_id":"sha256:d5537e9bdb68e4fb0f53bdb27c060c01ff5bcbd85bb4929de7ccb100d430f2d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RZLZTRTQ2DKUZ775SYBZLYB5FS/bundle.json","state_url":"https://pith.science/pith/RZLZTRTQ2DKUZ775SYBZLYB5FS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RZLZTRTQ2DKUZ775SYBZLYB5FS/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":"2026-06-07T14:34:19Z","links":{"resolver":"https://pith.science/pith/RZLZTRTQ2DKUZ775SYBZLYB5FS","bundle":"https://pith.science/pith/RZLZTRTQ2DKUZ775SYBZLYB5FS/bundle.json","state":"https://pith.science/pith/RZLZTRTQ2DKUZ775SYBZLYB5FS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RZLZTRTQ2DKUZ775SYBZLYB5FS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:RZLZTRTQ2DKUZ775SYBZLYB5FS","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":"d70aa27ea15dbaf917bc8ee517cd1323f4f12b93109d7e9661c036e6b1ba1e51","cross_cats_sorted":["cond-mat.dis-nn"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-07-27T10:33:26Z","title_canon_sha256":"85d879c9dc2b54652df514397efd8c7048168901697e9c195cf410cb4883aca5"},"schema_version":"1.0","source":{"id":"cond-mat/0507633","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0507633","created_at":"2026-05-18T01:39:50Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0507633v2","created_at":"2026-05-18T01:39:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0507633","created_at":"2026-05-18T01:39:50Z"},{"alias_kind":"pith_short_12","alias_value":"RZLZTRTQ2DKU","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"RZLZTRTQ2DKUZ775","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"RZLZTRTQ","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:d5537e9bdb68e4fb0f53bdb27c060c01ff5bcbd85bb4929de7ccb100d430f2d5","target":"graph","created_at":"2026-05-18T01:39:50Z","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":"There are two independent critical exponents that describe the behavior of systems near their critical point. However, at the critical point only the exponent $\\eta$, which describes the decay of the correlation function, is usually discussed. We emphasize that there is a second independent exponent $\\eta'$ that describes the decay of the fourth-order correlation function. The exponent $\\eta'$ is related to the exponents determining the behavior of thermodynamic functions near criticality via a fluctuation-response equation for the specific heat. We also discuss a scaling law for $\\eta'$.","authors_text":"S. Davatolhagh","cross_cats":["cond-mat.dis-nn"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-07-27T10:33:26Z","title":"Scaling laws at the critical point"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0507633","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:e21d9a0bb549050da483f69b38a38695686d8631806d3c722e431d4305110ae4","target":"record","created_at":"2026-05-18T01:39:50Z","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":"d70aa27ea15dbaf917bc8ee517cd1323f4f12b93109d7e9661c036e6b1ba1e51","cross_cats_sorted":["cond-mat.dis-nn"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-07-27T10:33:26Z","title_canon_sha256":"85d879c9dc2b54652df514397efd8c7048168901697e9c195cf410cb4883aca5"},"schema_version":"1.0","source":{"id":"cond-mat/0507633","kind":"arxiv","version":2}},"canonical_sha256":"8e5799c670d0d54cfffd960395e03d2c977035fcd495f2d95499ef277fea5b05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e5799c670d0d54cfffd960395e03d2c977035fcd495f2d95499ef277fea5b05","first_computed_at":"2026-05-18T01:39:50.671360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:50.671360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CDn/gwU1NrJYrYZwQYcEhsbbHt0VBXVlZXzU/l6DM+Jj1UtqiIqCCm5bHf1TsNliUk81chyUvzc8GiyRSaQDAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:50.672097Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0507633","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e21d9a0bb549050da483f69b38a38695686d8631806d3c722e431d4305110ae4","sha256:d5537e9bdb68e4fb0f53bdb27c060c01ff5bcbd85bb4929de7ccb100d430f2d5"],"state_sha256":"7917175d17f2003ffd8a04e545975a18dc9fa759615bbc5909490631a39d5caf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J4pGsy0gjdBT6YowjYFopi0UJj0Nx6PW2IxMG2c4+lDeG3SnrgbO2OoS1HGHfThBEj0ru3hG2kutbumjslJXDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T14:34:19.482292Z","bundle_sha256":"6ec840cae056d87e823cca9aa3872cd41d919fab1c68249adf22e7c6e92e569a"}}