{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:7LEQRUD6NQEPTYBTVPEEYUK6OK","short_pith_number":"pith:7LEQRUD6","canonical_record":{"source":{"id":"cond-mat/0401260","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2004-01-15T10:47:29Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"cdb38471bcf0b4b42f1b0dfb7a4d39a02a093141d7b86ab1b8a7f65e2b4e8cea","abstract_canon_sha256":"e1fbcb6692c584c4aa2e8357867829d6714b36042fe75a06fe3edfaca8c89ab7"},"schema_version":"1.0"},"canonical_sha256":"fac908d07e6c08f9e033abc84c515e72a4967a44448919c6f206f5017ca8e1a4","source":{"kind":"arxiv","id":"cond-mat/0401260","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0401260","created_at":"2026-07-04T16:45:39Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0401260v2","created_at":"2026-07-04T16:45:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0401260","created_at":"2026-07-04T16:45:39Z"},{"alias_kind":"pith_short_12","alias_value":"7LEQRUD6NQEP","created_at":"2026-07-04T16:45:39Z"},{"alias_kind":"pith_short_16","alias_value":"7LEQRUD6NQEPTYBT","created_at":"2026-07-04T16:45:39Z"},{"alias_kind":"pith_short_8","alias_value":"7LEQRUD6","created_at":"2026-07-04T16:45:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:7LEQRUD6NQEPTYBTVPEEYUK6OK","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0401260","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2004-01-15T10:47:29Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"cdb38471bcf0b4b42f1b0dfb7a4d39a02a093141d7b86ab1b8a7f65e2b4e8cea","abstract_canon_sha256":"e1fbcb6692c584c4aa2e8357867829d6714b36042fe75a06fe3edfaca8c89ab7"},"schema_version":"1.0"},"canonical_sha256":"fac908d07e6c08f9e033abc84c515e72a4967a44448919c6f206f5017ca8e1a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:45:39.212031Z","signature_b64":"IkdXi9yr5rWVPZmwt7V65Ek0OJNM6bCu9TKQO8Ln9Mu6CNonnX0dydjlCJ4Kvh4EuxD2/ywI4NoCGMQlEUL0DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fac908d07e6c08f9e033abc84c515e72a4967a44448919c6f206f5017ca8e1a4","last_reissued_at":"2026-07-04T16:45:39.211707Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:45:39.211707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0401260","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":"2026-07-04T16:45:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IE/BVIsXakify7lz7H/2ujMD/sWrDK6uXOc8uvTC2DX7ltZeQY+eqcrMiTxdsRZfqYU88b+gkA3pZ7IE/H/PBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T16:15:25.811278Z"},"content_sha256":"3dbf35ae9cbd7021a45f03ad2326665f9f74dec6b26a23528777b9b42b8715c2","schema_version":"1.0","event_id":"sha256:3dbf35ae9cbd7021a45f03ad2326665f9f74dec6b26a23528777b9b42b8715c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:7LEQRUD6NQEPTYBTVPEEYUK6OK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transition","license":"","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Giulio Biroli, Jean-Philippe Bouchaud","submitted_at":"2004-01-15T10:47:29Z","abstract_excerpt":"We show that the glass transition predicted by the Mode-Coupling Theory (MCT) is a critical phenomenon with a diverging length and time scale associated to the cooperativity of the dynamics. We obtain the scaling exponents nu and z that relate space and time scales to the distance from criticality, as well as the scaling form of the critical four-point correlation function. However, both these predictions and other well known MCT results are mean-field in nature and are thus expected to change below the upper critical dimension dc=6, as suggested by different forms of the Ginzburg criterion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0401260","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/cond-mat/0401260/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T16:45:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IUaCWtEd21dTycfZb4O88pYwGzkStjSU7QlViCV7FF+SWj6gJFwnyxzHxhuRyp84fdFN7yVpBSjGk6ZiLkeKAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T16:15:25.812297Z"},"content_sha256":"0adb2608558d8452830044902b99a93b653881d89ee4ecd180bba858e3f30cff","schema_version":"1.0","event_id":"sha256:0adb2608558d8452830044902b99a93b653881d89ee4ecd180bba858e3f30cff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7LEQRUD6NQEPTYBTVPEEYUK6OK/bundle.json","state_url":"https://pith.science/pith/7LEQRUD6NQEPTYBTVPEEYUK6OK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7LEQRUD6NQEPTYBTVPEEYUK6OK/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":"2026-08-12T16:15:25Z","links":{"resolver":"https://pith.science/pith/7LEQRUD6NQEPTYBTVPEEYUK6OK","bundle":"https://pith.science/pith/7LEQRUD6NQEPTYBTVPEEYUK6OK/bundle.json","state":"https://pith.science/pith/7LEQRUD6NQEPTYBTVPEEYUK6OK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7LEQRUD6NQEPTYBTVPEEYUK6OK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:7LEQRUD6NQEPTYBTVPEEYUK6OK","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":"e1fbcb6692c584c4aa2e8357867829d6714b36042fe75a06fe3edfaca8c89ab7","cross_cats_sorted":["cond-mat.dis-nn"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2004-01-15T10:47:29Z","title_canon_sha256":"cdb38471bcf0b4b42f1b0dfb7a4d39a02a093141d7b86ab1b8a7f65e2b4e8cea"},"schema_version":"1.0","source":{"id":"cond-mat/0401260","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0401260","created_at":"2026-07-04T16:45:39Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0401260v2","created_at":"2026-07-04T16:45:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0401260","created_at":"2026-07-04T16:45:39Z"},{"alias_kind":"pith_short_12","alias_value":"7LEQRUD6NQEP","created_at":"2026-07-04T16:45:39Z"},{"alias_kind":"pith_short_16","alias_value":"7LEQRUD6NQEPTYBT","created_at":"2026-07-04T16:45:39Z"},{"alias_kind":"pith_short_8","alias_value":"7LEQRUD6","created_at":"2026-07-04T16:45:39Z"}],"graph_snapshots":[{"event_id":"sha256:0adb2608558d8452830044902b99a93b653881d89ee4ecd180bba858e3f30cff","target":"graph","created_at":"2026-07-04T16:45:39Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/cond-mat/0401260/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the glass transition predicted by the Mode-Coupling Theory (MCT) is a critical phenomenon with a diverging length and time scale associated to the cooperativity of the dynamics. We obtain the scaling exponents nu and z that relate space and time scales to the distance from criticality, as well as the scaling form of the critical four-point correlation function. However, both these predictions and other well known MCT results are mean-field in nature and are thus expected to change below the upper critical dimension dc=6, as suggested by different forms of the Ginzburg criterion.","authors_text":"Giulio Biroli, Jean-Philippe Bouchaud","cross_cats":["cond-mat.dis-nn"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2004-01-15T10:47:29Z","title":"Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0401260","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":"sha256:3dbf35ae9cbd7021a45f03ad2326665f9f74dec6b26a23528777b9b42b8715c2","target":"record","created_at":"2026-07-04T16:45:39Z","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":"e1fbcb6692c584c4aa2e8357867829d6714b36042fe75a06fe3edfaca8c89ab7","cross_cats_sorted":["cond-mat.dis-nn"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2004-01-15T10:47:29Z","title_canon_sha256":"cdb38471bcf0b4b42f1b0dfb7a4d39a02a093141d7b86ab1b8a7f65e2b4e8cea"},"schema_version":"1.0","source":{"id":"cond-mat/0401260","kind":"arxiv","version":2}},"canonical_sha256":"fac908d07e6c08f9e033abc84c515e72a4967a44448919c6f206f5017ca8e1a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fac908d07e6c08f9e033abc84c515e72a4967a44448919c6f206f5017ca8e1a4","first_computed_at":"2026-07-04T16:45:39.211707Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:45:39.211707Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IkdXi9yr5rWVPZmwt7V65Ek0OJNM6bCu9TKQO8Ln9Mu6CNonnX0dydjlCJ4Kvh4EuxD2/ywI4NoCGMQlEUL0DQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:45:39.212031Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0401260","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3dbf35ae9cbd7021a45f03ad2326665f9f74dec6b26a23528777b9b42b8715c2","sha256:0adb2608558d8452830044902b99a93b653881d89ee4ecd180bba858e3f30cff"],"state_sha256":"80a2adb0300e2994b26d83ace72c11b3b3c9b381cd51d97b9b7d6cd3e634dbd6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B37M0oyt89QtYAZhV8XKuiTkcaMhVzzRsWUeY9clRJ/v5MVqy4kFKvubhlhGCjV541WjmOdsnr+9e4f12bUfDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T16:15:25.819461Z","bundle_sha256":"98bb3718f823ddf68d06d961665827264a43eedc52322ad873b601572463eb5a"}}