{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:W3GDSOZJT57K7F6IQDD7QH2HGD","short_pith_number":"pith:W3GDSOZJ","canonical_record":{"source":{"id":"cond-mat/0110603","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2001-10-29T19:31:43Z","cross_cats_sorted":["cond-mat.str-el"],"title_canon_sha256":"6198c35db4fc5c3cc2b0bbffd2f4770644a96feccb97084544749efc58044032","abstract_canon_sha256":"9a606cc536f8850328ee9a80aed32bcd21cffb21e2690043ab8bef7e5fd84dac"},"schema_version":"1.0"},"canonical_sha256":"b6cc393b299f7eaf97c880c7f81f4730dcc3677883a852521a72dde74e181467","source":{"kind":"arxiv","id":"cond-mat/0110603","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0110603","created_at":"2026-05-18T01:40:06Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0110603v1","created_at":"2026-05-18T01:40:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0110603","created_at":"2026-05-18T01:40:06Z"},{"alias_kind":"pith_short_12","alias_value":"W3GDSOZJT57K","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"W3GDSOZJT57K7F6I","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"W3GDSOZJ","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:W3GDSOZJT57K7F6IQDD7QH2HGD","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0110603","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2001-10-29T19:31:43Z","cross_cats_sorted":["cond-mat.str-el"],"title_canon_sha256":"6198c35db4fc5c3cc2b0bbffd2f4770644a96feccb97084544749efc58044032","abstract_canon_sha256":"9a606cc536f8850328ee9a80aed32bcd21cffb21e2690043ab8bef7e5fd84dac"},"schema_version":"1.0"},"canonical_sha256":"b6cc393b299f7eaf97c880c7f81f4730dcc3677883a852521a72dde74e181467","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:40:06.457565Z","signature_b64":"NoQ31rul31E8Ir2qYYSZcKAEEIDbP1rtFWhiDw42Pylc2YhY/FpZo8/sLtSjG0iMarP3GNieRbqEKbs5dsltCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6cc393b299f7eaf97c880c7f81f4730dcc3677883a852521a72dde74e181467","last_reissued_at":"2026-05-18T01:40:06.457060Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:40:06.457060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0110603","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":"2026-05-18T01:40:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r/otLdYCZxQwDRFJCK8rV79T0re6HwgaNfPv/PBusUNB6V0mgsIl7qVBdQFxIFaskszAJsASuVqTJE8dJ2yoAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:19:02.110928Z"},"content_sha256":"ab612936cae05b4235c28fa3ca0186c98a1c1c5c1661e546ace0db1c2fb637e3","schema_version":"1.0","event_id":"sha256:ab612936cae05b4235c28fa3ca0186c98a1c1c5c1661e546ace0db1c2fb637e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:W3GDSOZJT57K7F6IQDD7QH2HGD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Long-Time Tails, Weak Localization, and Classical and Quantum Critical Behavior","license":"","headline":"","cross_cats":["cond-mat.str-el"],"primary_cat":"cond-mat.stat-mech","authors_text":"D. Belitz, J.V. Sengers, T.R. Kirkpatrick","submitted_at":"2001-10-29T19:31:43Z","abstract_excerpt":"An overview is given of the long-time and long-distance behavior of correlation functions in both classical and quantum statistical mechanics. After a simple derivation of the classical long-time tails in equilibrium time correlation functions, we discuss analogous long-distance phenomena in nonequilibrium classical systems. The paper then draws analogies between these phenomena and similar effects in quantum statistical mechanics, with emphasis on the soft modes that underly long-time tails and related phenomena. We also elucidate the interplay between critical phenomena and long-time tails, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0110603","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":"2026-05-18T01:40:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hpWC1ukGltYr2K7EzqucAvtFPoUaaCTbi/KG4+5GSMv5ou8AbLeWI81AuFGtSq+4a1UdS7XxbcFxBwWCvWxABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:19:02.111275Z"},"content_sha256":"009d9536e3956cb225f8c021ab27bbad5a41a503ad6238c87d1aab3004f0265a","schema_version":"1.0","event_id":"sha256:009d9536e3956cb225f8c021ab27bbad5a41a503ad6238c87d1aab3004f0265a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W3GDSOZJT57K7F6IQDD7QH2HGD/bundle.json","state_url":"https://pith.science/pith/W3GDSOZJT57K7F6IQDD7QH2HGD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W3GDSOZJT57K7F6IQDD7QH2HGD/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":"2026-05-31T08:19:02Z","links":{"resolver":"https://pith.science/pith/W3GDSOZJT57K7F6IQDD7QH2HGD","bundle":"https://pith.science/pith/W3GDSOZJT57K7F6IQDD7QH2HGD/bundle.json","state":"https://pith.science/pith/W3GDSOZJT57K7F6IQDD7QH2HGD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W3GDSOZJT57K7F6IQDD7QH2HGD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:W3GDSOZJT57K7F6IQDD7QH2HGD","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":"9a606cc536f8850328ee9a80aed32bcd21cffb21e2690043ab8bef7e5fd84dac","cross_cats_sorted":["cond-mat.str-el"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2001-10-29T19:31:43Z","title_canon_sha256":"6198c35db4fc5c3cc2b0bbffd2f4770644a96feccb97084544749efc58044032"},"schema_version":"1.0","source":{"id":"cond-mat/0110603","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0110603","created_at":"2026-05-18T01:40:06Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0110603v1","created_at":"2026-05-18T01:40:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0110603","created_at":"2026-05-18T01:40:06Z"},{"alias_kind":"pith_short_12","alias_value":"W3GDSOZJT57K","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"W3GDSOZJT57K7F6I","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"W3GDSOZJ","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:009d9536e3956cb225f8c021ab27bbad5a41a503ad6238c87d1aab3004f0265a","target":"graph","created_at":"2026-05-18T01:40:06Z","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":"An overview is given of the long-time and long-distance behavior of correlation functions in both classical and quantum statistical mechanics. After a simple derivation of the classical long-time tails in equilibrium time correlation functions, we discuss analogous long-distance phenomena in nonequilibrium classical systems. The paper then draws analogies between these phenomena and similar effects in quantum statistical mechanics, with emphasis on the soft modes that underly long-time tails and related phenomena. We also elucidate the interplay between critical phenomena and long-time tails, ","authors_text":"D. Belitz, J.V. Sengers, T.R. Kirkpatrick","cross_cats":["cond-mat.str-el"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2001-10-29T19:31:43Z","title":"Long-Time Tails, Weak Localization, and Classical and Quantum Critical Behavior"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0110603","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:ab612936cae05b4235c28fa3ca0186c98a1c1c5c1661e546ace0db1c2fb637e3","target":"record","created_at":"2026-05-18T01:40:06Z","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":"9a606cc536f8850328ee9a80aed32bcd21cffb21e2690043ab8bef7e5fd84dac","cross_cats_sorted":["cond-mat.str-el"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2001-10-29T19:31:43Z","title_canon_sha256":"6198c35db4fc5c3cc2b0bbffd2f4770644a96feccb97084544749efc58044032"},"schema_version":"1.0","source":{"id":"cond-mat/0110603","kind":"arxiv","version":1}},"canonical_sha256":"b6cc393b299f7eaf97c880c7f81f4730dcc3677883a852521a72dde74e181467","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6cc393b299f7eaf97c880c7f81f4730dcc3677883a852521a72dde74e181467","first_computed_at":"2026-05-18T01:40:06.457060Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:40:06.457060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NoQ31rul31E8Ir2qYYSZcKAEEIDbP1rtFWhiDw42Pylc2YhY/FpZo8/sLtSjG0iMarP3GNieRbqEKbs5dsltCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:40:06.457565Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0110603","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab612936cae05b4235c28fa3ca0186c98a1c1c5c1661e546ace0db1c2fb637e3","sha256:009d9536e3956cb225f8c021ab27bbad5a41a503ad6238c87d1aab3004f0265a"],"state_sha256":"d20782d4a6b756054d75d1cda0590f234ab0a90cbbc79628fa0dc9a4fe5f2f69"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EBYGr4y6966T5lu205fc5KA95JWxhjvPyVtoi1c25DwiqPZpphjwWaVlNru7vY1mOx+YizWzBjFsrZBwaiFmCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:19:02.113234Z","bundle_sha256":"704b7d01a72f6b5de3b56f1304bad7ef732438d894f472bb6dd11b4ff2717a0f"}}