{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7K25QBPBQCSZJKR27AJ3MPXRX3","short_pith_number":"pith:7K25QBPB","canonical_record":{"source":{"id":"1103.2835","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-03-15T03:13:46Z","cross_cats_sorted":[],"title_canon_sha256":"c1031a28d0847949f5a51495c14b5a3db429f2c72c42c75d897f0effdd06c513","abstract_canon_sha256":"bdb6ded045786f62f231797501dc0895c9b1915903adcd32f2e5b5c3074e5499"},"schema_version":"1.0"},"canonical_sha256":"fab5d805e180a594aa3af813b63ef1bef9d3da1cc68cddfe768539ec8fb57b28","source":{"kind":"arxiv","id":"1103.2835","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2835","created_at":"2026-05-18T03:00:37Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2835v6","created_at":"2026-05-18T03:00:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2835","created_at":"2026-05-18T03:00:37Z"},{"alias_kind":"pith_short_12","alias_value":"7K25QBPBQCSZ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7K25QBPBQCSZJKR2","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7K25QBPB","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7K25QBPBQCSZJKR27AJ3MPXRX3","target":"record","payload":{"canonical_record":{"source":{"id":"1103.2835","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-03-15T03:13:46Z","cross_cats_sorted":[],"title_canon_sha256":"c1031a28d0847949f5a51495c14b5a3db429f2c72c42c75d897f0effdd06c513","abstract_canon_sha256":"bdb6ded045786f62f231797501dc0895c9b1915903adcd32f2e5b5c3074e5499"},"schema_version":"1.0"},"canonical_sha256":"fab5d805e180a594aa3af813b63ef1bef9d3da1cc68cddfe768539ec8fb57b28","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:37.632927Z","signature_b64":"MQADESfgeQoTt6eKqm3cVfzscZZpeEFagVbsHs8x2dtFUSVQ9YvAMzNoNB/4OlU7jsIzn9d8+OXs1pUWKA/9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fab5d805e180a594aa3af813b63ef1bef9d3da1cc68cddfe768539ec8fb57b28","last_reissued_at":"2026-05-18T03:00:37.632230Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:37.632230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.2835","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:00:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q1x272D2EnFrNgEpQ76tXMslecEELQGt++arBAe38UZlmpNtYRiAW3Evo9j4fIGzHUVDwFllO7+x49V8yHaEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:16:01.818189Z"},"content_sha256":"7aae603470042aa4d547b6eb9559b21ffa659e8866ed7566d9865301d5de92ae","schema_version":"1.0","event_id":"sha256:7aae603470042aa4d547b6eb9559b21ffa659e8866ed7566d9865301d5de92ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7K25QBPBQCSZJKR27AJ3MPXRX3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Anomalous Heat Diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Baowen Li, Jie Ren, Nianbei Li, Peter H\\\"anggi, Sha Liu","submitted_at":"2011-03-15T03:13:46Z","abstract_excerpt":"Consider anomalous energy spread in solid phases, i.e., $MSD= \\int (x -{\\langle x \\rangle}_E)^2 \\rho_E(x,t)dx \\propto t^{\\beta}$, as induced by a small initial excess energy perturbation distribution $\\rho_{E}(x,t=0)$ away from equilibrium. The associated total thermal equilibrium heat flux autocorrelation function $C_{JJ}(t)$ is shown to obey rigorously the intriguing relation, $d^2 MSD/dt^2 = 2C_{JJ}(t)/(k_BT^2c)$, where $c$ is the specific volumetric heat capacity. Its integral assumes a time-local Helfand-moment relation; i.e. $ dMSD/dt|_{t=t_s} = 2/(k_BT^2c)\\int_0^{t_s} C_{JJ}(s)ds$, wher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2835","kind":"arxiv","version":6},"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":"2026-05-18T03:00:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1u7lEqSdWfwF2Bzv/NK37c6DxOWYWH6d0rZgj5vbcL1qx5nEjnFRvhcRvJekKyzIaKiL1eempm4/iwta5qCFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:16:01.818564Z"},"content_sha256":"577c76605d778a83d91bae7ae5d7a33f6a3ed670b42361da9dc3c612a9fd0388","schema_version":"1.0","event_id":"sha256:577c76605d778a83d91bae7ae5d7a33f6a3ed670b42361da9dc3c612a9fd0388"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7K25QBPBQCSZJKR27AJ3MPXRX3/bundle.json","state_url":"https://pith.science/pith/7K25QBPBQCSZJKR27AJ3MPXRX3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7K25QBPBQCSZJKR27AJ3MPXRX3/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":"2026-05-28T13:16:01Z","links":{"resolver":"https://pith.science/pith/7K25QBPBQCSZJKR27AJ3MPXRX3","bundle":"https://pith.science/pith/7K25QBPBQCSZJKR27AJ3MPXRX3/bundle.json","state":"https://pith.science/pith/7K25QBPBQCSZJKR27AJ3MPXRX3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7K25QBPBQCSZJKR27AJ3MPXRX3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7K25QBPBQCSZJKR27AJ3MPXRX3","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":"bdb6ded045786f62f231797501dc0895c9b1915903adcd32f2e5b5c3074e5499","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-03-15T03:13:46Z","title_canon_sha256":"c1031a28d0847949f5a51495c14b5a3db429f2c72c42c75d897f0effdd06c513"},"schema_version":"1.0","source":{"id":"1103.2835","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2835","created_at":"2026-05-18T03:00:37Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2835v6","created_at":"2026-05-18T03:00:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2835","created_at":"2026-05-18T03:00:37Z"},{"alias_kind":"pith_short_12","alias_value":"7K25QBPBQCSZ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7K25QBPBQCSZJKR2","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7K25QBPB","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:577c76605d778a83d91bae7ae5d7a33f6a3ed670b42361da9dc3c612a9fd0388","target":"graph","created_at":"2026-05-18T03:00:37Z","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":"Consider anomalous energy spread in solid phases, i.e., $MSD= \\int (x -{\\langle x \\rangle}_E)^2 \\rho_E(x,t)dx \\propto t^{\\beta}$, as induced by a small initial excess energy perturbation distribution $\\rho_{E}(x,t=0)$ away from equilibrium. The associated total thermal equilibrium heat flux autocorrelation function $C_{JJ}(t)$ is shown to obey rigorously the intriguing relation, $d^2 MSD/dt^2 = 2C_{JJ}(t)/(k_BT^2c)$, where $c$ is the specific volumetric heat capacity. Its integral assumes a time-local Helfand-moment relation; i.e. $ dMSD/dt|_{t=t_s} = 2/(k_BT^2c)\\int_0^{t_s} C_{JJ}(s)ds$, wher","authors_text":"Baowen Li, Jie Ren, Nianbei Li, Peter H\\\"anggi, Sha Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-03-15T03:13:46Z","title":"Anomalous Heat Diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2835","kind":"arxiv","version":6},"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":"sha256:7aae603470042aa4d547b6eb9559b21ffa659e8866ed7566d9865301d5de92ae","target":"record","created_at":"2026-05-18T03:00:37Z","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":"bdb6ded045786f62f231797501dc0895c9b1915903adcd32f2e5b5c3074e5499","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-03-15T03:13:46Z","title_canon_sha256":"c1031a28d0847949f5a51495c14b5a3db429f2c72c42c75d897f0effdd06c513"},"schema_version":"1.0","source":{"id":"1103.2835","kind":"arxiv","version":6}},"canonical_sha256":"fab5d805e180a594aa3af813b63ef1bef9d3da1cc68cddfe768539ec8fb57b28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fab5d805e180a594aa3af813b63ef1bef9d3da1cc68cddfe768539ec8fb57b28","first_computed_at":"2026-05-18T03:00:37.632230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:37.632230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MQADESfgeQoTt6eKqm3cVfzscZZpeEFagVbsHs8x2dtFUSVQ9YvAMzNoNB/4OlU7jsIzn9d8+OXs1pUWKA/9BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:37.632927Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2835","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7aae603470042aa4d547b6eb9559b21ffa659e8866ed7566d9865301d5de92ae","sha256:577c76605d778a83d91bae7ae5d7a33f6a3ed670b42361da9dc3c612a9fd0388"],"state_sha256":"5403350ecc02959ae074b0da219b2772f3a7c5bdf238a6f99d3961945046b371"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UQpBFltL4R64qIDqAyIJQ6OBvTUShnMAckGtTItXZDvcsg4eFxzchL2m8L7QzK3p5jui2lfrHWW+AEr23f1MDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:16:01.820654Z","bundle_sha256":"ff5d3098c8cc11c0594efe058c5391b046ce23442fa3f851cf9a92b9b6f88e88"}}