{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UR6D364IXEPUTE3LKWH4SUKEFY","short_pith_number":"pith:UR6D364I","canonical_record":{"source":{"id":"1404.5694","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-23T03:37:20Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR"],"title_canon_sha256":"37cab775fc57adfb7df5a4f2762a904a8b5bfa132af46fa2c71eb4ec1c857ff1","abstract_canon_sha256":"3b64d597307272887013fdc58849b07c0779b82b09295068240384ea22b0349d"},"schema_version":"1.0"},"canonical_sha256":"a47c3dfb88b91f49936b558fc951442e23b1570f2c2b603941f07a8a08416a90","source":{"kind":"arxiv","id":"1404.5694","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5694","created_at":"2026-05-18T01:43:26Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5694v4","created_at":"2026-05-18T01:43:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5694","created_at":"2026-05-18T01:43:26Z"},{"alias_kind":"pith_short_12","alias_value":"UR6D364IXEPU","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UR6D364IXEPUTE3L","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UR6D364I","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UR6D364IXEPUTE3LKWH4SUKEFY","target":"record","payload":{"canonical_record":{"source":{"id":"1404.5694","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-23T03:37:20Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR"],"title_canon_sha256":"37cab775fc57adfb7df5a4f2762a904a8b5bfa132af46fa2c71eb4ec1c857ff1","abstract_canon_sha256":"3b64d597307272887013fdc58849b07c0779b82b09295068240384ea22b0349d"},"schema_version":"1.0"},"canonical_sha256":"a47c3dfb88b91f49936b558fc951442e23b1570f2c2b603941f07a8a08416a90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:43:26.145703Z","signature_b64":"1Ppl1rhyPlXH7TFYS/ydYoVp35Di4pfwDF5s1xOBxvLad7g1xLJDF0Lx5pEKbwSz+IqBX/Evx4IQiOVMirAyDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a47c3dfb88b91f49936b558fc951442e23b1570f2c2b603941f07a8a08416a90","last_reissued_at":"2026-05-18T01:43:26.144729Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:43:26.144729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.5694","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:43:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dmUDhO2lbjJ0tdbFkX5cCZHtjzX9E3lb+ok61zW1tnR566AH1mjMXXM0jqcWH+1ywQ8vkLm8oEnHXzdLnmSdBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T03:55:11.304838Z"},"content_sha256":"dc1ad4da7e2b281c2f926d0eea42e2aafdea210b3efc69235e8fa2e1def11b5f","schema_version":"1.0","event_id":"sha256:dc1ad4da7e2b281c2f926d0eea42e2aafdea210b3efc69235e8fa2e1def11b5f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UR6D364IXEPUTE3LKWH4SUKEFY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fick's law in a random lattice Lorentz gas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Raphael Lefevere","submitted_at":"2014-04-23T03:37:20Z","abstract_excerpt":"We provide a proof that the stationary macroscopic current of particles in a random lattice Lorentz gas satisfies Fick's law when connected to particles reservoirs. We consider a box on a d+1 dimensional lattice and when $d\\geq7$, we show that under a diffusive rescaling of space and time, the probability to find a current different from its stationary value is exponentially small in time. Its stationary value is given by the conductivity times the difference of chemical potentials of the reservoirs. The proof is based on the fact that in high dimension, random walks have a small probability o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5694","kind":"arxiv","version":4},"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":"2026-05-18T01:43:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kfihj2Eo4zuII5tmuxECdnJEDAZwnmErB++CaLEYlOzsrlhEKy6BV7c5xlApjnxekfN5wG7ZeWJCJm4aIg4gDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T03:55:11.305639Z"},"content_sha256":"e2a27f2e9145392b6c42100cedece9c76de37bf16946cb7cd8aeaee35ce4edc8","schema_version":"1.0","event_id":"sha256:e2a27f2e9145392b6c42100cedece9c76de37bf16946cb7cd8aeaee35ce4edc8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UR6D364IXEPUTE3LKWH4SUKEFY/bundle.json","state_url":"https://pith.science/pith/UR6D364IXEPUTE3LKWH4SUKEFY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UR6D364IXEPUTE3LKWH4SUKEFY/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":"2026-06-06T03:55:11Z","links":{"resolver":"https://pith.science/pith/UR6D364IXEPUTE3LKWH4SUKEFY","bundle":"https://pith.science/pith/UR6D364IXEPUTE3LKWH4SUKEFY/bundle.json","state":"https://pith.science/pith/UR6D364IXEPUTE3LKWH4SUKEFY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UR6D364IXEPUTE3LKWH4SUKEFY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UR6D364IXEPUTE3LKWH4SUKEFY","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":"3b64d597307272887013fdc58849b07c0779b82b09295068240384ea22b0349d","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-23T03:37:20Z","title_canon_sha256":"37cab775fc57adfb7df5a4f2762a904a8b5bfa132af46fa2c71eb4ec1c857ff1"},"schema_version":"1.0","source":{"id":"1404.5694","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5694","created_at":"2026-05-18T01:43:26Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5694v4","created_at":"2026-05-18T01:43:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5694","created_at":"2026-05-18T01:43:26Z"},{"alias_kind":"pith_short_12","alias_value":"UR6D364IXEPU","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UR6D364IXEPUTE3L","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UR6D364I","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:e2a27f2e9145392b6c42100cedece9c76de37bf16946cb7cd8aeaee35ce4edc8","target":"graph","created_at":"2026-05-18T01:43:26Z","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 provide a proof that the stationary macroscopic current of particles in a random lattice Lorentz gas satisfies Fick's law when connected to particles reservoirs. We consider a box on a d+1 dimensional lattice and when $d\\geq7$, we show that under a diffusive rescaling of space and time, the probability to find a current different from its stationary value is exponentially small in time. Its stationary value is given by the conductivity times the difference of chemical potentials of the reservoirs. The proof is based on the fact that in high dimension, random walks have a small probability o","authors_text":"Raphael Lefevere","cross_cats":["cond-mat.stat-mech","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-23T03:37:20Z","title":"Fick's law in a random lattice Lorentz gas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5694","kind":"arxiv","version":4},"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:dc1ad4da7e2b281c2f926d0eea42e2aafdea210b3efc69235e8fa2e1def11b5f","target":"record","created_at":"2026-05-18T01:43:26Z","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":"3b64d597307272887013fdc58849b07c0779b82b09295068240384ea22b0349d","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-23T03:37:20Z","title_canon_sha256":"37cab775fc57adfb7df5a4f2762a904a8b5bfa132af46fa2c71eb4ec1c857ff1"},"schema_version":"1.0","source":{"id":"1404.5694","kind":"arxiv","version":4}},"canonical_sha256":"a47c3dfb88b91f49936b558fc951442e23b1570f2c2b603941f07a8a08416a90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a47c3dfb88b91f49936b558fc951442e23b1570f2c2b603941f07a8a08416a90","first_computed_at":"2026-05-18T01:43:26.144729Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:43:26.144729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Ppl1rhyPlXH7TFYS/ydYoVp35Di4pfwDF5s1xOBxvLad7g1xLJDF0Lx5pEKbwSz+IqBX/Evx4IQiOVMirAyDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:43:26.145703Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5694","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc1ad4da7e2b281c2f926d0eea42e2aafdea210b3efc69235e8fa2e1def11b5f","sha256:e2a27f2e9145392b6c42100cedece9c76de37bf16946cb7cd8aeaee35ce4edc8"],"state_sha256":"fa081146af54b034930665104d640049ccaa3e9ac37a69a7feae8423d769e407"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yrlQJK9sqgNnZz9JesZZF8KSto17zRa+Rc3me7X3Cwc8HIANJ7tk/1utNS6W3tdiIwtMCkhFCrs2CyIkr+zsCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T03:55:11.309791Z","bundle_sha256":"4fc1323304ffbdf5bd4624d5b942cc6ffe3f940c9ea65e03ce7a3cf9628553e4"}}