{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EZDBPLGZWKM7TJVL5CC2SJ5YX4","short_pith_number":"pith:EZDBPLGZ","canonical_record":{"source":{"id":"1302.4339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-18T16:27:55Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f01f5c23ea3033e4334fa60f87bfafa4a1b4f36f5f299151e7468f9450142f4e","abstract_canon_sha256":"1209de4e3afed1dbcd4a9fe954383b3bad7b0b5155c071368d8a0fc718fdc5d4"},"schema_version":"1.0"},"canonical_sha256":"264617acd9b299f9a6abe885a927b8bf2c20781675a6c1d23f2fe14f2872be93","source":{"kind":"arxiv","id":"1302.4339","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4339","created_at":"2026-05-18T00:12:02Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4339v1","created_at":"2026-05-18T00:12:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4339","created_at":"2026-05-18T00:12:02Z"},{"alias_kind":"pith_short_12","alias_value":"EZDBPLGZWKM7","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EZDBPLGZWKM7TJVL","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EZDBPLGZ","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EZDBPLGZWKM7TJVL5CC2SJ5YX4","target":"record","payload":{"canonical_record":{"source":{"id":"1302.4339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-18T16:27:55Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f01f5c23ea3033e4334fa60f87bfafa4a1b4f36f5f299151e7468f9450142f4e","abstract_canon_sha256":"1209de4e3afed1dbcd4a9fe954383b3bad7b0b5155c071368d8a0fc718fdc5d4"},"schema_version":"1.0"},"canonical_sha256":"264617acd9b299f9a6abe885a927b8bf2c20781675a6c1d23f2fe14f2872be93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:02.751354Z","signature_b64":"TeNnfqmACRLY08l/N73LJ8X6fvVfTbsKdHyH1/oBBiDbhXp5T4480lGty+EZ3WGi+q9urF/WecygP+AuCdrhBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"264617acd9b299f9a6abe885a927b8bf2c20781675a6c1d23f2fe14f2872be93","last_reissued_at":"2026-05-18T00:12:02.750639Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:02.750639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.4339","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":"2026-05-18T00:12:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mFZSI1tz/z+neJFo9F8q642n1u/ai+OOv0oUgZgxYogH6C3356NNfMSNymE+g67KcsAz/lwTSQhg8x9NzPOIBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T09:06:46.830520Z"},"content_sha256":"b3bcf0fce60052ad41791df70a64abcba4c6f8064cc6bb17d8f6ca603b9a2470","schema_version":"1.0","event_id":"sha256:b3bcf0fce60052ad41791df70a64abcba4c6f8064cc6bb17d8f6ca603b9a2470"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EZDBPLGZWKM7TJVL5CC2SJ5YX4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diffusivity in multiple scattering systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Hong-Kun Zhang, Renato Feres, Timothy Chumley","submitted_at":"2013-02-18T16:27:55Z","abstract_excerpt":"We consider random flights of point particles inside $n$-dimensional channels of the form $\\mathbb{R}^{k} \\times \\mathbb{B}^{n-k}$, where $\\mathbb{B}^{n-k}$ is a ball of radius $r$ in dimension $n-k$. The particle velocities immediately after each collision with the boundary of the channel comprise a Markov chain with a transition probabilities operator $P$ that is determined by a choice of (billiard-like) random mechanical model of the particle-surface interaction at the \"microscopic\" scale. Our central concern is the relationship between the scattering properties encoded in $P$ and the const"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4339","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":"2026-05-18T00:12:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LwEDMx/jZ+cgMnjyImFwv8KuwHlVVpDCsDfoYhQSxGRRNCt6tlmeiNEH/BiUv9XsKCbgRlTeuRPk6x1k+7yKDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T09:06:46.831166Z"},"content_sha256":"d6dff61b85844e8e26e30f22311077143094f6c8bd016a607244bbe999375cd6","schema_version":"1.0","event_id":"sha256:d6dff61b85844e8e26e30f22311077143094f6c8bd016a607244bbe999375cd6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EZDBPLGZWKM7TJVL5CC2SJ5YX4/bundle.json","state_url":"https://pith.science/pith/EZDBPLGZWKM7TJVL5CC2SJ5YX4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EZDBPLGZWKM7TJVL5CC2SJ5YX4/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":"2026-05-22T09:06:46Z","links":{"resolver":"https://pith.science/pith/EZDBPLGZWKM7TJVL5CC2SJ5YX4","bundle":"https://pith.science/pith/EZDBPLGZWKM7TJVL5CC2SJ5YX4/bundle.json","state":"https://pith.science/pith/EZDBPLGZWKM7TJVL5CC2SJ5YX4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EZDBPLGZWKM7TJVL5CC2SJ5YX4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EZDBPLGZWKM7TJVL5CC2SJ5YX4","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":"1209de4e3afed1dbcd4a9fe954383b3bad7b0b5155c071368d8a0fc718fdc5d4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-18T16:27:55Z","title_canon_sha256":"f01f5c23ea3033e4334fa60f87bfafa4a1b4f36f5f299151e7468f9450142f4e"},"schema_version":"1.0","source":{"id":"1302.4339","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4339","created_at":"2026-05-18T00:12:02Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4339v1","created_at":"2026-05-18T00:12:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4339","created_at":"2026-05-18T00:12:02Z"},{"alias_kind":"pith_short_12","alias_value":"EZDBPLGZWKM7","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EZDBPLGZWKM7TJVL","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EZDBPLGZ","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:d6dff61b85844e8e26e30f22311077143094f6c8bd016a607244bbe999375cd6","target":"graph","created_at":"2026-05-18T00:12:02Z","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 consider random flights of point particles inside $n$-dimensional channels of the form $\\mathbb{R}^{k} \\times \\mathbb{B}^{n-k}$, where $\\mathbb{B}^{n-k}$ is a ball of radius $r$ in dimension $n-k$. The particle velocities immediately after each collision with the boundary of the channel comprise a Markov chain with a transition probabilities operator $P$ that is determined by a choice of (billiard-like) random mechanical model of the particle-surface interaction at the \"microscopic\" scale. Our central concern is the relationship between the scattering properties encoded in $P$ and the const","authors_text":"Hong-Kun Zhang, Renato Feres, Timothy Chumley","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-18T16:27:55Z","title":"Diffusivity in multiple scattering systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4339","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:b3bcf0fce60052ad41791df70a64abcba4c6f8064cc6bb17d8f6ca603b9a2470","target":"record","created_at":"2026-05-18T00:12:02Z","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":"1209de4e3afed1dbcd4a9fe954383b3bad7b0b5155c071368d8a0fc718fdc5d4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-18T16:27:55Z","title_canon_sha256":"f01f5c23ea3033e4334fa60f87bfafa4a1b4f36f5f299151e7468f9450142f4e"},"schema_version":"1.0","source":{"id":"1302.4339","kind":"arxiv","version":1}},"canonical_sha256":"264617acd9b299f9a6abe885a927b8bf2c20781675a6c1d23f2fe14f2872be93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"264617acd9b299f9a6abe885a927b8bf2c20781675a6c1d23f2fe14f2872be93","first_computed_at":"2026-05-18T00:12:02.750639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:02.750639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TeNnfqmACRLY08l/N73LJ8X6fvVfTbsKdHyH1/oBBiDbhXp5T4480lGty+EZ3WGi+q9urF/WecygP+AuCdrhBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:02.751354Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.4339","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3bcf0fce60052ad41791df70a64abcba4c6f8064cc6bb17d8f6ca603b9a2470","sha256:d6dff61b85844e8e26e30f22311077143094f6c8bd016a607244bbe999375cd6"],"state_sha256":"e8b2d23f2226c40e74acd1fb3ee183c282415b4a7c576acbcb7f031bb864bab1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FquN70a2pKGY2y1dZL4g5KrrUE+TUo1MN3xSPX39cVunvi6mMmgSGtJ1QLdw0Rj3l0X4MKDokZ/uOLpe/eRRBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T09:06:46.834545Z","bundle_sha256":"ebef23e0d184a5253ac01a593dbe35520293f3a73b6edea37c936ea6674ca990"}}