{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:IYUQPJLI3KQIH2QMKMVJDNAFAD","short_pith_number":"pith:IYUQPJLI","canonical_record":{"source":{"id":"1002.0599","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-02T21:18:41Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"38a327f20c4a96a732b2d1242dec81e87e07987f4b4970d2864d10fbfcb699b0","abstract_canon_sha256":"337102ba613c67b92f4e7c2d66f8bc4949d1d18d28dcba07d185c80909918ca8"},"schema_version":"1.0"},"canonical_sha256":"462907a568daa083ea0c532a91b40500d1420f984a2eac714615ad39d7652fbf","source":{"kind":"arxiv","id":"1002.0599","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.0599","created_at":"2026-05-18T01:24:38Z"},{"alias_kind":"arxiv_version","alias_value":"1002.0599v3","created_at":"2026-05-18T01:24:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0599","created_at":"2026-05-18T01:24:38Z"},{"alias_kind":"pith_short_12","alias_value":"IYUQPJLI3KQI","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IYUQPJLI3KQIH2QM","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IYUQPJLI","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:IYUQPJLI3KQIH2QMKMVJDNAFAD","target":"record","payload":{"canonical_record":{"source":{"id":"1002.0599","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-02T21:18:41Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"38a327f20c4a96a732b2d1242dec81e87e07987f4b4970d2864d10fbfcb699b0","abstract_canon_sha256":"337102ba613c67b92f4e7c2d66f8bc4949d1d18d28dcba07d185c80909918ca8"},"schema_version":"1.0"},"canonical_sha256":"462907a568daa083ea0c532a91b40500d1420f984a2eac714615ad39d7652fbf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:38.937299Z","signature_b64":"VUETDE7+eoYpyfAUCo2U+ZgJUdclHwypQi3dCrr6wsNm+36wauX4tlRQ6D6X8M0LCef2RN5QVL5ABmMQsEsfDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"462907a568daa083ea0c532a91b40500d1420f984a2eac714615ad39d7652fbf","last_reissued_at":"2026-05-18T01:24:38.936859Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:38.936859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.0599","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:24:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2NXjWa81px9/NejVnXm5z+fuvY6plQTm8tM9xxTFGpVoBtjb7MDzlCETjOeCTQ7TRFYu8D3cZg0Gess6ECUZDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:07:42.147857Z"},"content_sha256":"d912c6218c043219fe976b37ffab7186b3732ab3421ba746bc1a991c99462c0b","schema_version":"1.0","event_id":"sha256:d912c6218c043219fe976b37ffab7186b3732ab3421ba746bc1a991c99462c0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:IYUQPJLI3KQIH2QMKMVJDNAFAD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diffusive propagation of wave packets in a fluctuating periodic potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Eman Hamza, Jeffrey Schenker, Yang Kang","submitted_at":"2010-02-02T21:18:41Z","abstract_excerpt":"We consider the evolution of a tight binding wave packet propagating in a fluctuating periodic potential. If the fluctuations stem from a stationary Markov process satisfying certain technical criteria, we show that the square amplitude of the wave packet after diffusive rescaling converges to a superposition of solutions of a heat equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0599","kind":"arxiv","version":3},"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":"2026-05-18T01:24:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1USqIRioABI2bbPiqxdGZ4CIOqtsxRtmw1jUx1ASiaftleMYLpVKTHaR/oO31k/xpFjYlMho0o+qYMBRjKv4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:07:42.148516Z"},"content_sha256":"8d38dafd406042c72fe60cd6da50a452c43eeb16c3721dcb6264c0c339af71a6","schema_version":"1.0","event_id":"sha256:8d38dafd406042c72fe60cd6da50a452c43eeb16c3721dcb6264c0c339af71a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IYUQPJLI3KQIH2QMKMVJDNAFAD/bundle.json","state_url":"https://pith.science/pith/IYUQPJLI3KQIH2QMKMVJDNAFAD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IYUQPJLI3KQIH2QMKMVJDNAFAD/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":"2026-06-04T17:07:42Z","links":{"resolver":"https://pith.science/pith/IYUQPJLI3KQIH2QMKMVJDNAFAD","bundle":"https://pith.science/pith/IYUQPJLI3KQIH2QMKMVJDNAFAD/bundle.json","state":"https://pith.science/pith/IYUQPJLI3KQIH2QMKMVJDNAFAD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IYUQPJLI3KQIH2QMKMVJDNAFAD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IYUQPJLI3KQIH2QMKMVJDNAFAD","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":"337102ba613c67b92f4e7c2d66f8bc4949d1d18d28dcba07d185c80909918ca8","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-02T21:18:41Z","title_canon_sha256":"38a327f20c4a96a732b2d1242dec81e87e07987f4b4970d2864d10fbfcb699b0"},"schema_version":"1.0","source":{"id":"1002.0599","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.0599","created_at":"2026-05-18T01:24:38Z"},{"alias_kind":"arxiv_version","alias_value":"1002.0599v3","created_at":"2026-05-18T01:24:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0599","created_at":"2026-05-18T01:24:38Z"},{"alias_kind":"pith_short_12","alias_value":"IYUQPJLI3KQI","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IYUQPJLI3KQIH2QM","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IYUQPJLI","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:8d38dafd406042c72fe60cd6da50a452c43eeb16c3721dcb6264c0c339af71a6","target":"graph","created_at":"2026-05-18T01:24:38Z","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 the evolution of a tight binding wave packet propagating in a fluctuating periodic potential. If the fluctuations stem from a stationary Markov process satisfying certain technical criteria, we show that the square amplitude of the wave packet after diffusive rescaling converges to a superposition of solutions of a heat equation.","authors_text":"Eman Hamza, Jeffrey Schenker, Yang Kang","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-02T21:18:41Z","title":"Diffusive propagation of wave packets in a fluctuating periodic potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0599","kind":"arxiv","version":3},"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:d912c6218c043219fe976b37ffab7186b3732ab3421ba746bc1a991c99462c0b","target":"record","created_at":"2026-05-18T01:24:38Z","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":"337102ba613c67b92f4e7c2d66f8bc4949d1d18d28dcba07d185c80909918ca8","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-02-02T21:18:41Z","title_canon_sha256":"38a327f20c4a96a732b2d1242dec81e87e07987f4b4970d2864d10fbfcb699b0"},"schema_version":"1.0","source":{"id":"1002.0599","kind":"arxiv","version":3}},"canonical_sha256":"462907a568daa083ea0c532a91b40500d1420f984a2eac714615ad39d7652fbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"462907a568daa083ea0c532a91b40500d1420f984a2eac714615ad39d7652fbf","first_computed_at":"2026-05-18T01:24:38.936859Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:38.936859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VUETDE7+eoYpyfAUCo2U+ZgJUdclHwypQi3dCrr6wsNm+36wauX4tlRQ6D6X8M0LCef2RN5QVL5ABmMQsEsfDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:38.937299Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.0599","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d912c6218c043219fe976b37ffab7186b3732ab3421ba746bc1a991c99462c0b","sha256:8d38dafd406042c72fe60cd6da50a452c43eeb16c3721dcb6264c0c339af71a6"],"state_sha256":"3737910271b7b85676ab662fc1661cf79d1bc3dba94ae921f8946bd08b93c65d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CgTKd3H9AWYpD81JUqII8YCGVJimBAJt0tOa9PXCGd8cIRLwekQDLKqyIStbgVl1mUt0q+8Bnkf0SuDGH5RpBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T17:07:42.151468Z","bundle_sha256":"e68ffde963242025f1f37daa3f57c9060c0d5451e975a18ac656d4f6a44457cb"}}