{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:LXOFWF7U2UWROXZDZZIK5L7QDH","short_pith_number":"pith:LXOFWF7U","canonical_record":{"source":{"id":"0909.0463","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2009-09-02T16:02:47Z","cross_cats_sorted":["cond-mat.other"],"title_canon_sha256":"a0341b16162d8fa64048f96af1f57d1e8e78d91b9bdfe21c4b4e9df4e008bc3b","abstract_canon_sha256":"553ce9f7c234162b8be83e6b6871a2571c399c6b7e2467f8ae9b4488bd58fd4b"},"schema_version":"1.0"},"canonical_sha256":"5ddc5b17f4d52d175f23ce50aeaff019cdcfd823c2797d88aaa52c136486806d","source":{"kind":"arxiv","id":"0909.0463","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.0463","created_at":"2026-05-18T04:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"0909.0463v1","created_at":"2026-05-18T04:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.0463","created_at":"2026-05-18T04:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"LXOFWF7U2UWR","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LXOFWF7U2UWROXZD","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LXOFWF7U","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:LXOFWF7U2UWROXZDZZIK5L7QDH","target":"record","payload":{"canonical_record":{"source":{"id":"0909.0463","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2009-09-02T16:02:47Z","cross_cats_sorted":["cond-mat.other"],"title_canon_sha256":"a0341b16162d8fa64048f96af1f57d1e8e78d91b9bdfe21c4b4e9df4e008bc3b","abstract_canon_sha256":"553ce9f7c234162b8be83e6b6871a2571c399c6b7e2467f8ae9b4488bd58fd4b"},"schema_version":"1.0"},"canonical_sha256":"5ddc5b17f4d52d175f23ce50aeaff019cdcfd823c2797d88aaa52c136486806d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:23.955195Z","signature_b64":"9ikH1+gXMnfLbpEhtbjKUUXalBqtJlYgdot0supIX9H1h9+pYPqeCjQ1vr3tufZzlA7K5pLPZveVIIBxY2BxBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ddc5b17f4d52d175f23ce50aeaff019cdcfd823c2797d88aaa52c136486806d","last_reissued_at":"2026-05-18T04:42:23.954720Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:23.954720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.0463","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":"2026-05-18T04:42:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z0QvWwCzJv6Wv0E4q4V3n1BN5Sqe+rEF/3nFl2dTBSuDoW9Ye0GyBHQ19RD3zrZFBiddKZ2tR+806PjkpJrxBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:19:11.078637Z"},"content_sha256":"d7b7c18844812a6e74017fd5058d1a2c45395984fe01d34d87a9537743d2f805","schema_version":"1.0","event_id":"sha256:d7b7c18844812a6e74017fd5058d1a2c45395984fe01d34d87a9537743d2f805"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:LXOFWF7U2UWROXZDZZIK5L7QDH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nature of electron Zitterbewegung in crystalline solids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other"],"primary_cat":"cond-mat.mes-hall","authors_text":"Tomasz M. Rusin, Wlodek Zawadzki","submitted_at":"2009-09-02T16:02:47Z","abstract_excerpt":"We demonstrate both classically and quantum mechanically that the Zitterbewegung (ZB, the trembling motion) of electrons in crystalline solids is nothing else, but oscillations of velocity assuring the energy conservation when the electron moves in a periodic potential. This means that the nature of electron ZB in a solid is completely different from that of relativistic electrons in a vacuum, as proposed by Schrodinger. Still, we show that the two-band {\\bf k.p} model of electronic band structure, formally similar to the Dirac equation for electrons in a vacuum, gives a very good description "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0463","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":"2026-05-18T04:42:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oH36C7yGnfQIqK3QojMTi/K/lTUOb5RHRa29/ZA/HdgWN4IcS6pSy+FNt/YMFmKjr81uCyQiUcpB7Pu81kiDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:19:11.079010Z"},"content_sha256":"a28587bc9a3343eda668badfd58b644187f1e7bd96e64a15f3db49c55be0e2e5","schema_version":"1.0","event_id":"sha256:a28587bc9a3343eda668badfd58b644187f1e7bd96e64a15f3db49c55be0e2e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LXOFWF7U2UWROXZDZZIK5L7QDH/bundle.json","state_url":"https://pith.science/pith/LXOFWF7U2UWROXZDZZIK5L7QDH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LXOFWF7U2UWROXZDZZIK5L7QDH/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":"2026-06-06T19:19:11Z","links":{"resolver":"https://pith.science/pith/LXOFWF7U2UWROXZDZZIK5L7QDH","bundle":"https://pith.science/pith/LXOFWF7U2UWROXZDZZIK5L7QDH/bundle.json","state":"https://pith.science/pith/LXOFWF7U2UWROXZDZZIK5L7QDH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LXOFWF7U2UWROXZDZZIK5L7QDH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:LXOFWF7U2UWROXZDZZIK5L7QDH","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":"553ce9f7c234162b8be83e6b6871a2571c399c6b7e2467f8ae9b4488bd58fd4b","cross_cats_sorted":["cond-mat.other"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2009-09-02T16:02:47Z","title_canon_sha256":"a0341b16162d8fa64048f96af1f57d1e8e78d91b9bdfe21c4b4e9df4e008bc3b"},"schema_version":"1.0","source":{"id":"0909.0463","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.0463","created_at":"2026-05-18T04:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"0909.0463v1","created_at":"2026-05-18T04:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.0463","created_at":"2026-05-18T04:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"LXOFWF7U2UWR","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LXOFWF7U2UWROXZD","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LXOFWF7U","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:a28587bc9a3343eda668badfd58b644187f1e7bd96e64a15f3db49c55be0e2e5","target":"graph","created_at":"2026-05-18T04:42:23Z","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 demonstrate both classically and quantum mechanically that the Zitterbewegung (ZB, the trembling motion) of electrons in crystalline solids is nothing else, but oscillations of velocity assuring the energy conservation when the electron moves in a periodic potential. This means that the nature of electron ZB in a solid is completely different from that of relativistic electrons in a vacuum, as proposed by Schrodinger. Still, we show that the two-band {\\bf k.p} model of electronic band structure, formally similar to the Dirac equation for electrons in a vacuum, gives a very good description ","authors_text":"Tomasz M. Rusin, Wlodek Zawadzki","cross_cats":["cond-mat.other"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2009-09-02T16:02:47Z","title":"Nature of electron Zitterbewegung in crystalline solids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0463","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:d7b7c18844812a6e74017fd5058d1a2c45395984fe01d34d87a9537743d2f805","target":"record","created_at":"2026-05-18T04:42:23Z","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":"553ce9f7c234162b8be83e6b6871a2571c399c6b7e2467f8ae9b4488bd58fd4b","cross_cats_sorted":["cond-mat.other"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2009-09-02T16:02:47Z","title_canon_sha256":"a0341b16162d8fa64048f96af1f57d1e8e78d91b9bdfe21c4b4e9df4e008bc3b"},"schema_version":"1.0","source":{"id":"0909.0463","kind":"arxiv","version":1}},"canonical_sha256":"5ddc5b17f4d52d175f23ce50aeaff019cdcfd823c2797d88aaa52c136486806d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ddc5b17f4d52d175f23ce50aeaff019cdcfd823c2797d88aaa52c136486806d","first_computed_at":"2026-05-18T04:42:23.954720Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:23.954720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ikH1+gXMnfLbpEhtbjKUUXalBqtJlYgdot0supIX9H1h9+pYPqeCjQ1vr3tufZzlA7K5pLPZveVIIBxY2BxBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:23.955195Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.0463","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7b7c18844812a6e74017fd5058d1a2c45395984fe01d34d87a9537743d2f805","sha256:a28587bc9a3343eda668badfd58b644187f1e7bd96e64a15f3db49c55be0e2e5"],"state_sha256":"17e99b38b46368cc63070cb060b2f95fc0c9b511bd7ac0398f598b169f9d4a2f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"52QzPJgBboR6hslue+z6zpvDNNpTpOldFntArKDUaorQWDpVF2LmcgpnGCx50vJR3mKMgmzLRLQvnxRhJ7yPAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:19:11.081145Z","bundle_sha256":"87dbda60ca42f69c8d0c2a1c5a14c70468ed24c18956d276969efd14a462db2c"}}