{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WYCZMPE2AZBQEAUO3AAUTDUXRE","short_pith_number":"pith:WYCZMPE2","canonical_record":{"source":{"id":"1304.5577","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-04-20T01:45:43Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"f98dbc6c055677e5b7c988b9bb25d6b42eedca29015e673e8b8a98e305cde0eb","abstract_canon_sha256":"df04be5482a85b5b7acf2f4baf85ffdd10a43b4041aa7ea04f1268ba2db77e1e"},"schema_version":"1.0"},"canonical_sha256":"b605963c9a064302028ed801498e978927b4c21ba3277ea3c5e28cbc4f9c0ba5","source":{"kind":"arxiv","id":"1304.5577","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5577","created_at":"2026-05-18T03:19:58Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5577v2","created_at":"2026-05-18T03:19:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5577","created_at":"2026-05-18T03:19:58Z"},{"alias_kind":"pith_short_12","alias_value":"WYCZMPE2AZBQ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WYCZMPE2AZBQEAUO","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WYCZMPE2","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WYCZMPE2AZBQEAUO3AAUTDUXRE","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5577","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-04-20T01:45:43Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"f98dbc6c055677e5b7c988b9bb25d6b42eedca29015e673e8b8a98e305cde0eb","abstract_canon_sha256":"df04be5482a85b5b7acf2f4baf85ffdd10a43b4041aa7ea04f1268ba2db77e1e"},"schema_version":"1.0"},"canonical_sha256":"b605963c9a064302028ed801498e978927b4c21ba3277ea3c5e28cbc4f9c0ba5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:58.805073Z","signature_b64":"/AXPHVXN2CPBW+bJulkdMnavhBYrl8+vrUNPPd+7De1rIJAQ/volvLlXs57KuRJj5cwUiZHViGhXEU6zPHI9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b605963c9a064302028ed801498e978927b4c21ba3277ea3c5e28cbc4f9c0ba5","last_reissued_at":"2026-05-18T03:19:58.804111Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:58.804111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5577","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:19:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N+SgdOjsloLyZ+a0AIjqn2zz/GlRk7Na4F0j2l7CKjAK1P9yaLX3ObmfzMQU9Z3N5MdKP1SSf8PBh538O6CqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:30:14.643808Z"},"content_sha256":"b33589f82e2c4b44875c321a5cbdaf32d3cf704854ce05ce5177aad34f289248","schema_version":"1.0","event_id":"sha256:b33589f82e2c4b44875c321a5cbdaf32d3cf704854ce05ce5177aad34f289248"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WYCZMPE2AZBQEAUO3AAUTDUXRE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distributional Ergodicity in Stored-Energy-Driven L\\'evy Flights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Takuma Akimoto, Tomoshige Miyaguchi","submitted_at":"2013-04-20T01:45:43Z","abstract_excerpt":"We study a class of random walk, the stored-energy-driven L\\'evy flight (SEDLF), whose jump length is determined by a stored energy during a trapped state. The SEDLF is a continuous-time random walk with jump lengths being coupled with the trapping times. It is analytically shown that the ensemble-averaged mean square displacements exhibit subdiffusion as well as superdiffusion, depending on the coupling parameter. We find that time-averaged mean square displacements increase linearly with time and the diffusion coefficients are intrinsically random, a manifestation of {\\it distributional ergo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5577","kind":"arxiv","version":2},"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":"2026-05-18T03:19:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rNkuSWRRpaBbXPRv+5sl98snEEoeV2AiDEOHieTjoPaHXuBGiYeLrEw7gSqnnu60PCtoJ+qp3MP6y5+qZ5JDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:30:14.644150Z"},"content_sha256":"1dfd39ec7221555fcd569f3cfe17a5a227c784c8163e4aad31d1d304621e445d","schema_version":"1.0","event_id":"sha256:1dfd39ec7221555fcd569f3cfe17a5a227c784c8163e4aad31d1d304621e445d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WYCZMPE2AZBQEAUO3AAUTDUXRE/bundle.json","state_url":"https://pith.science/pith/WYCZMPE2AZBQEAUO3AAUTDUXRE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WYCZMPE2AZBQEAUO3AAUTDUXRE/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":"2026-06-25T22:30:14Z","links":{"resolver":"https://pith.science/pith/WYCZMPE2AZBQEAUO3AAUTDUXRE","bundle":"https://pith.science/pith/WYCZMPE2AZBQEAUO3AAUTDUXRE/bundle.json","state":"https://pith.science/pith/WYCZMPE2AZBQEAUO3AAUTDUXRE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WYCZMPE2AZBQEAUO3AAUTDUXRE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WYCZMPE2AZBQEAUO3AAUTDUXRE","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":"df04be5482a85b5b7acf2f4baf85ffdd10a43b4041aa7ea04f1268ba2db77e1e","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-04-20T01:45:43Z","title_canon_sha256":"f98dbc6c055677e5b7c988b9bb25d6b42eedca29015e673e8b8a98e305cde0eb"},"schema_version":"1.0","source":{"id":"1304.5577","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5577","created_at":"2026-05-18T03:19:58Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5577v2","created_at":"2026-05-18T03:19:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5577","created_at":"2026-05-18T03:19:58Z"},{"alias_kind":"pith_short_12","alias_value":"WYCZMPE2AZBQ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WYCZMPE2AZBQEAUO","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WYCZMPE2","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:1dfd39ec7221555fcd569f3cfe17a5a227c784c8163e4aad31d1d304621e445d","target":"graph","created_at":"2026-05-18T03:19:58Z","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 study a class of random walk, the stored-energy-driven L\\'evy flight (SEDLF), whose jump length is determined by a stored energy during a trapped state. The SEDLF is a continuous-time random walk with jump lengths being coupled with the trapping times. It is analytically shown that the ensemble-averaged mean square displacements exhibit subdiffusion as well as superdiffusion, depending on the coupling parameter. We find that time-averaged mean square displacements increase linearly with time and the diffusion coefficients are intrinsically random, a manifestation of {\\it distributional ergo","authors_text":"Takuma Akimoto, Tomoshige Miyaguchi","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-04-20T01:45:43Z","title":"Distributional Ergodicity in Stored-Energy-Driven L\\'evy Flights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5577","kind":"arxiv","version":2},"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:b33589f82e2c4b44875c321a5cbdaf32d3cf704854ce05ce5177aad34f289248","target":"record","created_at":"2026-05-18T03:19:58Z","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":"df04be5482a85b5b7acf2f4baf85ffdd10a43b4041aa7ea04f1268ba2db77e1e","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-04-20T01:45:43Z","title_canon_sha256":"f98dbc6c055677e5b7c988b9bb25d6b42eedca29015e673e8b8a98e305cde0eb"},"schema_version":"1.0","source":{"id":"1304.5577","kind":"arxiv","version":2}},"canonical_sha256":"b605963c9a064302028ed801498e978927b4c21ba3277ea3c5e28cbc4f9c0ba5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b605963c9a064302028ed801498e978927b4c21ba3277ea3c5e28cbc4f9c0ba5","first_computed_at":"2026-05-18T03:19:58.804111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:58.804111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/AXPHVXN2CPBW+bJulkdMnavhBYrl8+vrUNPPd+7De1rIJAQ/volvLlXs57KuRJj5cwUiZHViGhXEU6zPHI9CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:58.805073Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5577","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b33589f82e2c4b44875c321a5cbdaf32d3cf704854ce05ce5177aad34f289248","sha256:1dfd39ec7221555fcd569f3cfe17a5a227c784c8163e4aad31d1d304621e445d"],"state_sha256":"371178eeeed836b902325b501a8d39300b6acf113166bfba9b5ea60f6a6a6406"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xbwVPcAgLmod0gOpyTZ9crmHEEkxT4EuruMMIeRGkUZrU/5hDKkdnyJAZC9PTeDt7F29hs7vnY3EgjMn+HyMBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T22:30:14.646082Z","bundle_sha256":"021ef2f5604dafac1341cf147c18a5ea143d2f37ac5ba0806aa3ee4e9e532edf"}}