{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7OEA33TES4MGTOI3RW33AN3BMZ","short_pith_number":"pith:7OEA33TE","canonical_record":{"source":{"id":"1207.1228","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2012-07-05T11:32:34Z","cross_cats_sorted":[],"title_canon_sha256":"984f458f40139ece5842271e725565034622b65d61a363b363094f0429760395","abstract_canon_sha256":"3825e0093218210df2a2b27050e35a834e98ec20ff53d0b20c2e8fbf906b8af9"},"schema_version":"1.0"},"canonical_sha256":"fb880dee64971869b91b8db7b03761667752fc55a73da7b707460620d3960fa2","source":{"kind":"arxiv","id":"1207.1228","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1228","created_at":"2026-05-18T03:47:52Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1228v2","created_at":"2026-05-18T03:47:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1228","created_at":"2026-05-18T03:47:52Z"},{"alias_kind":"pith_short_12","alias_value":"7OEA33TES4MG","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7OEA33TES4MGTOI3","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7OEA33TE","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7OEA33TES4MGTOI3RW33AN3BMZ","target":"record","payload":{"canonical_record":{"source":{"id":"1207.1228","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2012-07-05T11:32:34Z","cross_cats_sorted":[],"title_canon_sha256":"984f458f40139ece5842271e725565034622b65d61a363b363094f0429760395","abstract_canon_sha256":"3825e0093218210df2a2b27050e35a834e98ec20ff53d0b20c2e8fbf906b8af9"},"schema_version":"1.0"},"canonical_sha256":"fb880dee64971869b91b8db7b03761667752fc55a73da7b707460620d3960fa2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:47:52.522631Z","signature_b64":"/givhAuZs0hlHTDkBg5jgvyRMibCogyXDaWeMjKWU8vNG3MrzcUqnrEX9OpvFeSh4hxFSq+H0kdpukikdcr6Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb880dee64971869b91b8db7b03761667752fc55a73da7b707460620d3960fa2","last_reissued_at":"2026-05-18T03:47:52.522187Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:47:52.522187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.1228","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":"2026-05-18T03:47:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G8HDhSlO3KPJrh0DhpuNrRd77WllCfdhdWIlE51rIuf/KlZr2Cvs9CyGTdl5F0LqjNGP+wHEX0OkzSYIJwKfDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:19:02.505147Z"},"content_sha256":"d0cb436c2f08af4b0f87a45b4870e94f0ecfa5d3e54341157affebdb4d87a591","schema_version":"1.0","event_id":"sha256:d0cb436c2f08af4b0f87a45b4870e94f0ecfa5d3e54341157affebdb4d87a591"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7OEA33TES4MGTOI3RW33AN3BMZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"1D analysis of 2D isotropic random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.QM","authors_text":"Claus Metzner","submitted_at":"2012-07-05T11:32:34Z","abstract_excerpt":"Many stochastic systems in physics and biology are investigated by recording the two-dimensional (2D) positions of a moving test particle in regular time intervals. The resulting sample trajectories are then used to induce the properties of the underlying stochastic process. Often, it can be assumed a priori that the underlying discrete-time random walk model is independent from absolute position (homogeneity), direction (isotropy) and time (stationarity), as well as ergodic. In this article we first review some common statistical methods for analyzing 2D trajectories, based on quantities with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1228","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":"2026-05-18T03:47:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6wkoizJ4l0L0cgnzNttyAAQCJc8mMlDop9VqzbI8VmLqYd5zdzisieR6AZCUT0g8ZtYyhiC2qEcBnTGecIJkBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:19:02.505721Z"},"content_sha256":"e8561bce54f98d7b9e287a30595d5d5805894d525cbdfdb6d83691239bece225","schema_version":"1.0","event_id":"sha256:e8561bce54f98d7b9e287a30595d5d5805894d525cbdfdb6d83691239bece225"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7OEA33TES4MGTOI3RW33AN3BMZ/bundle.json","state_url":"https://pith.science/pith/7OEA33TES4MGTOI3RW33AN3BMZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7OEA33TES4MGTOI3RW33AN3BMZ/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":"2026-05-27T03:19:02Z","links":{"resolver":"https://pith.science/pith/7OEA33TES4MGTOI3RW33AN3BMZ","bundle":"https://pith.science/pith/7OEA33TES4MGTOI3RW33AN3BMZ/bundle.json","state":"https://pith.science/pith/7OEA33TES4MGTOI3RW33AN3BMZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7OEA33TES4MGTOI3RW33AN3BMZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7OEA33TES4MGTOI3RW33AN3BMZ","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":"3825e0093218210df2a2b27050e35a834e98ec20ff53d0b20c2e8fbf906b8af9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2012-07-05T11:32:34Z","title_canon_sha256":"984f458f40139ece5842271e725565034622b65d61a363b363094f0429760395"},"schema_version":"1.0","source":{"id":"1207.1228","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1228","created_at":"2026-05-18T03:47:52Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1228v2","created_at":"2026-05-18T03:47:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1228","created_at":"2026-05-18T03:47:52Z"},{"alias_kind":"pith_short_12","alias_value":"7OEA33TES4MG","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7OEA33TES4MGTOI3","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7OEA33TE","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:e8561bce54f98d7b9e287a30595d5d5805894d525cbdfdb6d83691239bece225","target":"graph","created_at":"2026-05-18T03:47:52Z","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":"Many stochastic systems in physics and biology are investigated by recording the two-dimensional (2D) positions of a moving test particle in regular time intervals. The resulting sample trajectories are then used to induce the properties of the underlying stochastic process. Often, it can be assumed a priori that the underlying discrete-time random walk model is independent from absolute position (homogeneity), direction (isotropy) and time (stationarity), as well as ergodic. In this article we first review some common statistical methods for analyzing 2D trajectories, based on quantities with","authors_text":"Claus Metzner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2012-07-05T11:32:34Z","title":"1D analysis of 2D isotropic random walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1228","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:d0cb436c2f08af4b0f87a45b4870e94f0ecfa5d3e54341157affebdb4d87a591","target":"record","created_at":"2026-05-18T03:47:52Z","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":"3825e0093218210df2a2b27050e35a834e98ec20ff53d0b20c2e8fbf906b8af9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2012-07-05T11:32:34Z","title_canon_sha256":"984f458f40139ece5842271e725565034622b65d61a363b363094f0429760395"},"schema_version":"1.0","source":{"id":"1207.1228","kind":"arxiv","version":2}},"canonical_sha256":"fb880dee64971869b91b8db7b03761667752fc55a73da7b707460620d3960fa2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb880dee64971869b91b8db7b03761667752fc55a73da7b707460620d3960fa2","first_computed_at":"2026-05-18T03:47:52.522187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:47:52.522187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/givhAuZs0hlHTDkBg5jgvyRMibCogyXDaWeMjKWU8vNG3MrzcUqnrEX9OpvFeSh4hxFSq+H0kdpukikdcr6Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:47:52.522631Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1228","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0cb436c2f08af4b0f87a45b4870e94f0ecfa5d3e54341157affebdb4d87a591","sha256:e8561bce54f98d7b9e287a30595d5d5805894d525cbdfdb6d83691239bece225"],"state_sha256":"b34b773c35003e84e98d5cc48b88a771c054940d6f91330542c00ef3688085ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t66+d8M4kjxWzld9krIJ4QaX9J/uOpAwWR6971XA/GAGT+mTLM3cZLcv44Arrr5pUPNk+MYzfAOJ3MU2S0ROBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T03:19:02.508824Z","bundle_sha256":"c8ef170eb331b3cdae813b13c5b1b5df3b52c5e0fd684126ae310499ff564482"}}