{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:KS7U7MQHQB6GH7KPWRUCOG5Q3O","short_pith_number":"pith:KS7U7MQH","canonical_record":{"source":{"id":"nlin/0402043","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.CG","submitted_at":"2004-02-23T16:10:00Z","cross_cats_sorted":[],"title_canon_sha256":"803d59227710e749759f60bed24031121f3fb512fccd0ec22c5d19c93f9c61d6","abstract_canon_sha256":"76150e739abf0ad80f77e8977028d27ceba9e4c280aa61e817140d64038ca621"},"schema_version":"1.0"},"canonical_sha256":"54bf4fb207807c63fd4fb468271bb0dbbef8dc74e948f9fab04de6de1e9ede19","source":{"kind":"arxiv","id":"nlin/0402043","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0402043","created_at":"2026-05-18T04:34:28Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0402043v1","created_at":"2026-05-18T04:34:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0402043","created_at":"2026-05-18T04:34:28Z"},{"alias_kind":"pith_short_12","alias_value":"KS7U7MQHQB6G","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"KS7U7MQHQB6GH7KP","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"KS7U7MQH","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:KS7U7MQHQB6GH7KPWRUCOG5Q3O","target":"record","payload":{"canonical_record":{"source":{"id":"nlin/0402043","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"nlin.CG","submitted_at":"2004-02-23T16:10:00Z","cross_cats_sorted":[],"title_canon_sha256":"803d59227710e749759f60bed24031121f3fb512fccd0ec22c5d19c93f9c61d6","abstract_canon_sha256":"76150e739abf0ad80f77e8977028d27ceba9e4c280aa61e817140d64038ca621"},"schema_version":"1.0"},"canonical_sha256":"54bf4fb207807c63fd4fb468271bb0dbbef8dc74e948f9fab04de6de1e9ede19","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:28.190743Z","signature_b64":"vgFTeFlkUJm6gARrmF83CMB+O1w4VFb9wO2o4v4TVh522B6zT1CAtn7uvehzfr0OYGw1lsNMRwHC9Acvh4DlBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54bf4fb207807c63fd4fb468271bb0dbbef8dc74e948f9fab04de6de1e9ede19","last_reissued_at":"2026-05-18T04:34:28.190183Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:28.190183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"nlin/0402043","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":"2026-05-18T04:34:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tAu4y8OhWXI8umWZM9XKHEUdJqcXZIxQudKIBJfYqb8aP0x8dlCKWFBIG2E725hEofmr014KST3lqUh/isOaCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:35:16.073575Z"},"content_sha256":"74d26de9fd51ae267135ecf76e6be3dd808a3dd7a732d191479feb00cfcbb64a","schema_version":"1.0","event_id":"sha256:74d26de9fd51ae267135ecf76e6be3dd808a3dd7a732d191479feb00cfcbb64a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:KS7U7MQHQB6GH7KPWRUCOG5Q3O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Markovian behaviour of $p$-adic random dynamical systems","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.CG","authors_text":"Andrei Khrennikov, Karl-Olof Lindahl, Matthias Gundlach, Sergio Albeverio","submitted_at":"2004-02-23T16:10:00Z","abstract_excerpt":"We study Markovian and non-Markovian behaviour of stochastic processes generated by $p$-adic random dynamical systems. Given a family of $p$-adic monomial random mappings generating a random dynamical system. Under which conditions do the orbits under such a random dynamical system form Markov chains? It is necessary that the mappings are Markov dependent. We show, however, that this is in general not sufficient. In fact, in many cases we have to require that the mappings are independent. Moreover we investigate some geometric and algebraic properties for $p-$adic monomial mappings as well as "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0402043","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":"2026-05-18T04:34:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7KM0mZXfLH34WFSYAULjr9BOesiqPgMdaBS+fluQg+GphgSDqXrqsxNOvNPNNuenmm9Cz1NlHZxNC0NLAtFtCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:35:16.074271Z"},"content_sha256":"3501ce20dace2718d5ff482ed64826ae3e1791e60a3b4c8fa9b4edd42c4f1e3f","schema_version":"1.0","event_id":"sha256:3501ce20dace2718d5ff482ed64826ae3e1791e60a3b4c8fa9b4edd42c4f1e3f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KS7U7MQHQB6GH7KPWRUCOG5Q3O/bundle.json","state_url":"https://pith.science/pith/KS7U7MQHQB6GH7KPWRUCOG5Q3O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KS7U7MQHQB6GH7KPWRUCOG5Q3O/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":"2026-06-11T21:35:16Z","links":{"resolver":"https://pith.science/pith/KS7U7MQHQB6GH7KPWRUCOG5Q3O","bundle":"https://pith.science/pith/KS7U7MQHQB6GH7KPWRUCOG5Q3O/bundle.json","state":"https://pith.science/pith/KS7U7MQHQB6GH7KPWRUCOG5Q3O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KS7U7MQHQB6GH7KPWRUCOG5Q3O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:KS7U7MQHQB6GH7KPWRUCOG5Q3O","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":"76150e739abf0ad80f77e8977028d27ceba9e4c280aa61e817140d64038ca621","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CG","submitted_at":"2004-02-23T16:10:00Z","title_canon_sha256":"803d59227710e749759f60bed24031121f3fb512fccd0ec22c5d19c93f9c61d6"},"schema_version":"1.0","source":{"id":"nlin/0402043","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0402043","created_at":"2026-05-18T04:34:28Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0402043v1","created_at":"2026-05-18T04:34:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0402043","created_at":"2026-05-18T04:34:28Z"},{"alias_kind":"pith_short_12","alias_value":"KS7U7MQHQB6G","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"KS7U7MQHQB6GH7KP","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"KS7U7MQH","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:3501ce20dace2718d5ff482ed64826ae3e1791e60a3b4c8fa9b4edd42c4f1e3f","target":"graph","created_at":"2026-05-18T04:34:28Z","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 Markovian and non-Markovian behaviour of stochastic processes generated by $p$-adic random dynamical systems. Given a family of $p$-adic monomial random mappings generating a random dynamical system. Under which conditions do the orbits under such a random dynamical system form Markov chains? It is necessary that the mappings are Markov dependent. We show, however, that this is in general not sufficient. In fact, in many cases we have to require that the mappings are independent. Moreover we investigate some geometric and algebraic properties for $p-$adic monomial mappings as well as ","authors_text":"Andrei Khrennikov, Karl-Olof Lindahl, Matthias Gundlach, Sergio Albeverio","cross_cats":[],"headline":"","license":"","primary_cat":"nlin.CG","submitted_at":"2004-02-23T16:10:00Z","title":"On Markovian behaviour of $p$-adic random dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0402043","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":"sha256:74d26de9fd51ae267135ecf76e6be3dd808a3dd7a732d191479feb00cfcbb64a","target":"record","created_at":"2026-05-18T04:34:28Z","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":"76150e739abf0ad80f77e8977028d27ceba9e4c280aa61e817140d64038ca621","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CG","submitted_at":"2004-02-23T16:10:00Z","title_canon_sha256":"803d59227710e749759f60bed24031121f3fb512fccd0ec22c5d19c93f9c61d6"},"schema_version":"1.0","source":{"id":"nlin/0402043","kind":"arxiv","version":1}},"canonical_sha256":"54bf4fb207807c63fd4fb468271bb0dbbef8dc74e948f9fab04de6de1e9ede19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54bf4fb207807c63fd4fb468271bb0dbbef8dc74e948f9fab04de6de1e9ede19","first_computed_at":"2026-05-18T04:34:28.190183Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:28.190183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vgFTeFlkUJm6gARrmF83CMB+O1w4VFb9wO2o4v4TVh522B6zT1CAtn7uvehzfr0OYGw1lsNMRwHC9Acvh4DlBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:28.190743Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0402043","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74d26de9fd51ae267135ecf76e6be3dd808a3dd7a732d191479feb00cfcbb64a","sha256:3501ce20dace2718d5ff482ed64826ae3e1791e60a3b4c8fa9b4edd42c4f1e3f"],"state_sha256":"cfd24ddc481a06e56e582ccc7791400e7c98b3ea020518de5ed8b466305a0f13"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mzr0UMTuRhaF3GDVry3k2DNWGJb+XjuB4L2+13FmQgRXB6jgfYBDEC4B9SavzjUu+4Ew7K2O9R90oU94mQBGAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T21:35:16.078819Z","bundle_sha256":"302335d8c035ef82ba79f92df3d752de1f15133f880464c7e28fd9220568dcbc"}}