{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZTRSYIOI4PHRL7MW2WSR3XQ7TJ","short_pith_number":"pith:ZTRSYIOI","canonical_record":{"source":{"id":"1508.00867","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-04T18:51:04Z","cross_cats_sorted":[],"title_canon_sha256":"3b404490cdeec6b370ab343d963476a0db1e86033c50055383f534aa4bf33e41","abstract_canon_sha256":"bfdecbe242cba107f178fd26ce3e26bf7548a04864728a10c39b9ab9def45ca5"},"schema_version":"1.0"},"canonical_sha256":"cce32c21c8e3cf15fd96d5a51dde1f9a671b9d18d5e085c0e38a95edf537d5ba","source":{"kind":"arxiv","id":"1508.00867","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00867","created_at":"2026-05-18T01:35:53Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00867v1","created_at":"2026-05-18T01:35:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00867","created_at":"2026-05-18T01:35:53Z"},{"alias_kind":"pith_short_12","alias_value":"ZTRSYIOI4PHR","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZTRSYIOI4PHRL7MW","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZTRSYIOI","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZTRSYIOI4PHRL7MW2WSR3XQ7TJ","target":"record","payload":{"canonical_record":{"source":{"id":"1508.00867","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-04T18:51:04Z","cross_cats_sorted":[],"title_canon_sha256":"3b404490cdeec6b370ab343d963476a0db1e86033c50055383f534aa4bf33e41","abstract_canon_sha256":"bfdecbe242cba107f178fd26ce3e26bf7548a04864728a10c39b9ab9def45ca5"},"schema_version":"1.0"},"canonical_sha256":"cce32c21c8e3cf15fd96d5a51dde1f9a671b9d18d5e085c0e38a95edf537d5ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:53.157477Z","signature_b64":"ojt2Ywk/i9f/dwpApdlazfUDK0v/jcPVKjsgv+OkUrGXdqEL9aaKZO8FDSjndD/seJ5CM8RpuCG15ydNRo1hCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cce32c21c8e3cf15fd96d5a51dde1f9a671b9d18d5e085c0e38a95edf537d5ba","last_reissued_at":"2026-05-18T01:35:53.156737Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:53.156737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.00867","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":"2026-05-18T01:35:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ljVU2ZQSsYji3sLBzSue3uHizkO4XOVLamLujmwA9fPLm/NtNXLMGWMvQGxw6yHToluBQE0DWfR4oqOjtOjwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:09:26.799168Z"},"content_sha256":"f01ef2a510ce99f5ff9db318975e863895b8336d2dbec48f60746131022dc6dc","schema_version":"1.0","event_id":"sha256:f01ef2a510ce99f5ff9db318975e863895b8336d2dbec48f60746131022dc6dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZTRSYIOI4PHRL7MW2WSR3XQ7TJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"One-dimensional infinite memory imitation models with noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Emilio De Santis, Mauro Piccioni","submitted_at":"2015-08-04T18:51:04Z","abstract_excerpt":"In this paper we study stochastic process indexed by $\\mathbb {Z}$ constructed from certain transition kernels depending on the whole past. These kernels prescribe that, at any time, the current state is selected by looking only at a previous random instant. We characterize uniqueness in terms of simple concepts concerning families of stochastic matrices, generalizing the results previously obtained in De Santis and Piccioni (J. Stat. Phys., 150(6):1017--1029, 2013)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00867","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":"2026-05-18T01:35:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+LtNGmlOq3rlfR2WMvjOfNp0CdIGep0qJujsK8fu1nQsd4wtJBXrNVsWjriDyQ7qN2erHQcWUUW6PVH9D8x1CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:09:26.799886Z"},"content_sha256":"abaf20fa2959166738d7180769aefec477ab4a7aab5f3851c596247f522236a4","schema_version":"1.0","event_id":"sha256:abaf20fa2959166738d7180769aefec477ab4a7aab5f3851c596247f522236a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZTRSYIOI4PHRL7MW2WSR3XQ7TJ/bundle.json","state_url":"https://pith.science/pith/ZTRSYIOI4PHRL7MW2WSR3XQ7TJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZTRSYIOI4PHRL7MW2WSR3XQ7TJ/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":"2026-06-07T22:09:26Z","links":{"resolver":"https://pith.science/pith/ZTRSYIOI4PHRL7MW2WSR3XQ7TJ","bundle":"https://pith.science/pith/ZTRSYIOI4PHRL7MW2WSR3XQ7TJ/bundle.json","state":"https://pith.science/pith/ZTRSYIOI4PHRL7MW2WSR3XQ7TJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZTRSYIOI4PHRL7MW2WSR3XQ7TJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZTRSYIOI4PHRL7MW2WSR3XQ7TJ","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":"bfdecbe242cba107f178fd26ce3e26bf7548a04864728a10c39b9ab9def45ca5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-04T18:51:04Z","title_canon_sha256":"3b404490cdeec6b370ab343d963476a0db1e86033c50055383f534aa4bf33e41"},"schema_version":"1.0","source":{"id":"1508.00867","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00867","created_at":"2026-05-18T01:35:53Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00867v1","created_at":"2026-05-18T01:35:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00867","created_at":"2026-05-18T01:35:53Z"},{"alias_kind":"pith_short_12","alias_value":"ZTRSYIOI4PHR","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZTRSYIOI4PHRL7MW","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZTRSYIOI","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:abaf20fa2959166738d7180769aefec477ab4a7aab5f3851c596247f522236a4","target":"graph","created_at":"2026-05-18T01:35:53Z","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":"In this paper we study stochastic process indexed by $\\mathbb {Z}$ constructed from certain transition kernels depending on the whole past. These kernels prescribe that, at any time, the current state is selected by looking only at a previous random instant. We characterize uniqueness in terms of simple concepts concerning families of stochastic matrices, generalizing the results previously obtained in De Santis and Piccioni (J. Stat. Phys., 150(6):1017--1029, 2013).","authors_text":"Emilio De Santis, Mauro Piccioni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-04T18:51:04Z","title":"One-dimensional infinite memory imitation models with noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00867","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:f01ef2a510ce99f5ff9db318975e863895b8336d2dbec48f60746131022dc6dc","target":"record","created_at":"2026-05-18T01:35:53Z","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":"bfdecbe242cba107f178fd26ce3e26bf7548a04864728a10c39b9ab9def45ca5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-04T18:51:04Z","title_canon_sha256":"3b404490cdeec6b370ab343d963476a0db1e86033c50055383f534aa4bf33e41"},"schema_version":"1.0","source":{"id":"1508.00867","kind":"arxiv","version":1}},"canonical_sha256":"cce32c21c8e3cf15fd96d5a51dde1f9a671b9d18d5e085c0e38a95edf537d5ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cce32c21c8e3cf15fd96d5a51dde1f9a671b9d18d5e085c0e38a95edf537d5ba","first_computed_at":"2026-05-18T01:35:53.156737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:53.156737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ojt2Ywk/i9f/dwpApdlazfUDK0v/jcPVKjsgv+OkUrGXdqEL9aaKZO8FDSjndD/seJ5CM8RpuCG15ydNRo1hCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:53.157477Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.00867","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f01ef2a510ce99f5ff9db318975e863895b8336d2dbec48f60746131022dc6dc","sha256:abaf20fa2959166738d7180769aefec477ab4a7aab5f3851c596247f522236a4"],"state_sha256":"1b0fbc7a6a8b76f443eb0c28291fbad45cefbb07465f0f6d24cf13cfccc0636c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4cjvkVAtVFuVh4vGySx13oZ2x00D/AIALxgaL6L+Db8ApgF/8jtMdJVTY+3S66jDyjK0u8YTM+uHTZSOGrQJCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T22:09:26.803580Z","bundle_sha256":"a45d077e9d17e9e6ea91dd74643a45cb5aa021546b1bec966abe2ff9cdda6360"}}