{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:FXZZJYPWPEYLZ46C2UZF6OPFGX","short_pith_number":"pith:FXZZJYPW","schema_version":"1.0","canonical_sha256":"2df394e1f67930bcf3c2d5325f39e535d5b14064ebdb57d1d83b5dd1c95830b5","source":{"kind":"arxiv","id":"math/0608310","version":1},"attestation_state":"computed","paper":{"title":"On processes which cannot be distinguished by finitary observation","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Michael Hochman, Yonatan Gutman","submitted_at":"2006-08-13T07:15:51Z","abstract_excerpt":"A function $J$ defined on a family $C$ of stationary processes is finitely observable if there is a sequence of functions $s_n$ such that $s_n(x_1 ... x_n)\\to J(X)$ in probability for every process $X=(x_n)\\in C$. Recently, Ornstein and Weiss roved the striking result that if $C$ is the class of aperiodic ergodic finite valued processes, then the only finitely observable isomorphism invariant on $C$ is entropy. We sharpen this in several ways. Our main theorem is that if $X \\to Y$ is a zero-entropy extension of finite entropy ergodic systems and $C$ is the family of processes arising from $X$ "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0608310","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2006-08-13T07:15:51Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"a036d1d1789a7a7634a5c34be66dda9f944c0c989c71a2b0f35cdc5022073385","abstract_canon_sha256":"7b0128c5c453ca3ac81bffe056ba43ce19ee86276493eeb632ef171dc9bf2437"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:13.409752Z","signature_b64":"1FxY/4Ce1CHC1Y2CgHkeyM5pm4fiUVpUAQ9L1JEKxGZDzurqG0S1tg9p7JhG0arXlf5XnyrIB9kFy97tePpkDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2df394e1f67930bcf3c2d5325f39e535d5b14064ebdb57d1d83b5dd1c95830b5","last_reissued_at":"2026-05-18T02:42:13.409295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:13.409295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On processes which cannot be distinguished by finitary observation","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Michael Hochman, Yonatan Gutman","submitted_at":"2006-08-13T07:15:51Z","abstract_excerpt":"A function $J$ defined on a family $C$ of stationary processes is finitely observable if there is a sequence of functions $s_n$ such that $s_n(x_1 ... x_n)\\to J(X)$ in probability for every process $X=(x_n)\\in C$. Recently, Ornstein and Weiss roved the striking result that if $C$ is the class of aperiodic ergodic finite valued processes, then the only finitely observable isomorphism invariant on $C$ is entropy. We sharpen this in several ways. Our main theorem is that if $X \\to Y$ is a zero-entropy extension of finite entropy ergodic systems and $C$ is the family of processes arising from $X$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608310","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0608310","created_at":"2026-05-18T02:42:13.409381+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0608310v1","created_at":"2026-05-18T02:42:13.409381+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608310","created_at":"2026-05-18T02:42:13.409381+00:00"},{"alias_kind":"pith_short_12","alias_value":"FXZZJYPWPEYL","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"FXZZJYPWPEYLZ46C","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"FXZZJYPW","created_at":"2026-05-18T12:25:53.939244+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FXZZJYPWPEYLZ46C2UZF6OPFGX","json":"https://pith.science/pith/FXZZJYPWPEYLZ46C2UZF6OPFGX.json","graph_json":"https://pith.science/api/pith-number/FXZZJYPWPEYLZ46C2UZF6OPFGX/graph.json","events_json":"https://pith.science/api/pith-number/FXZZJYPWPEYLZ46C2UZF6OPFGX/events.json","paper":"https://pith.science/paper/FXZZJYPW"},"agent_actions":{"view_html":"https://pith.science/pith/FXZZJYPWPEYLZ46C2UZF6OPFGX","download_json":"https://pith.science/pith/FXZZJYPWPEYLZ46C2UZF6OPFGX.json","view_paper":"https://pith.science/paper/FXZZJYPW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0608310&json=true","fetch_graph":"https://pith.science/api/pith-number/FXZZJYPWPEYLZ46C2UZF6OPFGX/graph.json","fetch_events":"https://pith.science/api/pith-number/FXZZJYPWPEYLZ46C2UZF6OPFGX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FXZZJYPWPEYLZ46C2UZF6OPFGX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FXZZJYPWPEYLZ46C2UZF6OPFGX/action/storage_attestation","attest_author":"https://pith.science/pith/FXZZJYPWPEYLZ46C2UZF6OPFGX/action/author_attestation","sign_citation":"https://pith.science/pith/FXZZJYPWPEYLZ46C2UZF6OPFGX/action/citation_signature","submit_replication":"https://pith.science/pith/FXZZJYPWPEYLZ46C2UZF6OPFGX/action/replication_record"}},"created_at":"2026-05-18T02:42:13.409381+00:00","updated_at":"2026-05-18T02:42:13.409381+00:00"}