{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WUBE4XIFKHINTEKFFI3OMPCCJV","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":"81b22e7b0233d3aa4860fd385a402d3d6cddaf7f7ad3de64d014774e0fd2a2cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-05T20:18:12Z","title_canon_sha256":"27237dfe8ddac49c4066a40f55a8f0ef3d5d96cbd675ae00c44b233c8c7d56b6"},"schema_version":"1.0","source":{"id":"1709.01579","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.01579","created_at":"2026-05-18T00:13:47Z"},{"alias_kind":"arxiv_version","alias_value":"1709.01579v2","created_at":"2026-05-18T00:13:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01579","created_at":"2026-05-18T00:13:47Z"},{"alias_kind":"pith_short_12","alias_value":"WUBE4XIFKHIN","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WUBE4XIFKHINTEKF","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WUBE4XIF","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:20780ad086c6c48f551036b8fe4bc6f1e62f3128ebfead45c6eaf56ba591fbf2","target":"graph","created_at":"2026-05-18T00:13:47Z","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 the following text for arbitrary $X$ with at least two elements, nonempty set $\\Gamma$ and self-map $\\varphi:\\Gamma\\to\\Gamma$ we prove the set-theoretical entropy of generalized shift $\\sigma_\\varphi:X^\\Gamma\\to X^\\Gamma$ ($\\sigma_\\varphi((x_\\alpha)_{\\alpha\\in\\Gamma})=(x_{\\varphi(\\alpha)})_{\\alpha\\in\\Gamma}$ (for $(x_\\alpha)_{\\alpha\\in\\Gamma}\\in X^\\Gamma$)) is either zero or infinity, moreover it is zero if and only if $\\varphi$ is quasi-periodic. We continue our study on contravariant set-theoretical entropy of generalized shift and motivate the text using counterexamples dealing with alge","authors_text":"Fatemah Ayatollah Zadeh Shirazi, Zahra Nili Ahmadabadi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-05T20:18:12Z","title":"Set-theoretical entropies of generalized shifts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01579","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:b3f41e87b068a8f0fdb31f856808baa96d10bf69e45b6c7911384813252a5d57","target":"record","created_at":"2026-05-18T00:13:47Z","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":"81b22e7b0233d3aa4860fd385a402d3d6cddaf7f7ad3de64d014774e0fd2a2cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-05T20:18:12Z","title_canon_sha256":"27237dfe8ddac49c4066a40f55a8f0ef3d5d96cbd675ae00c44b233c8c7d56b6"},"schema_version":"1.0","source":{"id":"1709.01579","kind":"arxiv","version":2}},"canonical_sha256":"b5024e5d0551d0d991452a36e63c424d7e6f1195abf9006f6a97d0ce5e058e7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5024e5d0551d0d991452a36e63c424d7e6f1195abf9006f6a97d0ce5e058e7a","first_computed_at":"2026-05-18T00:13:47.616772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:47.616772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bBqMCCIX9KQ9OhsV1cixuu0HkJQ6kGcwFOxRY5Zbqf93ZRfKeZ4vtiz/kcaRvP9KjEG2DYCVOY2bSIyZDfwYCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:47.617426Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.01579","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3f41e87b068a8f0fdb31f856808baa96d10bf69e45b6c7911384813252a5d57","sha256:20780ad086c6c48f551036b8fe4bc6f1e62f3128ebfead45c6eaf56ba591fbf2"],"state_sha256":"025d25696ff50116fa9632a0fd08f3875850545d5efa07b6d09dbcf19f814f4e"}