{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JIJVGPXSW6JHE33OP6BFHOMDHA","short_pith_number":"pith:JIJVGPXS","canonical_record":{"source":{"id":"1311.4524","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-18T20:28:32Z","cross_cats_sorted":[],"title_canon_sha256":"cd7ad7d5dac50e8ffd070f7ffb3e32a71decc067740179500da7df1c4981f39e","abstract_canon_sha256":"2b7a5cfb28f7014f0342e7303f19363d3d8be4872347d434d00f542a02f43c1e"},"schema_version":"1.0"},"canonical_sha256":"4a13533ef2b792726f6e7f8253b983383e32940164ceec46ca58730c94421034","source":{"kind":"arxiv","id":"1311.4524","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.4524","created_at":"2026-05-18T03:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"1311.4524v3","created_at":"2026-05-18T03:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4524","created_at":"2026-05-18T03:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"JIJVGPXSW6JH","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JIJVGPXSW6JHE33O","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JIJVGPXS","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JIJVGPXSW6JHE33OP6BFHOMDHA","target":"record","payload":{"canonical_record":{"source":{"id":"1311.4524","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-18T20:28:32Z","cross_cats_sorted":[],"title_canon_sha256":"cd7ad7d5dac50e8ffd070f7ffb3e32a71decc067740179500da7df1c4981f39e","abstract_canon_sha256":"2b7a5cfb28f7014f0342e7303f19363d3d8be4872347d434d00f542a02f43c1e"},"schema_version":"1.0"},"canonical_sha256":"4a13533ef2b792726f6e7f8253b983383e32940164ceec46ca58730c94421034","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:47.281166Z","signature_b64":"AlUWxTcrVUAak7SI6nSV6SkgcwFQU7A9UlErRT2h6zotWIxuqwrgrkXwqlLWIwbNKNWc6dTh85eYI6k/HEfaCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a13533ef2b792726f6e7f8253b983383e32940164ceec46ca58730c94421034","last_reissued_at":"2026-05-18T03:05:47.280430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:47.280430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.4524","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:05:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RUf0X+7zf00kyxxQkOqpbvwMyX9Rmj9gfHD/dcxwqGjkCuiWopvKC8r2/DDipaQ4QtLMzMOO6KKlj6s0YsIyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:40:14.648020Z"},"content_sha256":"d262134f12f98f9c16b88a8a4e301a7d2f3afc637625f92dfaddbe40b6002b26","schema_version":"1.0","event_id":"sha256:d262134f12f98f9c16b88a8a4e301a7d2f3afc637625f92dfaddbe40b6002b26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JIJVGPXSW6JHE33OP6BFHOMDHA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chacon's Type Ergodic Transformations with Unbounded Arithmetic Spacers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"V.V. Ryzhikov","submitted_at":"2013-11-18T20:28:32Z","abstract_excerpt":"The following generalizations of the Chacon map are proposed: instead of classical constant spacer sequence $(0,1,0)$ let a sequence $(0,s_j,0)$ be one with unbounded $s_j$. (We mention also an analogue of the historical Chacon map with spacer sequences in the form $(0,s_j)$.) This narrow class of rank-one transformations may be abundant source of open questions. All such constructions have partial rigidity, but some other properties could be different. For root sequence, $ s_j= [\\sqrt{j}]$, (or $ s_j= [\\ln{j}]$) the corresponding action is rigid, moreover it possesses all polynomials in its w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4524","kind":"arxiv","version":3},"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":"2026-05-18T03:05:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jr2aMNRv/JOU8YUajKod95FQ3VV3cGCPDl2teAN5CQ1ihBLXw91WOrTNSND6hD8OeO2BfPl18GCrovnhXhfsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T15:40:14.648535Z"},"content_sha256":"e57572572420419e414d8d093b7847b4dbdf9879d0ca15a47a34eb8971684ab6","schema_version":"1.0","event_id":"sha256:e57572572420419e414d8d093b7847b4dbdf9879d0ca15a47a34eb8971684ab6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JIJVGPXSW6JHE33OP6BFHOMDHA/bundle.json","state_url":"https://pith.science/pith/JIJVGPXSW6JHE33OP6BFHOMDHA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JIJVGPXSW6JHE33OP6BFHOMDHA/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":"2026-05-31T15:40:14Z","links":{"resolver":"https://pith.science/pith/JIJVGPXSW6JHE33OP6BFHOMDHA","bundle":"https://pith.science/pith/JIJVGPXSW6JHE33OP6BFHOMDHA/bundle.json","state":"https://pith.science/pith/JIJVGPXSW6JHE33OP6BFHOMDHA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JIJVGPXSW6JHE33OP6BFHOMDHA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JIJVGPXSW6JHE33OP6BFHOMDHA","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":"2b7a5cfb28f7014f0342e7303f19363d3d8be4872347d434d00f542a02f43c1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-18T20:28:32Z","title_canon_sha256":"cd7ad7d5dac50e8ffd070f7ffb3e32a71decc067740179500da7df1c4981f39e"},"schema_version":"1.0","source":{"id":"1311.4524","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.4524","created_at":"2026-05-18T03:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"1311.4524v3","created_at":"2026-05-18T03:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4524","created_at":"2026-05-18T03:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"JIJVGPXSW6JH","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JIJVGPXSW6JHE33O","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JIJVGPXS","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:e57572572420419e414d8d093b7847b4dbdf9879d0ca15a47a34eb8971684ab6","target":"graph","created_at":"2026-05-18T03:05:47Z","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":"The following generalizations of the Chacon map are proposed: instead of classical constant spacer sequence $(0,1,0)$ let a sequence $(0,s_j,0)$ be one with unbounded $s_j$. (We mention also an analogue of the historical Chacon map with spacer sequences in the form $(0,s_j)$.) This narrow class of rank-one transformations may be abundant source of open questions. All such constructions have partial rigidity, but some other properties could be different. For root sequence, $ s_j= [\\sqrt{j}]$, (or $ s_j= [\\ln{j}]$) the corresponding action is rigid, moreover it possesses all polynomials in its w","authors_text":"V.V. Ryzhikov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-18T20:28:32Z","title":"Chacon's Type Ergodic Transformations with Unbounded Arithmetic Spacers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4524","kind":"arxiv","version":3},"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:d262134f12f98f9c16b88a8a4e301a7d2f3afc637625f92dfaddbe40b6002b26","target":"record","created_at":"2026-05-18T03:05:47Z","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":"2b7a5cfb28f7014f0342e7303f19363d3d8be4872347d434d00f542a02f43c1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-18T20:28:32Z","title_canon_sha256":"cd7ad7d5dac50e8ffd070f7ffb3e32a71decc067740179500da7df1c4981f39e"},"schema_version":"1.0","source":{"id":"1311.4524","kind":"arxiv","version":3}},"canonical_sha256":"4a13533ef2b792726f6e7f8253b983383e32940164ceec46ca58730c94421034","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a13533ef2b792726f6e7f8253b983383e32940164ceec46ca58730c94421034","first_computed_at":"2026-05-18T03:05:47.280430Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:47.280430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AlUWxTcrVUAak7SI6nSV6SkgcwFQU7A9UlErRT2h6zotWIxuqwrgrkXwqlLWIwbNKNWc6dTh85eYI6k/HEfaCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:47.281166Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.4524","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d262134f12f98f9c16b88a8a4e301a7d2f3afc637625f92dfaddbe40b6002b26","sha256:e57572572420419e414d8d093b7847b4dbdf9879d0ca15a47a34eb8971684ab6"],"state_sha256":"dbca12f570ba3b4e118c6b1a0727b4d9a237c6a8f4f7b52955e318274b3bedc7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"no5JgUFx0JaAN4m1WJjVrQY9fGAb0ZP6BM5GD7JNooqG9ctMOPABuZxDEe6GVgiei4QdfR9sOn3MxbWDJ4tLDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T15:40:14.651296Z","bundle_sha256":"578fd9b90488519f7540f6b3f193b1b1fb5c8397341f3a5e85a31e38eb63bd4d"}}