{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PYLWTISBHG5OEYRPV7IU6WERW3","short_pith_number":"pith:PYLWTISB","canonical_record":{"source":{"id":"1610.09927","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-31T13:57:44Z","cross_cats_sorted":[],"title_canon_sha256":"1fdc188ac38a2148f5dac0c618fa309b230a4bc4c6084d973f865811f71e9caf","abstract_canon_sha256":"9f6586fa4b432ec7ca9064e19d7bf1e5189550c5334d09324b955ee3d6080f90"},"schema_version":"1.0"},"canonical_sha256":"7e1769a24139bae2622fafd14f5891b6dd3c7a7359542ff113addf89a1418cde","source":{"kind":"arxiv","id":"1610.09927","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09927","created_at":"2026-05-18T00:59:18Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09927v2","created_at":"2026-05-18T00:59:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09927","created_at":"2026-05-18T00:59:18Z"},{"alias_kind":"pith_short_12","alias_value":"PYLWTISBHG5O","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PYLWTISBHG5OEYRP","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PYLWTISB","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PYLWTISBHG5OEYRPV7IU6WERW3","target":"record","payload":{"canonical_record":{"source":{"id":"1610.09927","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-31T13:57:44Z","cross_cats_sorted":[],"title_canon_sha256":"1fdc188ac38a2148f5dac0c618fa309b230a4bc4c6084d973f865811f71e9caf","abstract_canon_sha256":"9f6586fa4b432ec7ca9064e19d7bf1e5189550c5334d09324b955ee3d6080f90"},"schema_version":"1.0"},"canonical_sha256":"7e1769a24139bae2622fafd14f5891b6dd3c7a7359542ff113addf89a1418cde","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:18.453055Z","signature_b64":"2KRDF5uD/VOhhSj1Txj9zRam+OrkyBPFLFk06y2kfPfcf2LWEWQg5t3nMZtEP04pU9r/2Rp4QcnSgMIdBVIZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e1769a24139bae2622fafd14f5891b6dd3c7a7359542ff113addf89a1418cde","last_reissued_at":"2026-05-18T00:59:18.452397Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:18.452397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.09927","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qtmkj04k32pysvS+uUw4Lg29MqiU9GFRdXgBxG0gIRF0+tw4zt+2rd4Hn4Kl10v6BE8Q3v1IsBQjZQZok4WfDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:19:05.867431Z"},"content_sha256":"d3478b9cd8566d3026cd353d6ddef615471f6996f92144654e67f9dbe48a4d84","schema_version":"1.0","event_id":"sha256:d3478b9cd8566d3026cd353d6ddef615471f6996f92144654e67f9dbe48a4d84"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PYLWTISBHG5OEYRPV7IU6WERW3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constructive symbolic presentations of rank one measure-preserving systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Karl Petersen, S\\'ebastien Ferenczi, Terrence Adams","submitted_at":"2016-10-31T13:57:44Z","abstract_excerpt":"Given a rank one measure-preserving system defined by cutting and stacking with spacers, we produce a rank one binary sequence such that its orbit closure under the shift transformation, with its unique {nonatomic} invariant probability, is isomorphic to the given system. In particular, the classical dyadic odometer is presented in terms of a recursive sequence of blocks on the two-symbol alphabet $\\{0,1\\}$. The construction is accomplished using a definition of rank one in the setting of adic, or Bratteli-Vershik, systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09927","kind":"arxiv","version":2},"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":"2026-05-18T00:59:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yQD2/3Y5A+WCxBU/7e/KUOld0oi0Mt5rEkAsk4ahBCBq1aRqheg1GhVJA6KT1kxv+dqdnMRNL2l3blaMpQUnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:19:05.868041Z"},"content_sha256":"438d3f3ed892c97ac0a63ab7a6cc998a47b867111d3103b779711c7dc2242b82","schema_version":"1.0","event_id":"sha256:438d3f3ed892c97ac0a63ab7a6cc998a47b867111d3103b779711c7dc2242b82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PYLWTISBHG5OEYRPV7IU6WERW3/bundle.json","state_url":"https://pith.science/pith/PYLWTISBHG5OEYRPV7IU6WERW3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PYLWTISBHG5OEYRPV7IU6WERW3/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":"2026-06-04T17:19:05Z","links":{"resolver":"https://pith.science/pith/PYLWTISBHG5OEYRPV7IU6WERW3","bundle":"https://pith.science/pith/PYLWTISBHG5OEYRPV7IU6WERW3/bundle.json","state":"https://pith.science/pith/PYLWTISBHG5OEYRPV7IU6WERW3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PYLWTISBHG5OEYRPV7IU6WERW3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PYLWTISBHG5OEYRPV7IU6WERW3","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":"9f6586fa4b432ec7ca9064e19d7bf1e5189550c5334d09324b955ee3d6080f90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-31T13:57:44Z","title_canon_sha256":"1fdc188ac38a2148f5dac0c618fa309b230a4bc4c6084d973f865811f71e9caf"},"schema_version":"1.0","source":{"id":"1610.09927","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09927","created_at":"2026-05-18T00:59:18Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09927v2","created_at":"2026-05-18T00:59:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09927","created_at":"2026-05-18T00:59:18Z"},{"alias_kind":"pith_short_12","alias_value":"PYLWTISBHG5O","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PYLWTISBHG5OEYRP","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PYLWTISB","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:438d3f3ed892c97ac0a63ab7a6cc998a47b867111d3103b779711c7dc2242b82","target":"graph","created_at":"2026-05-18T00:59:18Z","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":"Given a rank one measure-preserving system defined by cutting and stacking with spacers, we produce a rank one binary sequence such that its orbit closure under the shift transformation, with its unique {nonatomic} invariant probability, is isomorphic to the given system. In particular, the classical dyadic odometer is presented in terms of a recursive sequence of blocks on the two-symbol alphabet $\\{0,1\\}$. The construction is accomplished using a definition of rank one in the setting of adic, or Bratteli-Vershik, systems.","authors_text":"Karl Petersen, S\\'ebastien Ferenczi, Terrence Adams","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-31T13:57:44Z","title":"Constructive symbolic presentations of rank one measure-preserving systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09927","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:d3478b9cd8566d3026cd353d6ddef615471f6996f92144654e67f9dbe48a4d84","target":"record","created_at":"2026-05-18T00:59:18Z","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":"9f6586fa4b432ec7ca9064e19d7bf1e5189550c5334d09324b955ee3d6080f90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-10-31T13:57:44Z","title_canon_sha256":"1fdc188ac38a2148f5dac0c618fa309b230a4bc4c6084d973f865811f71e9caf"},"schema_version":"1.0","source":{"id":"1610.09927","kind":"arxiv","version":2}},"canonical_sha256":"7e1769a24139bae2622fafd14f5891b6dd3c7a7359542ff113addf89a1418cde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e1769a24139bae2622fafd14f5891b6dd3c7a7359542ff113addf89a1418cde","first_computed_at":"2026-05-18T00:59:18.452397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:18.452397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2KRDF5uD/VOhhSj1Txj9zRam+OrkyBPFLFk06y2kfPfcf2LWEWQg5t3nMZtEP04pU9r/2Rp4QcnSgMIdBVIZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:18.453055Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09927","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3478b9cd8566d3026cd353d6ddef615471f6996f92144654e67f9dbe48a4d84","sha256:438d3f3ed892c97ac0a63ab7a6cc998a47b867111d3103b779711c7dc2242b82"],"state_sha256":"4287a6f8e5bc1ec354477a743b5561758d85d32510d0cc74c0c06ef088c25826"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UdY67ZwY0asICsuX4fv2oTiVOkSwyX4amvkFheF+vTxUEjBCYjdgfrlz/Uc8NfDDshxmv5iZAQA/dY3jHxTRCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T17:19:05.871079Z","bundle_sha256":"edb9eaa31778882740953b7f69c2c1687b5287b65675e64cbe853bdcf5ff302f"}}