{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QGMHZHYVJK6I74YX2W42ALXX2T","short_pith_number":"pith:QGMHZHYV","canonical_record":{"source":{"id":"1203.4695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-03-21T09:57:53Z","cross_cats_sorted":[],"title_canon_sha256":"e64587758aa16508845b857130cb136f8534d4afddaa7651ceb5780637580af8","abstract_canon_sha256":"7df8de0271e4b2ef6772214f9261fdb47d9587b4dc0481816e5c82bd14652abb"},"schema_version":"1.0"},"canonical_sha256":"81987c9f154abc8ff317d5b9a02ef7d4e3f0a556dcddeadbef927d5e461a6f71","source":{"kind":"arxiv","id":"1203.4695","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4695","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4695v1","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4695","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"QGMHZHYVJK6I","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QGMHZHYVJK6I74YX","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QGMHZHYV","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QGMHZHYVJK6I74YX2W42ALXX2T","target":"record","payload":{"canonical_record":{"source":{"id":"1203.4695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-03-21T09:57:53Z","cross_cats_sorted":[],"title_canon_sha256":"e64587758aa16508845b857130cb136f8534d4afddaa7651ceb5780637580af8","abstract_canon_sha256":"7df8de0271e4b2ef6772214f9261fdb47d9587b4dc0481816e5c82bd14652abb"},"schema_version":"1.0"},"canonical_sha256":"81987c9f154abc8ff317d5b9a02ef7d4e3f0a556dcddeadbef927d5e461a6f71","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:36.258418Z","signature_b64":"zJlAb1cPRJncrH3yMuP71M8UzZODqVfgcjIxGJDO+hrStQEmUTSjaDXracs+jXR6Q3t0uC33UkbsUBi1W2ycBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81987c9f154abc8ff317d5b9a02ef7d4e3f0a556dcddeadbef927d5e461a6f71","last_reissued_at":"2026-05-17T23:53:36.257765Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:36.257765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.4695","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":"2026-05-17T23:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3/WwUmktabRVY/X+4D5lIuVWFSqOsLXJM2XvrBmCOObA7uSLnq1EqUseQF2c/0SJOffygBIHq/V3UwGqTTA6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T11:52:05.672149Z"},"content_sha256":"a4b8853995b962c1e85c5bff38704c63dab62c51db236ffe7f1d8402eea5b263","schema_version":"1.0","event_id":"sha256:a4b8853995b962c1e85c5bff38704c63dab62c51db236ffe7f1d8402eea5b263"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QGMHZHYVJK6I74YX2W42ALXX2T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isomorphisms between positive and negative beta-transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Charlene Kalle","submitted_at":"2012-03-21T09:57:53Z","abstract_excerpt":"We compare a piecewise linear map with constant slope beta>1 and a piecewise linear map with constant slope -beta. These maps are called the positive and negative beta-transformations. We show that for a certain set of beta's, the multinacci numbers, there exists a measurable isomorphism between these two maps. We further show that for for all other values of beta between 1 and 2 the two maps cannot be isomorphic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4695","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":"2026-05-17T23:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eYwHDtVCBkpaaKrsz9SbGa97yV6gwFvPL5JNsAUTjzqEHCwmzxzWZSZdvJQjmmufHkr9t8m3cdvEGkDYddEAAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T11:52:05.672504Z"},"content_sha256":"79a3071dbb9073710721e108ff8f60178a762704b540ad8e964ef765879b9596","schema_version":"1.0","event_id":"sha256:79a3071dbb9073710721e108ff8f60178a762704b540ad8e964ef765879b9596"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QGMHZHYVJK6I74YX2W42ALXX2T/bundle.json","state_url":"https://pith.science/pith/QGMHZHYVJK6I74YX2W42ALXX2T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QGMHZHYVJK6I74YX2W42ALXX2T/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":"2026-06-27T11:52:05Z","links":{"resolver":"https://pith.science/pith/QGMHZHYVJK6I74YX2W42ALXX2T","bundle":"https://pith.science/pith/QGMHZHYVJK6I74YX2W42ALXX2T/bundle.json","state":"https://pith.science/pith/QGMHZHYVJK6I74YX2W42ALXX2T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QGMHZHYVJK6I74YX2W42ALXX2T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QGMHZHYVJK6I74YX2W42ALXX2T","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":"7df8de0271e4b2ef6772214f9261fdb47d9587b4dc0481816e5c82bd14652abb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-03-21T09:57:53Z","title_canon_sha256":"e64587758aa16508845b857130cb136f8534d4afddaa7651ceb5780637580af8"},"schema_version":"1.0","source":{"id":"1203.4695","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4695","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4695v1","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4695","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"QGMHZHYVJK6I","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QGMHZHYVJK6I74YX","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QGMHZHYV","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:79a3071dbb9073710721e108ff8f60178a762704b540ad8e964ef765879b9596","target":"graph","created_at":"2026-05-17T23:53:36Z","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":"We compare a piecewise linear map with constant slope beta>1 and a piecewise linear map with constant slope -beta. These maps are called the positive and negative beta-transformations. We show that for a certain set of beta's, the multinacci numbers, there exists a measurable isomorphism between these two maps. We further show that for for all other values of beta between 1 and 2 the two maps cannot be isomorphic.","authors_text":"Charlene Kalle","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-03-21T09:57:53Z","title":"Isomorphisms between positive and negative beta-transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4695","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:a4b8853995b962c1e85c5bff38704c63dab62c51db236ffe7f1d8402eea5b263","target":"record","created_at":"2026-05-17T23:53:36Z","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":"7df8de0271e4b2ef6772214f9261fdb47d9587b4dc0481816e5c82bd14652abb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-03-21T09:57:53Z","title_canon_sha256":"e64587758aa16508845b857130cb136f8534d4afddaa7651ceb5780637580af8"},"schema_version":"1.0","source":{"id":"1203.4695","kind":"arxiv","version":1}},"canonical_sha256":"81987c9f154abc8ff317d5b9a02ef7d4e3f0a556dcddeadbef927d5e461a6f71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81987c9f154abc8ff317d5b9a02ef7d4e3f0a556dcddeadbef927d5e461a6f71","first_computed_at":"2026-05-17T23:53:36.257765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:36.257765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zJlAb1cPRJncrH3yMuP71M8UzZODqVfgcjIxGJDO+hrStQEmUTSjaDXracs+jXR6Q3t0uC33UkbsUBi1W2ycBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:36.258418Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.4695","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4b8853995b962c1e85c5bff38704c63dab62c51db236ffe7f1d8402eea5b263","sha256:79a3071dbb9073710721e108ff8f60178a762704b540ad8e964ef765879b9596"],"state_sha256":"b85b957e31cfd43465ae9ab2c4ebeb7eca0112acf7b2d102fdebe24cb330b44d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/K+ZuvM1MOAX6SfyBZBs2oaMrNGJb4Pj5HakA+NXNvH/inY0ehB1MMUZWC4iTsqXBmTFiyE90KCiCTA+erUKBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T11:52:05.674350Z","bundle_sha256":"5ad77220d856ecb334873d637a3e990ac478eff36047f84e606cac93b5ecb8b4"}}