{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:JVK47FAINT25QFOY64QTXJHTXW","short_pith_number":"pith:JVK47FAI","canonical_record":{"source":{"id":"1008.0850","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-08-04T19:33:06Z","cross_cats_sorted":[],"title_canon_sha256":"cadaa7108ba82630f98030d11bc6fd40bc01219a2419544fb9cee6469d6820f0","abstract_canon_sha256":"72a4e6eab3bf4dae3a30c052526a75ab9a47d9c113cd701715f12802823f4028"},"schema_version":"1.0"},"canonical_sha256":"4d55cf94086cf5d815d8f7213ba4f3bdbfb04af6098f53c47bd7212f9311f0af","source":{"kind":"arxiv","id":"1008.0850","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0850","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0850v2","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0850","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"JVK47FAINT25","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JVK47FAINT25QFOY","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JVK47FAI","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:JVK47FAINT25QFOY64QTXJHTXW","target":"record","payload":{"canonical_record":{"source":{"id":"1008.0850","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-08-04T19:33:06Z","cross_cats_sorted":[],"title_canon_sha256":"cadaa7108ba82630f98030d11bc6fd40bc01219a2419544fb9cee6469d6820f0","abstract_canon_sha256":"72a4e6eab3bf4dae3a30c052526a75ab9a47d9c113cd701715f12802823f4028"},"schema_version":"1.0"},"canonical_sha256":"4d55cf94086cf5d815d8f7213ba4f3bdbfb04af6098f53c47bd7212f9311f0af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:09.256553Z","signature_b64":"IivyfST7tSj6aXsnINy+XvPhNiDK+S97ShByzlZlkphWs6ZwY7hszG9NhEBoORI+o9h2aeEu5ToW7kUA6sQHBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d55cf94086cf5d815d8f7213ba4f3bdbfb04af6098f53c47bd7212f9311f0af","last_reissued_at":"2026-05-18T04:40:09.256009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:09.256009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.0850","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":"2026-05-18T04:40:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RlKOKqrGOFU36LqtPuAHftIN/LOcHfa/lgVGJMG0YhSDW+1nuegKOiRC3MCVbOiE9Wms8fLPii0NuD37YNyCCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:15:54.628835Z"},"content_sha256":"93d758cd379bee5a9a1987745318e3724ea56c7f50ba0a381918bdeff1017fb7","schema_version":"1.0","event_id":"sha256:93d758cd379bee5a9a1987745318e3724ea56c7f50ba0a381918bdeff1017fb7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:JVK47FAINT25QFOY64QTXJHTXW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homeomorphic measures on stationary Bratteli diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"O. Karpel, S. Bezuglyi","submitted_at":"2010-08-04T19:33:06Z","abstract_excerpt":"We study the set S of ergodic probability Borel measures on stationary non-simple Bratteli diagrams which are invariant with respect to the tail equivalence relation. Equivalently, the set S is formed by ergodic probability measures invariant with respect to aperiodic substitution dynamical systems. The paper is devoted to the classification of measures $\\mu$ from S with respect to a homeomorphism. The properties of these measures related to the clopen values set $S(\\mu)$ are studied. It is shown that for every measure $\\mu$ in S there exists a subgroup G of $\\mathbb R$ such that $S(\\mu)$ is t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0850","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":"2026-05-18T04:40:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Jhl1dVZ2xTF1c5QTb1t9q3EH42ZO97+HsL0a/VCTk4hPhkCbYmaRuFGbhP33rHMFuI/F6GUATHKapasMvaUAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:15:54.629546Z"},"content_sha256":"76a5fda53b9c095f988722d5b49b5f2d4f129862faf0ded60739a27fcda9c552","schema_version":"1.0","event_id":"sha256:76a5fda53b9c095f988722d5b49b5f2d4f129862faf0ded60739a27fcda9c552"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JVK47FAINT25QFOY64QTXJHTXW/bundle.json","state_url":"https://pith.science/pith/JVK47FAINT25QFOY64QTXJHTXW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JVK47FAINT25QFOY64QTXJHTXW/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":"2026-06-07T20:15:54Z","links":{"resolver":"https://pith.science/pith/JVK47FAINT25QFOY64QTXJHTXW","bundle":"https://pith.science/pith/JVK47FAINT25QFOY64QTXJHTXW/bundle.json","state":"https://pith.science/pith/JVK47FAINT25QFOY64QTXJHTXW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JVK47FAINT25QFOY64QTXJHTXW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JVK47FAINT25QFOY64QTXJHTXW","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":"72a4e6eab3bf4dae3a30c052526a75ab9a47d9c113cd701715f12802823f4028","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-08-04T19:33:06Z","title_canon_sha256":"cadaa7108ba82630f98030d11bc6fd40bc01219a2419544fb9cee6469d6820f0"},"schema_version":"1.0","source":{"id":"1008.0850","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0850","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0850v2","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0850","created_at":"2026-05-18T04:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"JVK47FAINT25","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JVK47FAINT25QFOY","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JVK47FAI","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:76a5fda53b9c095f988722d5b49b5f2d4f129862faf0ded60739a27fcda9c552","target":"graph","created_at":"2026-05-18T04:40:09Z","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 study the set S of ergodic probability Borel measures on stationary non-simple Bratteli diagrams which are invariant with respect to the tail equivalence relation. Equivalently, the set S is formed by ergodic probability measures invariant with respect to aperiodic substitution dynamical systems. The paper is devoted to the classification of measures $\\mu$ from S with respect to a homeomorphism. The properties of these measures related to the clopen values set $S(\\mu)$ are studied. It is shown that for every measure $\\mu$ in S there exists a subgroup G of $\\mathbb R$ such that $S(\\mu)$ is t","authors_text":"O. Karpel, S. Bezuglyi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-08-04T19:33:06Z","title":"Homeomorphic measures on stationary Bratteli diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0850","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":"sha256:93d758cd379bee5a9a1987745318e3724ea56c7f50ba0a381918bdeff1017fb7","target":"record","created_at":"2026-05-18T04:40:09Z","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":"72a4e6eab3bf4dae3a30c052526a75ab9a47d9c113cd701715f12802823f4028","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-08-04T19:33:06Z","title_canon_sha256":"cadaa7108ba82630f98030d11bc6fd40bc01219a2419544fb9cee6469d6820f0"},"schema_version":"1.0","source":{"id":"1008.0850","kind":"arxiv","version":2}},"canonical_sha256":"4d55cf94086cf5d815d8f7213ba4f3bdbfb04af6098f53c47bd7212f9311f0af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d55cf94086cf5d815d8f7213ba4f3bdbfb04af6098f53c47bd7212f9311f0af","first_computed_at":"2026-05-18T04:40:09.256009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:09.256009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IivyfST7tSj6aXsnINy+XvPhNiDK+S97ShByzlZlkphWs6ZwY7hszG9NhEBoORI+o9h2aeEu5ToW7kUA6sQHBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:09.256553Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.0850","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93d758cd379bee5a9a1987745318e3724ea56c7f50ba0a381918bdeff1017fb7","sha256:76a5fda53b9c095f988722d5b49b5f2d4f129862faf0ded60739a27fcda9c552"],"state_sha256":"cebbb769d5800234c1fe1efb09a5f61e4a1b0e2d51985a66a07daff5a38c453e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AkN11LYEVXtzAP9anLZeB9R/IvixZJk49Ii6r+shzW4I67I++/+5PLz4YH3s317T6cyAYPVX8l/Yxbh031XjCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T20:15:54.633508Z","bundle_sha256":"111968deacf1779d0385a68586cbb77c93482d4381d5e62c565d6057b5e46e15"}}