{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:KV5JIXN6S3FHQMKM6S5XDAJ23H","short_pith_number":"pith:KV5JIXN6","canonical_record":{"source":{"id":"1009.5887","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-09-29T14:08:50Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"aeb95264cd90b3e5bc9853a38c51b962c77d8140cc77860281bc5013bb2f1fa9","abstract_canon_sha256":"af07d2926a4288084d6e56507e6843f1e866b1770c7bdb0727b5644c0a09c50c"},"schema_version":"1.0"},"canonical_sha256":"557a945dbe96ca78314cf4bb71813ad9f3e847c57f1a7b0fec3fe46dfda1da76","source":{"kind":"arxiv","id":"1009.5887","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5887","created_at":"2026-05-18T04:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5887v1","created_at":"2026-05-18T04:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5887","created_at":"2026-05-18T04:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"KV5JIXN6S3FH","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KV5JIXN6S3FHQMKM","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KV5JIXN6","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:KV5JIXN6S3FHQMKM6S5XDAJ23H","target":"record","payload":{"canonical_record":{"source":{"id":"1009.5887","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-09-29T14:08:50Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"aeb95264cd90b3e5bc9853a38c51b962c77d8140cc77860281bc5013bb2f1fa9","abstract_canon_sha256":"af07d2926a4288084d6e56507e6843f1e866b1770c7bdb0727b5644c0a09c50c"},"schema_version":"1.0"},"canonical_sha256":"557a945dbe96ca78314cf4bb71813ad9f3e847c57f1a7b0fec3fe46dfda1da76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:08.674601Z","signature_b64":"fl41Eul4hJufmhBKF8ioC+RBWyg/ctmBORuXou4zPstdDWlyZ1cKXdfePyT+Q4043kfLcqSQYFtjAAmzXRvdCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"557a945dbe96ca78314cf4bb71813ad9f3e847c57f1a7b0fec3fe46dfda1da76","last_reissued_at":"2026-05-18T04:40:08.673970Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:08.673970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.5887","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":"2026-05-18T04:40:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xLRd//s8OIQEmecNhthhg1NtIrK2GGyxprfSN/Ogd/mV+b6CA1YKOS4CT8ioQewhcWKve7MTXnDnepaNQjxnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:13:15.543378Z"},"content_sha256":"95b67022a0ff4daff3933c34851fab5502ff631a2026fd64830c175782772a87","schema_version":"1.0","event_id":"sha256:95b67022a0ff4daff3933c34851fab5502ff631a2026fd64830c175782772a87"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:KV5JIXN6S3FHQMKM6S5XDAJ23H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral triples and Gibbs measures for expanding maps on Cantor sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.DS","authors_text":"Richard Sharp","submitted_at":"2010-09-29T14:08:50Z","abstract_excerpt":"Let $T : \\Lambda \\to \\Lambda$ be an expanding map on a Cantor set. For each suitably normalized H\\\"older continuous potential, we construct a spectral triple from which one may recover the associated Gibbs measure as a noncommutative measure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5887","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":"2026-05-18T04:40:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GBJlzaqNoTYoKp3+INO3Gh4CTCLugbXRyhuBzDHMC3VqBtQp0jS7iNqtktjwKDstyP+SlX6hNEoCX2scigMZAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:13:15.543720Z"},"content_sha256":"4465a615eac832a26ba378c578669b0d567804f3cc1a6d65c0adf02d9425981d","schema_version":"1.0","event_id":"sha256:4465a615eac832a26ba378c578669b0d567804f3cc1a6d65c0adf02d9425981d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KV5JIXN6S3FHQMKM6S5XDAJ23H/bundle.json","state_url":"https://pith.science/pith/KV5JIXN6S3FHQMKM6S5XDAJ23H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KV5JIXN6S3FHQMKM6S5XDAJ23H/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":"2026-06-27T04:13:15Z","links":{"resolver":"https://pith.science/pith/KV5JIXN6S3FHQMKM6S5XDAJ23H","bundle":"https://pith.science/pith/KV5JIXN6S3FHQMKM6S5XDAJ23H/bundle.json","state":"https://pith.science/pith/KV5JIXN6S3FHQMKM6S5XDAJ23H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KV5JIXN6S3FHQMKM6S5XDAJ23H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KV5JIXN6S3FHQMKM6S5XDAJ23H","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":"af07d2926a4288084d6e56507e6843f1e866b1770c7bdb0727b5644c0a09c50c","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-09-29T14:08:50Z","title_canon_sha256":"aeb95264cd90b3e5bc9853a38c51b962c77d8140cc77860281bc5013bb2f1fa9"},"schema_version":"1.0","source":{"id":"1009.5887","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5887","created_at":"2026-05-18T04:40:08Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5887v1","created_at":"2026-05-18T04:40:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5887","created_at":"2026-05-18T04:40:08Z"},{"alias_kind":"pith_short_12","alias_value":"KV5JIXN6S3FH","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KV5JIXN6S3FHQMKM","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KV5JIXN6","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:4465a615eac832a26ba378c578669b0d567804f3cc1a6d65c0adf02d9425981d","target":"graph","created_at":"2026-05-18T04:40:08Z","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":"Let $T : \\Lambda \\to \\Lambda$ be an expanding map on a Cantor set. For each suitably normalized H\\\"older continuous potential, we construct a spectral triple from which one may recover the associated Gibbs measure as a noncommutative measure.","authors_text":"Richard Sharp","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-09-29T14:08:50Z","title":"Spectral triples and Gibbs measures for expanding maps on Cantor sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5887","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":"sha256:95b67022a0ff4daff3933c34851fab5502ff631a2026fd64830c175782772a87","target":"record","created_at":"2026-05-18T04:40:08Z","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":"af07d2926a4288084d6e56507e6843f1e866b1770c7bdb0727b5644c0a09c50c","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-09-29T14:08:50Z","title_canon_sha256":"aeb95264cd90b3e5bc9853a38c51b962c77d8140cc77860281bc5013bb2f1fa9"},"schema_version":"1.0","source":{"id":"1009.5887","kind":"arxiv","version":1}},"canonical_sha256":"557a945dbe96ca78314cf4bb71813ad9f3e847c57f1a7b0fec3fe46dfda1da76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"557a945dbe96ca78314cf4bb71813ad9f3e847c57f1a7b0fec3fe46dfda1da76","first_computed_at":"2026-05-18T04:40:08.673970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:08.673970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fl41Eul4hJufmhBKF8ioC+RBWyg/ctmBORuXou4zPstdDWlyZ1cKXdfePyT+Q4043kfLcqSQYFtjAAmzXRvdCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:08.674601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.5887","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95b67022a0ff4daff3933c34851fab5502ff631a2026fd64830c175782772a87","sha256:4465a615eac832a26ba378c578669b0d567804f3cc1a6d65c0adf02d9425981d"],"state_sha256":"4944336dfa182215d1f10974df9999f61c807953fe52b3c483582a4aa69b0ab4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fgx1UsjC+O24+Dd6qHyNKI5Kkma7hYksIucMdqkzDXr/a1ZlQ26ctUWtj90kn3srjuuRi4Lt/WcBPi/0OOozBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T04:13:15.545694Z","bundle_sha256":"cfbc696c8b42841b43d1013caeaf2a16e4097bbdadf91702152a1b8ba3d28649"}}