{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:JAHU5BPKHMIJMOZJFPGCFPHD7H","short_pith_number":"pith:JAHU5BPK","canonical_record":{"source":{"id":"1908.02930","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-08T04:51:52Z","cross_cats_sorted":[],"title_canon_sha256":"b6f9a8462e78a838942951d428d7cfa1d79e2ed5105ea56567566b2d9b58292a","abstract_canon_sha256":"56510ee366c45f5f98ff6ffc81c0f9fce97c7bab28af0aab3cf79857573e8721"},"schema_version":"1.0"},"canonical_sha256":"480f4e85ea3b10963b292bcc22bce3f9e2e892d0c76635180088958b10e8f714","source":{"kind":"arxiv","id":"1908.02930","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.02930","created_at":"2026-07-05T02:53:50Z"},{"alias_kind":"arxiv_version","alias_value":"1908.02930v3","created_at":"2026-07-05T02:53:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02930","created_at":"2026-07-05T02:53:50Z"},{"alias_kind":"pith_short_12","alias_value":"JAHU5BPKHMIJ","created_at":"2026-07-05T02:53:50Z"},{"alias_kind":"pith_short_16","alias_value":"JAHU5BPKHMIJMOZJ","created_at":"2026-07-05T02:53:50Z"},{"alias_kind":"pith_short_8","alias_value":"JAHU5BPK","created_at":"2026-07-05T02:53:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:JAHU5BPKHMIJMOZJFPGCFPHD7H","target":"record","payload":{"canonical_record":{"source":{"id":"1908.02930","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-08T04:51:52Z","cross_cats_sorted":[],"title_canon_sha256":"b6f9a8462e78a838942951d428d7cfa1d79e2ed5105ea56567566b2d9b58292a","abstract_canon_sha256":"56510ee366c45f5f98ff6ffc81c0f9fce97c7bab28af0aab3cf79857573e8721"},"schema_version":"1.0"},"canonical_sha256":"480f4e85ea3b10963b292bcc22bce3f9e2e892d0c76635180088958b10e8f714","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:53:50.215531Z","signature_b64":"anCLeozhi1/6OgBrEqGYg8jpSSvqDQlHlIDxfVcLkI0QmAFFc6byyNDnYaISs68I/Z2+42rNVdDiafN6OHL8Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"480f4e85ea3b10963b292bcc22bce3f9e2e892d0c76635180088958b10e8f714","last_reissued_at":"2026-07-05T02:53:50.215064Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:53:50.215064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.02930","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":"2026-07-05T02:53:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5soOO7TmtEWg7l24lmIPr2i0tWi1fpVnXNe45lmyPZRjLRnXO4yiHQrkOsNrrj0jcdAdbk9KzfA6lpNpcIi0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T05:06:44.332026Z"},"content_sha256":"0a72841a68dac622bd27503d5fa57793bc50ebf5ffc61843d7ab5f72f77f168b","schema_version":"1.0","event_id":"sha256:0a72841a68dac622bd27503d5fa57793bc50ebf5ffc61843d7ab5f72f77f168b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:JAHU5BPKHMIJMOZJFPGCFPHD7H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characteristic measures of symbolic dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Joshua Frisch, Omer Tamuz","submitted_at":"2019-08-08T04:51:52Z","abstract_excerpt":"A probability measure is a characteristic measure of a topological dynamical system if it is invariant to the automorphism group of the system. We show that zero entropy shifts always admit characteristic measures. We use similar techniques to show that automorphism groups of minimal zero entropy shifts are sofic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02930","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.02930/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:53:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZiiHYwoiQ20SqdxaGx1Yq6FzxCM2/gx4a+Ob1RoFfisZuTVGHihnhfSElRfbiJpJOjUpm4szXC0rgpFagWXvDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T05:06:44.332527Z"},"content_sha256":"04f1ed1cafc52284ca98065b0cbb479ab6105354146e611ac7e156ec8c1f83ce","schema_version":"1.0","event_id":"sha256:04f1ed1cafc52284ca98065b0cbb479ab6105354146e611ac7e156ec8c1f83ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JAHU5BPKHMIJMOZJFPGCFPHD7H/bundle.json","state_url":"https://pith.science/pith/JAHU5BPKHMIJMOZJFPGCFPHD7H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JAHU5BPKHMIJMOZJFPGCFPHD7H/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":"2026-08-16T05:06:44Z","links":{"resolver":"https://pith.science/pith/JAHU5BPKHMIJMOZJFPGCFPHD7H","bundle":"https://pith.science/pith/JAHU5BPKHMIJMOZJFPGCFPHD7H/bundle.json","state":"https://pith.science/pith/JAHU5BPKHMIJMOZJFPGCFPHD7H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JAHU5BPKHMIJMOZJFPGCFPHD7H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JAHU5BPKHMIJMOZJFPGCFPHD7H","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":"56510ee366c45f5f98ff6ffc81c0f9fce97c7bab28af0aab3cf79857573e8721","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-08T04:51:52Z","title_canon_sha256":"b6f9a8462e78a838942951d428d7cfa1d79e2ed5105ea56567566b2d9b58292a"},"schema_version":"1.0","source":{"id":"1908.02930","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.02930","created_at":"2026-07-05T02:53:50Z"},{"alias_kind":"arxiv_version","alias_value":"1908.02930v3","created_at":"2026-07-05T02:53:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02930","created_at":"2026-07-05T02:53:50Z"},{"alias_kind":"pith_short_12","alias_value":"JAHU5BPKHMIJ","created_at":"2026-07-05T02:53:50Z"},{"alias_kind":"pith_short_16","alias_value":"JAHU5BPKHMIJMOZJ","created_at":"2026-07-05T02:53:50Z"},{"alias_kind":"pith_short_8","alias_value":"JAHU5BPK","created_at":"2026-07-05T02:53:50Z"}],"graph_snapshots":[{"event_id":"sha256:04f1ed1cafc52284ca98065b0cbb479ab6105354146e611ac7e156ec8c1f83ce","target":"graph","created_at":"2026-07-05T02:53:50Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.02930/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A probability measure is a characteristic measure of a topological dynamical system if it is invariant to the automorphism group of the system. We show that zero entropy shifts always admit characteristic measures. We use similar techniques to show that automorphism groups of minimal zero entropy shifts are sofic.","authors_text":"Joshua Frisch, Omer Tamuz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-08T04:51:52Z","title":"Characteristic measures of symbolic dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02930","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":"sha256:0a72841a68dac622bd27503d5fa57793bc50ebf5ffc61843d7ab5f72f77f168b","target":"record","created_at":"2026-07-05T02:53:50Z","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":"56510ee366c45f5f98ff6ffc81c0f9fce97c7bab28af0aab3cf79857573e8721","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-08T04:51:52Z","title_canon_sha256":"b6f9a8462e78a838942951d428d7cfa1d79e2ed5105ea56567566b2d9b58292a"},"schema_version":"1.0","source":{"id":"1908.02930","kind":"arxiv","version":3}},"canonical_sha256":"480f4e85ea3b10963b292bcc22bce3f9e2e892d0c76635180088958b10e8f714","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"480f4e85ea3b10963b292bcc22bce3f9e2e892d0c76635180088958b10e8f714","first_computed_at":"2026-07-05T02:53:50.215064Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:53:50.215064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"anCLeozhi1/6OgBrEqGYg8jpSSvqDQlHlIDxfVcLkI0QmAFFc6byyNDnYaISs68I/Z2+42rNVdDiafN6OHL8Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T02:53:50.215531Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.02930","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a72841a68dac622bd27503d5fa57793bc50ebf5ffc61843d7ab5f72f77f168b","sha256:04f1ed1cafc52284ca98065b0cbb479ab6105354146e611ac7e156ec8c1f83ce"],"state_sha256":"3c367630c8fdbe9dcb77718fc63f20855e51dd7e9faad92ad7e7ab9306a40e38"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wWIvGeSEG/UBGrdEJv42LGtpBDj9agddbGJiiTOTu9g+tFml//Ckh4vJtEFTY6U0CjksChNKDCyEvBsyy6beAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T05:06:44.337103Z","bundle_sha256":"1910c560fbbebd10e08c2b4b99172cc961e7d4b7f81612de12f73bc52a781a83"}}