{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PY3BLMKMSYASBOHF6MPT5KLQWK","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":"382eb663718b948a1e2a3af68f339eb3a5d072876770d7f0679c3d7ee87344c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-09-28T18:07:39Z","title_canon_sha256":"485c7f85dac455da181504a96068f205adff3c2df7fe959f855c795fd769e20a"},"schema_version":"1.0","source":{"id":"1509.08415","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08415","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08415v1","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08415","created_at":"2026-05-18T01:31:53Z"},{"alias_kind":"pith_short_12","alias_value":"PY3BLMKMSYAS","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PY3BLMKMSYASBOHF","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PY3BLMKM","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:cff85c5ef03cbc2d543a2b0c6d3f070002e0c49cce2af07c87fe73a29cffa2d6","target":"graph","created_at":"2026-05-18T01:31:53Z","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":"In this paper we consider dynamical properties of set-valued mappings and their implications on the associated inverse limit space. Specifically, we define the specification property and topological entropy for set-valued functions and prove some elementary results of these properties. We end with a few results regarding invariant measures for set-valued functions and their associated inverse limits.","authors_text":"Brian Raines, Tim Tennant","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-09-28T18:07:39Z","title":"The specification property on a set-valued map and its inverse limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08415","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":"sha256:871090981b009c2c788ba91339a6611f971a09788589b98f38f09d0925221a73","target":"record","created_at":"2026-05-18T01:31:53Z","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":"382eb663718b948a1e2a3af68f339eb3a5d072876770d7f0679c3d7ee87344c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-09-28T18:07:39Z","title_canon_sha256":"485c7f85dac455da181504a96068f205adff3c2df7fe959f855c795fd769e20a"},"schema_version":"1.0","source":{"id":"1509.08415","kind":"arxiv","version":1}},"canonical_sha256":"7e3615b14c960120b8e5f31f3ea970b2869611cf0224e220cb7f6af0bea19186","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e3615b14c960120b8e5f31f3ea970b2869611cf0224e220cb7f6af0bea19186","first_computed_at":"2026-05-18T01:31:53.917884Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:53.917884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O1ndn9ddqoRAIe7nDdGSuF3ciLQMJygHIN90aMdZ5t54LeHphkfq1CvDvZYgSMmxwZsqRYP+Ql7ozM/SxepTCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:53.918380Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.08415","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:871090981b009c2c788ba91339a6611f971a09788589b98f38f09d0925221a73","sha256:cff85c5ef03cbc2d543a2b0c6d3f070002e0c49cce2af07c87fe73a29cffa2d6"],"state_sha256":"b1b17ddeab67748b7e0996d2102440c98b2975e61a7bfb96479eec6965977e1f"}