{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HFYCYUGFZTL37SUTI3IWXSKVDX","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":"8dc283c8f44c01cd7f7ee049fd4479c4d99c7fce00eb5c6d96b088609d0f452c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-04-27T21:42:09Z","title_canon_sha256":"10db39ee95d9895e74c5c41ea0cc15d714631e5a4af73e57b2f2dd83f56ae7e8"},"schema_version":"1.0","source":{"id":"1604.08252","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.08252","created_at":"2026-05-18T00:33:32Z"},{"alias_kind":"arxiv_version","alias_value":"1604.08252v1","created_at":"2026-05-18T00:33:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08252","created_at":"2026-05-18T00:33:32Z"},{"alias_kind":"pith_short_12","alias_value":"HFYCYUGFZTL3","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HFYCYUGFZTL37SUT","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HFYCYUGF","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:22badfa8b96d39dbbd74169391ddbd21f6320d2a897ee1077e48a1fefa0383b4","target":"graph","created_at":"2026-05-18T00:33:32Z","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 prove a complex Ruelle-Perron-Frobenius theorem for Markov shifts over an infinite alphabet, whence extending results by M. Pollicott from the finite to the infinite alphabet setting. As an application we obtain an extension of renewal theory in symbolic dynamics, as developed by S. P. Lalley and in the sequel generalised by the second author, now covering the infinite alphabet case.","authors_text":"Mark Kesseb\\\"ohmer, Sabrina Kombrink","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-04-27T21:42:09Z","title":"A complex Ruelle-Perron-Frobenius theorem for infinite Markov shifts with applications to renewal theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08252","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":"sha256:6f64d235649ca2fb4f51e69f2591c9fd3feb7ce23ff261c0922e31ec6c8f19d9","target":"record","created_at":"2026-05-18T00:33:32Z","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":"8dc283c8f44c01cd7f7ee049fd4479c4d99c7fce00eb5c6d96b088609d0f452c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-04-27T21:42:09Z","title_canon_sha256":"10db39ee95d9895e74c5c41ea0cc15d714631e5a4af73e57b2f2dd83f56ae7e8"},"schema_version":"1.0","source":{"id":"1604.08252","kind":"arxiv","version":1}},"canonical_sha256":"39702c50c5ccd7bfca9346d16bc9551dfe0d44780a996c8a2aa5bd39b8264300","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39702c50c5ccd7bfca9346d16bc9551dfe0d44780a996c8a2aa5bd39b8264300","first_computed_at":"2026-05-18T00:33:32.554596Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:32.554596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0wNH3J/AVB2vTKuo7CK4lCh13rmUM0RXzm8fMwgfO1uVyKZXlyPxfkQbR2sAHvKbWm2FNWGtHO1z7+aUxE9YBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:32.555230Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.08252","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f64d235649ca2fb4f51e69f2591c9fd3feb7ce23ff261c0922e31ec6c8f19d9","sha256:22badfa8b96d39dbbd74169391ddbd21f6320d2a897ee1077e48a1fefa0383b4"],"state_sha256":"833884310e92eaef57ed2299ff38ceab318f3c20106fc65254451585104fd1bb"}