{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:OSQTHIIYJPOXCHOOO3ZI2VI5Y3","short_pith_number":"pith:OSQTHIIY","canonical_record":{"source":{"id":"1902.08387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-22T07:55:18Z","cross_cats_sorted":[],"title_canon_sha256":"ac378232ac7370fb36f36272470dc095147d7f81983395e0cd23206483a11f8b","abstract_canon_sha256":"1c7ae2e6e1b51082fff9bec2ca8b30509efb6c93ffe559660b052518870eb88c"},"schema_version":"1.0"},"canonical_sha256":"74a133a1184bdd711dce76f28d551dc6e5e6d99dc744bac75306fc43f4e0c002","source":{"kind":"arxiv","id":"1902.08387","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.08387","created_at":"2026-05-17T23:52:57Z"},{"alias_kind":"arxiv_version","alias_value":"1902.08387v1","created_at":"2026-05-17T23:52:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08387","created_at":"2026-05-17T23:52:57Z"},{"alias_kind":"pith_short_12","alias_value":"OSQTHIIYJPOX","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"OSQTHIIYJPOXCHOO","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"OSQTHIIY","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:OSQTHIIYJPOXCHOOO3ZI2VI5Y3","target":"record","payload":{"canonical_record":{"source":{"id":"1902.08387","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-22T07:55:18Z","cross_cats_sorted":[],"title_canon_sha256":"ac378232ac7370fb36f36272470dc095147d7f81983395e0cd23206483a11f8b","abstract_canon_sha256":"1c7ae2e6e1b51082fff9bec2ca8b30509efb6c93ffe559660b052518870eb88c"},"schema_version":"1.0"},"canonical_sha256":"74a133a1184bdd711dce76f28d551dc6e5e6d99dc744bac75306fc43f4e0c002","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:57.416872Z","signature_b64":"srX9lpp2ho52enB8HLFb6Kq8QagwFOMVhKJEhxYc5XO95q0UtIOOxPlQ70X7U2E2HSV0Pz9RsrSiGE1Z+P1iBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74a133a1184bdd711dce76f28d551dc6e5e6d99dc744bac75306fc43f4e0c002","last_reissued_at":"2026-05-17T23:52:57.416320Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:57.416320Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.08387","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":"2026-05-17T23:52:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f8rIgZoZJC8Ctq7IJYmTK2Yi9WfHLhjc2Z7l5Sd8h0M2nVbKarhvaMciclHBVca0ru0LlYF3J9g8/GtulFQEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T08:15:44.981410Z"},"content_sha256":"4ae73f340194cf3b78e2bc32f095905684f165610ad8a55e6c5d388d22008ed8","schema_version":"1.0","event_id":"sha256:4ae73f340194cf3b78e2bc32f095905684f165610ad8a55e6c5d388d22008ed8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:OSQTHIIYJPOXCHOOO3ZI2VI5Y3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complexity and invariant measure of the period-doubling subshift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Miroslava Pol\\'akov\\'a","submitted_at":"2019-02-22T07:55:18Z","abstract_excerpt":"Explicit formulas for complexity and unique invariant measure of the period-doubling subshift can be derived from those for the Thue-Morse subshift, obtained by Brlek, De Luca and Varricchio, and Dekking. In this note we give direct proofs based on combinatorial properties of the period-doubling sequence. We also derive explicit formulas for correlation integral and other recurrence characteristics of the period-doubling subshift. As a corollary we obtain that the determinism of this subshift converges to 1 as the distance threshold approaches 0."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08387","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":"2026-05-17T23:52:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2r/PYGBYCO1ij1/dg1qq8VLbbGjD/0dsWtbPyTjTGVgnrvzWso4qCyZKk8lBjWuXuTzbXv+PU4VFnFYmDP3nDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T08:15:44.981869Z"},"content_sha256":"199e8b88e209dfefd5d72258c8371b29bb39203089a716b969dfed9828527721","schema_version":"1.0","event_id":"sha256:199e8b88e209dfefd5d72258c8371b29bb39203089a716b969dfed9828527721"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OSQTHIIYJPOXCHOOO3ZI2VI5Y3/bundle.json","state_url":"https://pith.science/pith/OSQTHIIYJPOXCHOOO3ZI2VI5Y3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OSQTHIIYJPOXCHOOO3ZI2VI5Y3/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":"2026-08-18T08:15:44Z","links":{"resolver":"https://pith.science/pith/OSQTHIIYJPOXCHOOO3ZI2VI5Y3","bundle":"https://pith.science/pith/OSQTHIIYJPOXCHOOO3ZI2VI5Y3/bundle.json","state":"https://pith.science/pith/OSQTHIIYJPOXCHOOO3ZI2VI5Y3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OSQTHIIYJPOXCHOOO3ZI2VI5Y3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OSQTHIIYJPOXCHOOO3ZI2VI5Y3","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":"1c7ae2e6e1b51082fff9bec2ca8b30509efb6c93ffe559660b052518870eb88c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-22T07:55:18Z","title_canon_sha256":"ac378232ac7370fb36f36272470dc095147d7f81983395e0cd23206483a11f8b"},"schema_version":"1.0","source":{"id":"1902.08387","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.08387","created_at":"2026-05-17T23:52:57Z"},{"alias_kind":"arxiv_version","alias_value":"1902.08387v1","created_at":"2026-05-17T23:52:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08387","created_at":"2026-05-17T23:52:57Z"},{"alias_kind":"pith_short_12","alias_value":"OSQTHIIYJPOX","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"OSQTHIIYJPOXCHOO","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"OSQTHIIY","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:199e8b88e209dfefd5d72258c8371b29bb39203089a716b969dfed9828527721","target":"graph","created_at":"2026-05-17T23:52:57Z","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":"Explicit formulas for complexity and unique invariant measure of the period-doubling subshift can be derived from those for the Thue-Morse subshift, obtained by Brlek, De Luca and Varricchio, and Dekking. In this note we give direct proofs based on combinatorial properties of the period-doubling sequence. We also derive explicit formulas for correlation integral and other recurrence characteristics of the period-doubling subshift. As a corollary we obtain that the determinism of this subshift converges to 1 as the distance threshold approaches 0.","authors_text":"Miroslava Pol\\'akov\\'a","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-22T07:55:18Z","title":"Complexity and invariant measure of the period-doubling subshift"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08387","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":"sha256:4ae73f340194cf3b78e2bc32f095905684f165610ad8a55e6c5d388d22008ed8","target":"record","created_at":"2026-05-17T23:52:57Z","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":"1c7ae2e6e1b51082fff9bec2ca8b30509efb6c93ffe559660b052518870eb88c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-22T07:55:18Z","title_canon_sha256":"ac378232ac7370fb36f36272470dc095147d7f81983395e0cd23206483a11f8b"},"schema_version":"1.0","source":{"id":"1902.08387","kind":"arxiv","version":1}},"canonical_sha256":"74a133a1184bdd711dce76f28d551dc6e5e6d99dc744bac75306fc43f4e0c002","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74a133a1184bdd711dce76f28d551dc6e5e6d99dc744bac75306fc43f4e0c002","first_computed_at":"2026-05-17T23:52:57.416320Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:57.416320Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"srX9lpp2ho52enB8HLFb6Kq8QagwFOMVhKJEhxYc5XO95q0UtIOOxPlQ70X7U2E2HSV0Pz9RsrSiGE1Z+P1iBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:57.416872Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.08387","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ae73f340194cf3b78e2bc32f095905684f165610ad8a55e6c5d388d22008ed8","sha256:199e8b88e209dfefd5d72258c8371b29bb39203089a716b969dfed9828527721"],"state_sha256":"47b8d4b675941644cbb6ce10bd8a79abb7f944a09baaa25621ca66935ecd03fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bEr4avxAm+NmJjARLjz3IPfNUne3gVWwd+QmAw6LkItyZ2swq9J7S1Z6VJXsRGBa+bPSgPZMN8wdDG7FDJuBDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T08:15:44.985306Z","bundle_sha256":"5567afd972ca2f0834723300f82565507b9514a785fa80713ed6003819cd7b4a"}}