{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:X6PQ4AGVQY2IBMQAGY63BKMT3Y","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":"a5a2d6a98dba92e95bf753cb0ef37397c8f8e788606e7612228ffcf0755ab45f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-18T03:22:22Z","title_canon_sha256":"94851623202aab2b5b604ff7fb847febc312560d4f1da0fb3226cce32ac1a9b8"},"schema_version":"1.0","source":{"id":"1601.04391","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04391","created_at":"2026-05-18T01:22:45Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04391v1","created_at":"2026-05-18T01:22:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04391","created_at":"2026-05-18T01:22:45Z"},{"alias_kind":"pith_short_12","alias_value":"X6PQ4AGVQY2I","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X6PQ4AGVQY2IBMQA","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X6PQ4AGV","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:de7779d82965e07cf9b6ba3df5a1d7423804f7b1340d87846cbbbb32801ba9f1","target":"graph","created_at":"2026-05-18T01:22:45Z","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 ${\\cal P}$ be the set of palindromes occurring in the Fibonacci sequence. In this note, we establish three structures of $\\mathcal{P}$ and and discuss their properties: cylinder structure, chain structure and recursive structure. Using these structures, we determine that the number of distinct palindrome occurrences in $\\mathbb{F}[1,n]$ is exactly $n$, where $\\mathbb{F}[1,n]$ is the prefix of the Fibonacci sequence of length $n$. Then we give an algorithm for counting the number of repeated palindrome occurrences in $\\mathbb{F}[1,n]$, and get explicit expressions for some special $n$, whic","authors_text":"Yuke Huang, Zhiying Wen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-18T03:22:22Z","title":"The structure of palindromes in the Fibonacci sequence and some applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04391","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:a3f81d1d1f16f24512b60726802de836fc722f3329cbeffbaf86880d2aff4cdf","target":"record","created_at":"2026-05-18T01:22:45Z","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":"a5a2d6a98dba92e95bf753cb0ef37397c8f8e788606e7612228ffcf0755ab45f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-18T03:22:22Z","title_canon_sha256":"94851623202aab2b5b604ff7fb847febc312560d4f1da0fb3226cce32ac1a9b8"},"schema_version":"1.0","source":{"id":"1601.04391","kind":"arxiv","version":1}},"canonical_sha256":"bf9f0e00d5863480b200363db0a993de3a1f3e315e4cd0db694da366f0013fac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf9f0e00d5863480b200363db0a993de3a1f3e315e4cd0db694da366f0013fac","first_computed_at":"2026-05-18T01:22:45.167431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:45.167431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oXQosmMn71nmRfgZLcMDKWf2G7fIFAbiVO/WfrstiE6sF61/jUn4T0QOqZaqGVW3u1v5xH12uFqzgOpxhVCyDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:45.167908Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.04391","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3f81d1d1f16f24512b60726802de836fc722f3329cbeffbaf86880d2aff4cdf","sha256:de7779d82965e07cf9b6ba3df5a1d7423804f7b1340d87846cbbbb32801ba9f1"],"state_sha256":"3fd9d5c7f696a2790fab26f7731dc29f89200bc8cf075d6475289e39eca8ce5c"}