{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LGDT3BGGWVYQTI57RV2GRFHLOK","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":"ed5734d42c0964d8e538379c41191bbf60a2bbe7b290414ce7eaa95a513a7776","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2016-09-01T17:59:16Z","title_canon_sha256":"521393202de1c8a0b9729a6cd4a1c9bedc5109eff2e3a2b31e65517a8f581426"},"schema_version":"1.0","source":{"id":"1609.01159","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01159","created_at":"2026-05-18T01:02:20Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01159v4","created_at":"2026-05-18T01:02:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01159","created_at":"2026-05-18T01:02:20Z"},{"alias_kind":"pith_short_12","alias_value":"LGDT3BGGWVYQ","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LGDT3BGGWVYQTI57","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LGDT3BGG","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:30449c118b4d2bbf60d71fc2d72f7015d0f8e7e4f64fae3312ee2c3d34403e91","target":"graph","created_at":"2026-05-18T01:02:20Z","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":"Quasicrystals are fractal due to their self similar property. In this paper, a new cycloidal fractal signature possessing the cardioid shape in the Mandelbrot set is presented in the Fourier space of a Fibonacci chain with two lengths, L and S, where L/S = \\{phi}. The corresponding pointwise dimension is 0.7. Various modifications, such as truncation from the head or tail, scrambling the orders of the sequence, and changing the ratio of the L and S, are done on the Fibonacci chain. The resulting patterns in the Fourier space show that that the fractal signature is very sensitive to changes in ","authors_text":"Fang Fang, Klee Irwin, Raymond Aschheim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2016-09-01T17:59:16Z","title":"The Unexpected Fractal Signatures in Fibonacci chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01159","kind":"arxiv","version":4},"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:f8efa58b1a424b0f03d000feb1c230b3af7cc8d9c7525fefa99173b3d95784ac","target":"record","created_at":"2026-05-18T01:02:20Z","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":"ed5734d42c0964d8e538379c41191bbf60a2bbe7b290414ce7eaa95a513a7776","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2016-09-01T17:59:16Z","title_canon_sha256":"521393202de1c8a0b9729a6cd4a1c9bedc5109eff2e3a2b31e65517a8f581426"},"schema_version":"1.0","source":{"id":"1609.01159","kind":"arxiv","version":4}},"canonical_sha256":"59873d84c6b57109a3bf8d746894eb72bcb4f347c6162631372feb451bc51178","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59873d84c6b57109a3bf8d746894eb72bcb4f347c6162631372feb451bc51178","first_computed_at":"2026-05-18T01:02:20.488013Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:20.488013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wukvPkIrPJSbRe83y+rrPcOm8zb2Ur2PJuKaGsU5E8getMfTfkR/t4XH+HwJtZUZrXbQpf+l3exFSRata5MvDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:20.488531Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01159","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8efa58b1a424b0f03d000feb1c230b3af7cc8d9c7525fefa99173b3d95784ac","sha256:30449c118b4d2bbf60d71fc2d72f7015d0f8e7e4f64fae3312ee2c3d34403e91"],"state_sha256":"0a749798590373fac6816cede293f5b3947460e85334658c19a709c8ff40678e"}