{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:6KW2ICKSLDJ454YAUQMWLXJIMF","short_pith_number":"pith:6KW2ICKS","schema_version":"1.0","canonical_sha256":"f2ada4095258d3cef300a41965dd286171a834c10f85055ecca595bf4f662d96","source":{"kind":"arxiv","id":"1906.10645","version":2},"attestation_state":"computed","paper":{"title":"Central Limit Theorems for Compound Paths on the 2-Dimensional Lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.NT","authors_text":"Daniel Li, Dilhan Salgado, Ethan Lu, Evan Fang, Jonathan Jenkins, Joshua M. Siktar, Steven J. Miller, Zack Lee","submitted_at":"2019-06-25T16:37:28Z","abstract_excerpt":"Zeckendorf proved that every integer can be written uniquely as a sum of non-consecutive Fibonacci numbers $\\{F_n\\}$, and later researchers showed that the distribution of the number of summands needed for such decompositions of integers in $[F_n, F_{n+1})$ converges to a Gaussian as $n\\to\\infty$. Decomposition problems have been studied extensively for a variety of different sequences and notions of a legal decompositions; for the Fibonacci numbers, a legal decomposition is one for which each summand is used at most once and no two consecutive summands may be chosen. Recently, Chen et al. [CC"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1906.10645","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-06-25T16:37:28Z","cross_cats_sorted":["math.CO","math.PR"],"title_canon_sha256":"9e078491dd9cadbcd007d12e567ccc6986097f7852d8769d9a22ef33ac565ee7","abstract_canon_sha256":"3da73cd4cae83c47936abbd79d7c9a998b522144d3c328657f89ed25993a273d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:04:59.627274Z","signature_b64":"45BBIbyITpEhGCgiAJbOjTAvCPlk79hRwdY5OJ9AhR13asqu/VZQtQlCU4cjEg5ZBvXwvxzIwTYkvJVtqpKGDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2ada4095258d3cef300a41965dd286171a834c10f85055ecca595bf4f662d96","last_reissued_at":"2026-07-05T01:04:59.626629Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:04:59.626629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Central Limit Theorems for Compound Paths on the 2-Dimensional Lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.NT","authors_text":"Daniel Li, Dilhan Salgado, Ethan Lu, Evan Fang, Jonathan Jenkins, Joshua M. Siktar, Steven J. Miller, Zack Lee","submitted_at":"2019-06-25T16:37:28Z","abstract_excerpt":"Zeckendorf proved that every integer can be written uniquely as a sum of non-consecutive Fibonacci numbers $\\{F_n\\}$, and later researchers showed that the distribution of the number of summands needed for such decompositions of integers in $[F_n, F_{n+1})$ converges to a Gaussian as $n\\to\\infty$. Decomposition problems have been studied extensively for a variety of different sequences and notions of a legal decompositions; for the Fibonacci numbers, a legal decomposition is one for which each summand is used at most once and no two consecutive summands may be chosen. Recently, Chen et al. [CC"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10645","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1906.10645/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1906.10645","created_at":"2026-07-05T01:04:59.626688+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.10645v2","created_at":"2026-07-05T01:04:59.626688+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10645","created_at":"2026-07-05T01:04:59.626688+00:00"},{"alias_kind":"pith_short_12","alias_value":"6KW2ICKSLDJ4","created_at":"2026-07-05T01:04:59.626688+00:00"},{"alias_kind":"pith_short_16","alias_value":"6KW2ICKSLDJ454YA","created_at":"2026-07-05T01:04:59.626688+00:00"},{"alias_kind":"pith_short_8","alias_value":"6KW2ICKS","created_at":"2026-07-05T01:04:59.626688+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1909.01935","citing_title":"Gaps of Summands of the Zeckendorf Lattice","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6KW2ICKSLDJ454YAUQMWLXJIMF","json":"https://pith.science/pith/6KW2ICKSLDJ454YAUQMWLXJIMF.json","graph_json":"https://pith.science/api/pith-number/6KW2ICKSLDJ454YAUQMWLXJIMF/graph.json","events_json":"https://pith.science/api/pith-number/6KW2ICKSLDJ454YAUQMWLXJIMF/events.json","paper":"https://pith.science/paper/6KW2ICKS"},"agent_actions":{"view_html":"https://pith.science/pith/6KW2ICKSLDJ454YAUQMWLXJIMF","download_json":"https://pith.science/pith/6KW2ICKSLDJ454YAUQMWLXJIMF.json","view_paper":"https://pith.science/paper/6KW2ICKS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.10645&json=true","fetch_graph":"https://pith.science/api/pith-number/6KW2ICKSLDJ454YAUQMWLXJIMF/graph.json","fetch_events":"https://pith.science/api/pith-number/6KW2ICKSLDJ454YAUQMWLXJIMF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6KW2ICKSLDJ454YAUQMWLXJIMF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6KW2ICKSLDJ454YAUQMWLXJIMF/action/storage_attestation","attest_author":"https://pith.science/pith/6KW2ICKSLDJ454YAUQMWLXJIMF/action/author_attestation","sign_citation":"https://pith.science/pith/6KW2ICKSLDJ454YAUQMWLXJIMF/action/citation_signature","submit_replication":"https://pith.science/pith/6KW2ICKSLDJ454YAUQMWLXJIMF/action/replication_record"}},"created_at":"2026-07-05T01:04:59.626688+00:00","updated_at":"2026-07-05T01:04:59.626688+00:00"}