{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:K6HPRPR7DTKGLKHCEQXTJYD4VM","short_pith_number":"pith:K6HPRPR7","schema_version":"1.0","canonical_sha256":"578ef8be3f1cd465a8e2242f34e07cab10d218192ca6091dd32e66adcfa511b8","source":{"kind":"arxiv","id":"2603.00658","version":1},"attestation_state":"computed","paper":{"title":"A Deterministic Fractal Set Derived from the Sequence of Prime Numbers","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Zhengqiang Li","submitted_at":"2026-02-28T14:04:51Z","abstract_excerpt":"We introduce a novel deterministic fractal set PF in the unit interval whose construction is driven by the sequence of prime numbers modulo 16. At each step of the recursive construction, two subintervals are retained based on the residues of consecutive primes, yielding a Cantor-like set with a uniform contraction ratio of 1/16 and a branching number of 2. We prove that PF is a non-empty, compact, nowhere dense set of Lebesgue measure zero. Its Hausdorff dimension and box-counting dimension are both equal to 1 4 . The dimension is universal in the sense that it does not depend on the specific"},"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":"2603.00658","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.GM","submitted_at":"2026-02-28T14:04:51Z","cross_cats_sorted":[],"title_canon_sha256":"aff6e495353f90570a8fa5fe84fd16bde1a1f13c52285b3ce6b87e82b1cbea17","abstract_canon_sha256":"a6c1e2796c3bed6891de0bea9b6fbdec4d1e9b911e587966d85e0decf65cd8da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T23:04:16.456923Z","signature_b64":"/v5rNhTebo0Emz1XwtaBCIaoFEjOiGMtkmz4L6ocIzH2BnhlLdV+JjoemrYk+ZOKvGRT6h0asM8og7F25awtCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"578ef8be3f1cd465a8e2242f34e07cab10d218192ca6091dd32e66adcfa511b8","last_reissued_at":"2026-05-26T23:04:16.454250Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T23:04:16.454250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Deterministic Fractal Set Derived from the Sequence of Prime Numbers","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Zhengqiang Li","submitted_at":"2026-02-28T14:04:51Z","abstract_excerpt":"We introduce a novel deterministic fractal set PF in the unit interval whose construction is driven by the sequence of prime numbers modulo 16. At each step of the recursive construction, two subintervals are retained based on the residues of consecutive primes, yielding a Cantor-like set with a uniform contraction ratio of 1/16 and a branching number of 2. We prove that PF is a non-empty, compact, nowhere dense set of Lebesgue measure zero. Its Hausdorff dimension and box-counting dimension are both equal to 1 4 . The dimension is universal in the sense that it does not depend on the specific"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.00658","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.00658/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":"2603.00658","created_at":"2026-05-26T23:04:16.454444+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.00658v1","created_at":"2026-05-26T23:04:16.454444+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.00658","created_at":"2026-05-26T23:04:16.454444+00:00"},{"alias_kind":"pith_short_12","alias_value":"K6HPRPR7DTKG","created_at":"2026-05-26T23:04:16.454444+00:00"},{"alias_kind":"pith_short_16","alias_value":"K6HPRPR7DTKGLKHC","created_at":"2026-05-26T23:04:16.454444+00:00"},{"alias_kind":"pith_short_8","alias_value":"K6HPRPR7","created_at":"2026-05-26T23:04:16.454444+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2604.14596","citing_title":"Prime--Zero Duality: Fractal Geometry, Renormalization-Group Flow, and an Information-Ontological Framework for Number Theory","ref_index":16,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/K6HPRPR7DTKGLKHCEQXTJYD4VM","json":"https://pith.science/pith/K6HPRPR7DTKGLKHCEQXTJYD4VM.json","graph_json":"https://pith.science/api/pith-number/K6HPRPR7DTKGLKHCEQXTJYD4VM/graph.json","events_json":"https://pith.science/api/pith-number/K6HPRPR7DTKGLKHCEQXTJYD4VM/events.json","paper":"https://pith.science/paper/K6HPRPR7"},"agent_actions":{"view_html":"https://pith.science/pith/K6HPRPR7DTKGLKHCEQXTJYD4VM","download_json":"https://pith.science/pith/K6HPRPR7DTKGLKHCEQXTJYD4VM.json","view_paper":"https://pith.science/paper/K6HPRPR7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.00658&json=true","fetch_graph":"https://pith.science/api/pith-number/K6HPRPR7DTKGLKHCEQXTJYD4VM/graph.json","fetch_events":"https://pith.science/api/pith-number/K6HPRPR7DTKGLKHCEQXTJYD4VM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K6HPRPR7DTKGLKHCEQXTJYD4VM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K6HPRPR7DTKGLKHCEQXTJYD4VM/action/storage_attestation","attest_author":"https://pith.science/pith/K6HPRPR7DTKGLKHCEQXTJYD4VM/action/author_attestation","sign_citation":"https://pith.science/pith/K6HPRPR7DTKGLKHCEQXTJYD4VM/action/citation_signature","submit_replication":"https://pith.science/pith/K6HPRPR7DTKGLKHCEQXTJYD4VM/action/replication_record"}},"created_at":"2026-05-26T23:04:16.454444+00:00","updated_at":"2026-05-26T23:04:16.454444+00:00"}