{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:WWDVH7QLLKXKWD3NJBWKEWARJN","short_pith_number":"pith:WWDVH7QL","schema_version":"1.0","canonical_sha256":"b58753fe0b5aaeab0f6d486ca258114b6afb06df9c6a234960cd2d1830e99cce","source":{"kind":"arxiv","id":"2508.01686","version":1},"attestation_state":"computed","paper":{"title":"On the Representation of Integers as Sums of Limited Prime Powers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Julius Stricker","submitted_at":"2025-08-03T09:37:25Z","abstract_excerpt":"We present a novel conjecture concerning the additive representation of natural numbers using prime powers. Based on extensive computational verification, we conjecture that every integer n > 23 can be expressed as a sum of at most five prime powers p^k, where p is a prime number and k is an integer greater than or equal to 2. This conjecture is supported by comprehensive computational evidence covering all integers up to 10^7(exhaustively) and specific large numbers up to 10^10 (via sampling), where no counterexample requiring more than five summands has been found. This work highlights a sur"},"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":"2508.01686","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GM","submitted_at":"2025-08-03T09:37:25Z","cross_cats_sorted":[],"title_canon_sha256":"96287f73b7de529f81fff043e7ede32df48f1f2de471c270bad7be2b2a32f1da","abstract_canon_sha256":"364d7829ec7fca7c1a1b49168b4aca3f5e10a2e6f9710b6af0515e68b07b3da1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:48:07.480345Z","signature_b64":"T87lFKycWbuwNI4p6n7fy05zYQSEZu3wL9M46kfThjtG4LLGhxBCPNC5QhypJ9iipAxTy3BF1S/C9WBm4nsqCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b58753fe0b5aaeab0f6d486ca258114b6afb06df9c6a234960cd2d1830e99cce","last_reissued_at":"2026-07-05T11:48:07.479702Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:48:07.479702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Representation of Integers as Sums of Limited Prime Powers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Julius Stricker","submitted_at":"2025-08-03T09:37:25Z","abstract_excerpt":"We present a novel conjecture concerning the additive representation of natural numbers using prime powers. Based on extensive computational verification, we conjecture that every integer n > 23 can be expressed as a sum of at most five prime powers p^k, where p is a prime number and k is an integer greater than or equal to 2. This conjecture is supported by comprehensive computational evidence covering all integers up to 10^7(exhaustively) and specific large numbers up to 10^10 (via sampling), where no counterexample requiring more than five summands has been found. This work highlights a sur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.01686","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/2508.01686/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":"2508.01686","created_at":"2026-07-05T11:48:07.479788+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.01686v1","created_at":"2026-07-05T11:48:07.479788+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.01686","created_at":"2026-07-05T11:48:07.479788+00:00"},{"alias_kind":"pith_short_12","alias_value":"WWDVH7QLLKXK","created_at":"2026-07-05T11:48:07.479788+00:00"},{"alias_kind":"pith_short_16","alias_value":"WWDVH7QLLKXKWD3N","created_at":"2026-07-05T11:48:07.479788+00:00"},{"alias_kind":"pith_short_8","alias_value":"WWDVH7QL","created_at":"2026-07-05T11:48:07.479788+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WWDVH7QLLKXKWD3NJBWKEWARJN","json":"https://pith.science/pith/WWDVH7QLLKXKWD3NJBWKEWARJN.json","graph_json":"https://pith.science/api/pith-number/WWDVH7QLLKXKWD3NJBWKEWARJN/graph.json","events_json":"https://pith.science/api/pith-number/WWDVH7QLLKXKWD3NJBWKEWARJN/events.json","paper":"https://pith.science/paper/WWDVH7QL"},"agent_actions":{"view_html":"https://pith.science/pith/WWDVH7QLLKXKWD3NJBWKEWARJN","download_json":"https://pith.science/pith/WWDVH7QLLKXKWD3NJBWKEWARJN.json","view_paper":"https://pith.science/paper/WWDVH7QL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.01686&json=true","fetch_graph":"https://pith.science/api/pith-number/WWDVH7QLLKXKWD3NJBWKEWARJN/graph.json","fetch_events":"https://pith.science/api/pith-number/WWDVH7QLLKXKWD3NJBWKEWARJN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WWDVH7QLLKXKWD3NJBWKEWARJN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WWDVH7QLLKXKWD3NJBWKEWARJN/action/storage_attestation","attest_author":"https://pith.science/pith/WWDVH7QLLKXKWD3NJBWKEWARJN/action/author_attestation","sign_citation":"https://pith.science/pith/WWDVH7QLLKXKWD3NJBWKEWARJN/action/citation_signature","submit_replication":"https://pith.science/pith/WWDVH7QLLKXKWD3NJBWKEWARJN/action/replication_record"}},"created_at":"2026-07-05T11:48:07.479788+00:00","updated_at":"2026-07-05T11:48:07.479788+00:00"}