{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:27TEJSGPNUWF32HERWE6OSA4IQ","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":"b016bc5b3fcbff4a657e38fb11afddc3c94b9c25dd682bab17a397a8e5c46253","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-05-15T03:18:13Z","title_canon_sha256":"9f3b267e7567b9e94cd517aed1296d660b124d493637355aa448e9c7051d3443"},"schema_version":"1.0","source":{"id":"2605.16450","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.16450","created_at":"2026-05-20T00:02:22Z"},{"alias_kind":"arxiv_version","alias_value":"2605.16450v1","created_at":"2026-05-20T00:02:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16450","created_at":"2026-05-20T00:02:22Z"},{"alias_kind":"pith_short_12","alias_value":"27TEJSGPNUWF","created_at":"2026-05-20T00:02:22Z"},{"alias_kind":"pith_short_16","alias_value":"27TEJSGPNUWF32HE","created_at":"2026-05-20T00:02:22Z"},{"alias_kind":"pith_short_8","alias_value":"27TEJSGP","created_at":"2026-05-20T00:02:22Z"}],"graph_snapshots":[{"event_id":"sha256:2dfd9ef2c7f5b23960c47293916d6e3795b60fe0ed666b1e51df5ae9e4985f8c","target":"graph","created_at":"2026-05-20T00:02:22Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We determine all non-abelian finite simple groups whose order has largest prime divisor not exceeding 10^4."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The classification of finite simple groups is complete and the orders of all known simple groups are correctly tabulated in the literature or databases used by the program."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"All non-abelian finite simple groups with largest prime divisor at most 10^4 are listed via exhaustive computational search over the known simple groups."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"All non-abelian finite simple groups whose order has largest prime divisor at most 10000 have been determined."}],"snapshot_sha256":"2b8f046e0694f463afc75126ef9fd1286f72a1d74ead309c675ccc7e4759ecfa"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"d990abfe1913e7199caa2699345562a5fa242b9ceed6a1ac30e22da11e96f9d7"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T22:01:30.345419Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T22:01:23.305927Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T19:34:35.256001Z","status":"skipped","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T19:21:57.082109Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.16450/integrity.json","findings":[],"snapshot_sha256":"7aeb7d315c56a6e14e5c45ffb0daddc9211b876b2c14c24e0196c43f8f6b2144","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Generalising a previous result, we determine all non-abelian finite simple groups whose order has largest prime divisor not exceeding $10^4$. The computer code for this and similar calculations is made available.","authors_text":"Andrei V. Zavarnitsine","cross_cats":[],"headline":"All non-abelian finite simple groups whose order has largest prime divisor at most 10000 have been determined.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-05-15T03:18:13Z","title":"Simple groups with narrow prime spectrum: Extended list"},"references":{"count":5,"internal_anchors":0,"resolved_work":5,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wil- son, Atlas of finite groups: maximal subgroups and ordinary characters for simple groups. Oxford. Clarendon Press (1985), xxxiii + 25","work_id":"73134111-3643-4078-a332-9e496b803c34","year":1985},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"URL: http://www.gap-system.org","work_id":"fc5f597f-b150-41a2-a544-6a632ae2a919","year":2025},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"V. D. Mazurov, On the set of orders of elements of a finite group, Algebra and Logic,33, N 1 (1994), 49–55","work_id":"0fb07358-1796-4e01-b634-4fd30730e2e7","year":1994},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"A. V. Zavarnitsine, Finite simple groups with narrow prime spectrum,Sib. Elect. Math. Reports,6(2009), 1–12. URL: http://semr.math.nsc.ru/v6/p1-12.pdf","work_id":"22b484d2-0d23-4559-ac51-5b71777b3870","year":2009},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"A. V. Zavarnitsine, GAP code accompanying this paper (2026). URL:https://github.com/zavandr/pi-simple The tables T able 1: Primes p∈ { 1000, . . . ,10000} with generic Sp 1009, 1013, 1019, 1033, 1039,","work_id":"6ce37b87-3648-440c-aa25-ccdb7e5b1226","year":2026}],"snapshot_sha256":"d3839cb247e94542cd158c622e838238d38a505fb6b40083872e713dc6b4b623"},"source":{"id":"2605.16450","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T21:52:51.046430Z","id":"090ff5b7-a67f-4bda-88ff-bc8d3e4f6a91","model_set":{"reader":"grok-4.3"},"one_line_summary":"All non-abelian finite simple groups with largest prime divisor at most 10^4 are listed via exhaustive computational search over the known simple groups.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"All non-abelian finite simple groups whose order has largest prime divisor at most 10000 have been determined.","strongest_claim":"We determine all non-abelian finite simple groups whose order has largest prime divisor not exceeding 10^4.","weakest_assumption":"The classification of finite simple groups is complete and the orders of all known simple groups are correctly tabulated in the literature or databases used by the program."}},"verdict_id":"090ff5b7-a67f-4bda-88ff-bc8d3e4f6a91"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9d91b4b2d30202a90cf817e3246e34466262fb94bd6f14eea3513363a371fb5e","target":"record","created_at":"2026-05-20T00:02:22Z","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":"b016bc5b3fcbff4a657e38fb11afddc3c94b9c25dd682bab17a397a8e5c46253","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-05-15T03:18:13Z","title_canon_sha256":"9f3b267e7567b9e94cd517aed1296d660b124d493637355aa448e9c7051d3443"},"schema_version":"1.0","source":{"id":"2605.16450","kind":"arxiv","version":1}},"canonical_sha256":"d7e644c8cf6d2c5de8e48d89e7481c4425dff74300d75cfdeaf38a6ca3cff177","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7e644c8cf6d2c5de8e48d89e7481c4425dff74300d75cfdeaf38a6ca3cff177","first_computed_at":"2026-05-20T00:02:22.696983Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:22.696983Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tWonOqsdp+Dcx2u7R6q7z3mG8M7Y5rdxBfZN3c8ze2dcJP9sF2Pgn9RBs7ow+5G9Sf3uVZoUAWbcNQufAStWDw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:22.697822Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16450","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d91b4b2d30202a90cf817e3246e34466262fb94bd6f14eea3513363a371fb5e","sha256:2dfd9ef2c7f5b23960c47293916d6e3795b60fe0ed666b1e51df5ae9e4985f8c"],"state_sha256":"63e6b478ef042eaa382d4366457d89ceaf484de54f774bef45cefd72ac15d0c3"}