{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:VBQIAAI5QDMY42ORYNRUX44AIS","short_pith_number":"pith:VBQIAAI5","schema_version":"1.0","canonical_sha256":"a86080011d80d98e69d1c3634bf38044bf1914ac5115be03db79b98ecfac58c9","source":{"kind":"arxiv","id":"1707.09652","version":1},"attestation_state":"computed","paper":{"title":"Choosing elements from finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Michael Vaughan-Lee","submitted_at":"2017-07-30T17:53:40Z","abstract_excerpt":"In two important papers from 1960 Graham Higman introduced the notion of PORC functions, and he proved that for any given positive integer $n$ the number of $p$-class two groups of order $p^n$ is a PORC function of $p$. A key result in his proof of this theorem is the following: \"The number of ways of choosing a finite number of elements from the finite field of order $q^n$ subject to a finite number of monomial equations and inequalities between them and their conjugates over GF($q$), considered as a function of $q$, is PORC.\" Higman's proof of this result involves five pages of homological a"},"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":"1707.09652","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-07-30T17:53:40Z","cross_cats_sorted":[],"title_canon_sha256":"28b6b24acfafa44a01c26a6b2974fb8fa44255c2859db84d47d34ffa2e82a5e2","abstract_canon_sha256":"0e721cfbdc8cbf58503cd1f5edb9fcedd85d1f518059481fbf58df9c15c95f9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:10.730758Z","signature_b64":"oimtNvSeUnNcWov0Ylpzy4Bxnr0Df/RjAb/LcO9tQyMOdZiPuYR7VKZ/Q+62YoLDJE9eD5t8xoJHCw88LOA3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a86080011d80d98e69d1c3634bf38044bf1914ac5115be03db79b98ecfac58c9","last_reissued_at":"2026-05-18T00:39:10.730110Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:10.730110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Choosing elements from finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Michael Vaughan-Lee","submitted_at":"2017-07-30T17:53:40Z","abstract_excerpt":"In two important papers from 1960 Graham Higman introduced the notion of PORC functions, and he proved that for any given positive integer $n$ the number of $p$-class two groups of order $p^n$ is a PORC function of $p$. A key result in his proof of this theorem is the following: \"The number of ways of choosing a finite number of elements from the finite field of order $q^n$ subject to a finite number of monomial equations and inequalities between them and their conjugates over GF($q$), considered as a function of $q$, is PORC.\" Higman's proof of this result involves five pages of homological a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.09652","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":""},"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":"1707.09652","created_at":"2026-05-18T00:39:10.730206+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.09652v1","created_at":"2026-05-18T00:39:10.730206+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.09652","created_at":"2026-05-18T00:39:10.730206+00:00"},{"alias_kind":"pith_short_12","alias_value":"VBQIAAI5QDMY","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"VBQIAAI5QDMY42OR","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"VBQIAAI5","created_at":"2026-05-18T12:31:49.984773+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/VBQIAAI5QDMY42ORYNRUX44AIS","json":"https://pith.science/pith/VBQIAAI5QDMY42ORYNRUX44AIS.json","graph_json":"https://pith.science/api/pith-number/VBQIAAI5QDMY42ORYNRUX44AIS/graph.json","events_json":"https://pith.science/api/pith-number/VBQIAAI5QDMY42ORYNRUX44AIS/events.json","paper":"https://pith.science/paper/VBQIAAI5"},"agent_actions":{"view_html":"https://pith.science/pith/VBQIAAI5QDMY42ORYNRUX44AIS","download_json":"https://pith.science/pith/VBQIAAI5QDMY42ORYNRUX44AIS.json","view_paper":"https://pith.science/paper/VBQIAAI5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.09652&json=true","fetch_graph":"https://pith.science/api/pith-number/VBQIAAI5QDMY42ORYNRUX44AIS/graph.json","fetch_events":"https://pith.science/api/pith-number/VBQIAAI5QDMY42ORYNRUX44AIS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VBQIAAI5QDMY42ORYNRUX44AIS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VBQIAAI5QDMY42ORYNRUX44AIS/action/storage_attestation","attest_author":"https://pith.science/pith/VBQIAAI5QDMY42ORYNRUX44AIS/action/author_attestation","sign_citation":"https://pith.science/pith/VBQIAAI5QDMY42ORYNRUX44AIS/action/citation_signature","submit_replication":"https://pith.science/pith/VBQIAAI5QDMY42ORYNRUX44AIS/action/replication_record"}},"created_at":"2026-05-18T00:39:10.730206+00:00","updated_at":"2026-05-18T00:39:10.730206+00:00"}