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A longer candidate (10.1080/00927872.2022.2065494.citedin) was visible in the surrounding text but could not be confirmed against doi.org as printed.","detected_doi":"10.1080/00927872.2022.2065494.citedin","detected_arxiv_id":null,"ref_index":9,"audited_at":"2026-05-19T16:42:17.620090Z"},{"detector":"doi_compliance","finding_type":"recoverable_identifier","severity":"advisory","verdict_class":"incontrovertible","note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/bf01894517.citedin) was visible in the surrounding text but could not be confirmed against doi.org as printed.","detected_doi":"10.1007/bf01894517.citedin","detected_arxiv_id":null,"ref_index":3,"audited_at":"2026-05-19T16:42:17.620090Z"},{"detector":"doi_compliance","finding_type":"recoverable_identifier","severity":"advisory","verdict_class":"incontrovertible","note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1515/crll.1940.182.130.citedin) was visible in the surrounding text but could not be confirmed against doi.org as printed.","detected_doi":"10.1515/crll.1940.182.130.citedin","detected_arxiv_id":null,"ref_index":7,"audited_at":"2026-05-19T16:42:17.620090Z"},{"detector":"doi_compliance","finding_type":"recoverable_identifier","severity":"advisory","verdict_class":"incontrovertible","note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1006/jabr.1995.1331.citedin) was visible in the surrounding text but could not be confirmed against doi.org as printed.","detected_doi":"10.1006/jabr.1995.1331.citedin","detected_arxiv_id":null,"ref_index":10,"audited_at":"2026-05-19T16:42:17.620090Z"},{"detector":"doi_compliance","finding_type":"recoverable_identifier","severity":"advisory","verdict_class":"incontrovertible","note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.2748/tmj/1178243172.citedin) was visible in the surrounding text but could not be confirmed against doi.org as printed.","detected_doi":"10.2748/tmj/1178243172.citedin","detected_arxiv_id":null,"ref_index":4,"audited_at":"2026-05-19T16:42:17.620090Z"},{"detector":"doi_compliance","finding_type":"recoverable_identifier","severity":"advisory","verdict_class":"incontrovertible","note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.4153/cmb-1967-006-3.citedin) was visible in the surrounding text but could not be confirmed against doi.org as printed.","detected_doi":"10.4153/cmb-1967-006-3.citedin","detected_arxiv_id":null,"ref_index":8,"audited_at":"2026-05-19T16:42:17.620090Z"},{"detector":"doi_compliance","finding_type":"recoverable_identifier","severity":"advisory","verdict_class":"incontrovertible","note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/s10801-021-01089-9.citedin) was visible in the surrounding text but could not be confirmed against doi.org as printed.","detected_doi":"10.1007/s10801-021-01089-9.citedin","detected_arxiv_id":null,"ref_index":14,"audited_at":"2026-05-19T16:42:17.620090Z"},{"detector":"doi_compliance","finding_type":"recoverable_identifier","severity":"advisory","verdict_class":"incontrovertible","note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1112/blms/bds055.citedin) was visible in the surrounding text but could not be confirmed against doi.org as printed.","detected_doi":"10.1112/blms/bds055.citedin","detected_arxiv_id":null,"ref_index":15,"audited_at":"2026-05-19T16:42:17.620090Z"}],"snapshot_sha256":"1a1780fdfa7abb81c95be18de8ec0194a163f9a23bccac491c7c263aad656fb0"},"events":[{"event_id":2116,"event_type":"pith.integrity.v1","payload_sha256":"6eea7b49ee9556a32d60263c7dc616a54e25b689ef6d09b994d978f849162828","signature_b64":"EH9tgXx+FpEBtTlwpvekKUbidM5KfaSAzqU1KC+FMyJb8qpKTlh43tqzW+5HH2n9rWO6WH8GZq7XhZ7B87FsDw==","signing_key_id":"pith-v1-2026-05","created_at":"2026-05-19T16:47:14.181644+00:00","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1112/blms/bds055.citedin) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"E. 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A longer candidate (10.1007/s10801-021-01089-9.citedin) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"R. Shwartz and V. E. Levit,Signed Hultman numbers and signed generalized commuting probability in finite groups, Journal of Algebraic Combinatorics55(2022), no. 4, 1171–1197. DOI: 10.1007/s10801-021-01089-9.Cited in:§1; pp. 2–3. 28","arxiv_id":"2605.02071","detector":"doi_compliance","evidence":{"ref_index":14,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"R. Shwartz and V. E. Levit,Signed Hultman numbers and signed generalized commuting probability in finite groups, Journal of Algebraic Combinatorics55(2022), no. 4, 1171–1197. 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A longer candidate (10.1006/jabr.1995.1331.citedin) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"P. Lescot,Isoclinism classes and commutativity degrees of finite groups, Journal of Algebra 177(1995), no. 3, 847–869. DOI: 10.1006/jabr.1995.1331.Cited in:§1;§2;§2.1; pp. 2, 4–5","arxiv_id":"2605.02071","detector":"doi_compliance","evidence":{"ref_index":10,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"P. Lescot,Isoclinism classes and commutativity degrees of finite groups, Journal of Algebra 177(1995), no. 3, 847–869. 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A longer candidate (10.1080/00927872.2022.2065494.citedin) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"D. Kaur, S. K. Prajapati, and A. Prasad,Simultaneous conjugacy classes as combinatorial invariants of finite groups, Communications in Algebra50(2022), no. 10, 4549–4559. DOI: 10.1080/00927872.2022.2065494.Cited in:§1;§4.1; pp. 4, 21–22","arxiv_id":"2605.02071","detector":"doi_compliance","evidence":{"ref_index":9,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"D. Kaur, S. K. Prajapati, and A. Prasad,Simultaneous conjugacy classes as combinatorial invariants of finite groups, Communications in Algebra50(2022), no. 10, 4549–4559. 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A longer candidate (10.4153/cmb-1967-006-3.citedin) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"A. Joyal, G. Labelle, and Q. I. Rahman,On the location of zeros of polynomials, Canadian Mathematical Bulletin10(1967), no. 1, 53–63. DOI: 10.4153/CMB-1967-006-3.Cited in: §4.1; p. 27","arxiv_id":"2605.02071","detector":"doi_compliance","evidence":{"ref_index":8,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"A. Joyal, G. Labelle, and Q. I. Rahman,On the location of zeros of polynomials, Canadian Mathematical Bulletin10(1967), no. 1, 53–63. DOI: 10.4153/CMB-1967-006-3.Cited in: §4.1; p. 27","reconstructed_doi":"10.4153/cmb-1967-006-3.citedin"},"severity":"advisory","ref_index":8,"audited_at":"2026-05-19T16:42:17.620090Z","event_type":"pith.integrity.v1","detected_doi":"10.4153/cmb-1967-006-3.citedin","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"3f1fe41f01e61ec9858951d06abc88af96050913b31b3d6b0e2a556ef52c90ba","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null}},{"event_id":2111,"event_type":"pith.integrity.v1","payload_sha256":"57a3f9226845ed0be60f9db04196c09b5d5a090e54b6d1924cd8523399e3cda0","signature_b64":"6xDfnPBTWvfkm9UQba0lpRCJiiw4N8HtgxksJvUwmgRUZxtg6gla4xN6knw2f0GAPuIRyWwxYrFfOF12WruXDQ==","signing_key_id":"pith-v1-2026-05","created_at":"2026-05-19T16:47:14.175622+00:00","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1515/crll.1940.182.130.citedin) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"P. Hall,The classification of prime-power groups, Journal f¨ ur die reine und angewandte Mathematik182(1940), 130–141. DOI: 10.1515/crll.1940.182.130.Cited in:§2.1; pp. 4–5","arxiv_id":"2605.02071","detector":"doi_compliance","evidence":{"ref_index":7,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"P. Hall,The classification of prime-power groups, Journal f¨ ur die reine und angewandte Mathematik182(1940), 130–141. DOI: 10.1515/crll.1940.182.130.Cited in:§2.1; pp. 4–5","reconstructed_doi":"10.1515/crll.1940.182.130.citedin"},"severity":"advisory","ref_index":7,"audited_at":"2026-05-19T16:42:17.620090Z","event_type":"pith.integrity.v1","detected_doi":"10.1515/crll.1940.182.130.citedin","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"8e5cd1aae4ed816efbe723fc36dce257aac4c146543519b094b591251dee8b9a","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null}},{"event_id":2110,"event_type":"pith.integrity.v1","payload_sha256":"7827dd288faed5d1dd5d83490e05336e3b4365fd4420d4150e91c5ecf4955acd","signature_b64":"exSTJ8lsXC6yoENuiLFzu7ZP5lbidOSDp23YXgYN/+7uO//TYQs48hcV2r/F71kn9lFF6mFTWm26lmfuCHcNCQ==","signing_key_id":"pith-v1-2026-05","created_at":"2026-05-19T16:47:14.174300+00:00","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1016/j.jalgebra.2005.09.044.citedin) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"R. M. Guralnick and G. R. Robinson,On the commuting probability in finite groups, Journal of Algebra300(2006), no. 2, 509–528. DOI: 10.1016/j.jalgebra.2005.09.044.Cited in:§1; p. 2","arxiv_id":"2605.02071","detector":"doi_compliance","evidence":{"ref_index":5,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"R. M. Guralnick and G. R. Robinson,On the commuting probability in finite groups, Journal of Algebra300(2006), no. 2, 509–528. DOI: 10.1016/j.jalgebra.2005.09.044.Cited in:§1; p. 2","reconstructed_doi":"10.1016/j.jalgebra.2005.09.044.citedin"},"severity":"advisory","ref_index":5,"audited_at":"2026-05-19T16:42:17.620090Z","event_type":"pith.integrity.v1","detected_doi":"10.1016/j.jalgebra.2005.09.044.citedin","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"90c95809b90eeb8f00bdf46cdd5d63ad8f5a6b96442cf669cb59e3930bdd431b","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null}},{"event_id":2109,"event_type":"pith.integrity.v1","payload_sha256":"f7b4e9c223c92cb1e7eeb51d6c40536a195f5fbaf60b9ba0b8a10197dbad286f","signature_b64":"xN1lPF2GgYHQ+BJFXMwL8MYmBLS9ilKMrzcCnQkQZgB8Gm2oiuQayfqbqIK+Cmv/FLhDqVt+HJ7ZNMfrP9OrCQ==","signing_key_id":"pith-v1-2026-05","created_at":"2026-05-19T16:47:14.172474+00:00","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.2748/tmj/1178243172.citedin) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"N. K. Govil and Q. I. Rahman,On the Enestr¨ om–Kakeya theorem, Tohoku Mathematical Journal (2)20(1968), no. 2, 126–136. DOI: 10.2748/tmj/1178243172.Cited in:§4.1; p. 27","arxiv_id":"2605.02071","detector":"doi_compliance","evidence":{"ref_index":4,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"N. K. Govil and Q. I. Rahman,On the Enestr¨ om–Kakeya theorem, Tohoku Mathematical Journal (2)20(1968), no. 2, 126–136. DOI: 10.2748/tmj/1178243172.Cited in:§4.1; p. 27","reconstructed_doi":"10.2748/tmj/1178243172.citedin"},"severity":"advisory","ref_index":4,"audited_at":"2026-05-19T16:42:17.620090Z","event_type":"pith.integrity.v1","detected_doi":"10.2748/tmj/1178243172.citedin","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"7830e5d264cb7c631b130291e2c7ed6f586c344b91f233c61b61627029191c95","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null}},{"event_id":2108,"event_type":"pith.integrity.v1","payload_sha256":"8c4d3eb2808bddc768b7b415c678210932d7dcc9fd4107dec3f3c592a14edfe7","signature_b64":"bS1lZBU3qSvDot8QU5bDz0O+23R3J8B4icCMC4DOTjSVslBs/pmL/Aj/CUxA+NkpSvB63wmWZWfwPXeNyXAtDA==","signing_key_id":"pith-v1-2026-05","created_at":"2026-05-19T16:47:14.169530+00:00","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. 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