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Denote by $h_{{\\rm OD}}(G)$ (resp. $h_{{\\rm OC}}(G)$) the number of isomorphism classes of finite groups $H$ satisfying conditions $|H|=|G|$ and ${\\rm D}(H)={\\rm D}(G)$ (resp. ${\\rm OC}(H)={\\rm OC}(G)$). A finite group $G$ is called OD-characterizable (resp. OC-characterizable) if $h_{\\rm OD}(G)=1$ (resp. $h_{\\rm OC}(G)=1$). Let $C=C_p(2)$ be a symplectic group over binary field, for which $2^p-1>7$ is a Mersenne prime. The aim of this article is to prove that"},"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":"1304.7343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-27T07:37:18Z","cross_cats_sorted":[],"title_canon_sha256":"9d00e473d81258d831f76daf555f4c143ab9d63b678c98ede30ea2599323f110","abstract_canon_sha256":"1b34c8323c36646617e6d08ba548454b2e2a263f91078d051eefa0d1d6b14976"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:53.134269Z","signature_b64":"Z7rcPrSXbu9PTjCnj+6CxEDIjk7QaJRWf/uV7/yD9R0pkOA6l24kQyCGwD3eFYgIL+R1HENYwH73Q1TIFY5yBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae79cc380de3cbcc8674e85cd3603c557efca8323a678792320263b5c31a44ce","last_reissued_at":"2026-05-18T02:26:53.133865Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:53.133865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some Quantitative Characterizations of Certain Symplectic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"A. R. Moghaddamfar, M. Akbari","submitted_at":"2013-04-27T07:37:18Z","abstract_excerpt":"Given a finite group $G$, denote by ${\\rm D}(G)$ the degree pattern of $G$ and by ${\\rm OC}(G)$ the set of all order components of $G$. Denote by $h_{{\\rm OD}}(G)$ (resp. $h_{{\\rm OC}}(G)$) the number of isomorphism classes of finite groups $H$ satisfying conditions $|H|=|G|$ and ${\\rm D}(H)={\\rm D}(G)$ (resp. ${\\rm OC}(H)={\\rm OC}(G)$). A finite group $G$ is called OD-characterizable (resp. OC-characterizable) if $h_{\\rm OD}(G)=1$ (resp. $h_{\\rm OC}(G)=1$). Let $C=C_p(2)$ be a symplectic group over binary field, for which $2^p-1>7$ is a Mersenne prime. The aim of this article is to prove that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7343","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":"1304.7343","created_at":"2026-05-18T02:26:53.133929+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.7343v1","created_at":"2026-05-18T02:26:53.133929+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7343","created_at":"2026-05-18T02:26:53.133929+00:00"},{"alias_kind":"pith_short_12","alias_value":"VZ44YOAN4PF4","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"VZ44YOAN4PF4ZBTU","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"VZ44YOAN","created_at":"2026-05-18T12:28:04.890932+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/VZ44YOAN4PF4ZBTU5BONGYB4KV","json":"https://pith.science/pith/VZ44YOAN4PF4ZBTU5BONGYB4KV.json","graph_json":"https://pith.science/api/pith-number/VZ44YOAN4PF4ZBTU5BONGYB4KV/graph.json","events_json":"https://pith.science/api/pith-number/VZ44YOAN4PF4ZBTU5BONGYB4KV/events.json","paper":"https://pith.science/paper/VZ44YOAN"},"agent_actions":{"view_html":"https://pith.science/pith/VZ44YOAN4PF4ZBTU5BONGYB4KV","download_json":"https://pith.science/pith/VZ44YOAN4PF4ZBTU5BONGYB4KV.json","view_paper":"https://pith.science/paper/VZ44YOAN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.7343&json=true","fetch_graph":"https://pith.science/api/pith-number/VZ44YOAN4PF4ZBTU5BONGYB4KV/graph.json","fetch_events":"https://pith.science/api/pith-number/VZ44YOAN4PF4ZBTU5BONGYB4KV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VZ44YOAN4PF4ZBTU5BONGYB4KV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VZ44YOAN4PF4ZBTU5BONGYB4KV/action/storage_attestation","attest_author":"https://pith.science/pith/VZ44YOAN4PF4ZBTU5BONGYB4KV/action/author_attestation","sign_citation":"https://pith.science/pith/VZ44YOAN4PF4ZBTU5BONGYB4KV/action/citation_signature","submit_replication":"https://pith.science/pith/VZ44YOAN4PF4ZBTU5BONGYB4KV/action/replication_record"}},"created_at":"2026-05-18T02:26:53.133929+00:00","updated_at":"2026-05-18T02:26:53.133929+00:00"}