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Also, for a Jacobson graph $\\mathfrak{J}_R$, we obtain the structure of group $\\mathrm{Aut}(\\mathfrak{J}_R)$ of all automorphisms of $\\mathfrak{J}_R$ and prove that under some conditions two semi-simple rings $R$ and $R'$ are isomorphic if and only if $\\mathrm{Aut}(\\mathfrak{J}_R)\\cong\\mathrm{Aut}(\\mathfrak{J}_{R'})$."},"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":"1401.6579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-01-25T20:45:15Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"2bfb457a7ff06c229afd70f78cd4c119dadb70c259427dd67ac99aba28996160","abstract_canon_sha256":"bbe9cae3d6d5f2dcc9012ee7347a29dcaff19c6cb83e1cb619de6d1c19552357"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:01.293376Z","signature_b64":"37tLzklua4zwyZ9cCZN75SzZ2Mwv1syvnc+ggl5L1DvtH1d0NMyOUAj7IbaFhQy/6+TycbSDsQI0McbsnsxpAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5512af12dc1fe5ad17648e17bd4776cf47f6b3aed93421df9def941425cf265c","last_reissued_at":"2026-05-18T03:01:01.292604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:01.292604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isomorphisms between Jacobson graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AC","authors_text":"Ahmad Erfanian, Ali Azimi, Mohammad Farrokhi Derakhshandeh Ghouchan","submitted_at":"2014-01-25T20:45:15Z","abstract_excerpt":"Let $R$ be a commutative ring with a non-zero identity and $\\mathfrak{J}_R$ be its Jacobson graph. We show that if $R$ and $R'$ are finite commutative rings, then $\\mathfrak{J}_R\\cong\\mathfrak{J}_{R'}$ if and only if $|J(R)|=|J(R')|$ and $R/J(R)\\cong R'/J(R')$. Also, for a Jacobson graph $\\mathfrak{J}_R$, we obtain the structure of group $\\mathrm{Aut}(\\mathfrak{J}_R)$ of all automorphisms of $\\mathfrak{J}_R$ and prove that under some conditions two semi-simple rings $R$ and $R'$ are isomorphic if and only if $\\mathrm{Aut}(\\mathfrak{J}_R)\\cong\\mathrm{Aut}(\\mathfrak{J}_{R'})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6579","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":"1401.6579","created_at":"2026-05-18T03:01:01.292740+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.6579v1","created_at":"2026-05-18T03:01:01.292740+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6579","created_at":"2026-05-18T03:01:01.292740+00:00"},{"alias_kind":"pith_short_12","alias_value":"KUJK6EW4D7S2","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"KUJK6EW4D7S22F3E","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"KUJK6EW4","created_at":"2026-05-18T12:28:35.611951+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/KUJK6EW4D7S22F3ERYL32R3WZ5","json":"https://pith.science/pith/KUJK6EW4D7S22F3ERYL32R3WZ5.json","graph_json":"https://pith.science/api/pith-number/KUJK6EW4D7S22F3ERYL32R3WZ5/graph.json","events_json":"https://pith.science/api/pith-number/KUJK6EW4D7S22F3ERYL32R3WZ5/events.json","paper":"https://pith.science/paper/KUJK6EW4"},"agent_actions":{"view_html":"https://pith.science/pith/KUJK6EW4D7S22F3ERYL32R3WZ5","download_json":"https://pith.science/pith/KUJK6EW4D7S22F3ERYL32R3WZ5.json","view_paper":"https://pith.science/paper/KUJK6EW4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.6579&json=true","fetch_graph":"https://pith.science/api/pith-number/KUJK6EW4D7S22F3ERYL32R3WZ5/graph.json","fetch_events":"https://pith.science/api/pith-number/KUJK6EW4D7S22F3ERYL32R3WZ5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KUJK6EW4D7S22F3ERYL32R3WZ5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KUJK6EW4D7S22F3ERYL32R3WZ5/action/storage_attestation","attest_author":"https://pith.science/pith/KUJK6EW4D7S22F3ERYL32R3WZ5/action/author_attestation","sign_citation":"https://pith.science/pith/KUJK6EW4D7S22F3ERYL32R3WZ5/action/citation_signature","submit_replication":"https://pith.science/pith/KUJK6EW4D7S22F3ERYL32R3WZ5/action/replication_record"}},"created_at":"2026-05-18T03:01:01.292740+00:00","updated_at":"2026-05-18T03:01:01.292740+00:00"}