{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:NEFBUFTA7DGPVRLVGTURLACLVQ","short_pith_number":"pith:NEFBUFTA","schema_version":"1.0","canonical_sha256":"690a1a1660f8ccfac57534e915804bac0b97128033eb79e1bc27774e0dc275d2","source":{"kind":"arxiv","id":"2605.12672","version":1},"attestation_state":"computed","paper":{"title":"Expander Evolution Algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Expander evolution algebras connect Cheeger graph expansion to algebraic connectivity and achieve the sharp Alon-Boppana eigenvalue bound over the complex numbers.","cross_cats":["math.CO"],"primary_cat":"math.RA","authors_text":"Piero Giacomelli","submitted_at":"2026-05-12T19:22:17Z","abstract_excerpt":"We introduce \\emph{expander evolution algebras} (EEAs), a class of nonassociative algebras defined over an arbitrary field $\\K$ in which the underlying undirected loopless graph of the algebra -- in the sense of Kowalski -- is an expander graph in the classical sense of Cheeger. Starting from the formal graph definition of Kowalski and the algebraic framework of Tian, we establish a dictionary between combinatorial expansion and algebraic structure: the Cheeger constant of the associated graph governs connectivity, the subalgebra lattice, the growth of the evolution sequence, and -- over $\\R$ "},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.12672","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-05-12T19:22:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"6f32f715e742e6364280721e1fee019b2b7356b36f7ed792405a048cf5a76b40","abstract_canon_sha256":"926b8f3123154322f465e06df1fc803cdd99f12c2a630651c96ecb57002598fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:50.163893Z","signature_b64":"6RBU2x/rZJJDOyE4NIqXYnUQAiNFJ3vUCB/nWCPBKaYwEgJD/FG3FqD9vEOldZG0EzSwQvuCnPncI2ny524XCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"690a1a1660f8ccfac57534e915804bac0b97128033eb79e1bc27774e0dc275d2","last_reissued_at":"2026-05-18T03:09:50.163094Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:50.163094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Expander Evolution Algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Expander evolution algebras connect Cheeger graph expansion to algebraic connectivity and achieve the sharp Alon-Boppana eigenvalue bound over the complex numbers.","cross_cats":["math.CO"],"primary_cat":"math.RA","authors_text":"Piero Giacomelli","submitted_at":"2026-05-12T19:22:17Z","abstract_excerpt":"We introduce \\emph{expander evolution algebras} (EEAs), a class of nonassociative algebras defined over an arbitrary field $\\K$ in which the underlying undirected loopless graph of the algebra -- in the sense of Kowalski -- is an expander graph in the classical sense of Cheeger. Starting from the formal graph definition of Kowalski and the algebraic framework of Tian, we establish a dictionary between combinatorial expansion and algebraic structure: the Cheeger constant of the associated graph governs connectivity, the subalgebra lattice, the growth of the evolution sequence, and -- over $\\R$ "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Over C we obtain the sharp Alon-Boppana lower bound for the second eigenvalue of the evolution operator, leading to the definition of Ramanujan evolution algebras as optimal expanders.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The underlying undirected loopless graph of the algebra, in the sense of Kowalski, is an expander graph in the classical sense of Cheeger.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Expander evolution algebras are nonassociative algebras whose graphs are expanders, proven connected and simple with Cheeger constant controlling subalgebra structure and spectral gaps over C.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Expander evolution algebras connect Cheeger graph expansion to algebraic connectivity and achieve the sharp Alon-Boppana eigenvalue bound over the complex numbers.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b45f7e7249ed45133013d708bdf36a32561768d3412b93438feca660932e7e71"},"source":{"id":"2605.12672","kind":"arxiv","version":1},"verdict":{"id":"0cb5ffef-8182-48dd-91de-d8b023d6ff79","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T20:06:23.788184Z","strongest_claim":"Over C we obtain the sharp Alon-Boppana lower bound for the second eigenvalue of the evolution operator, leading to the definition of Ramanujan evolution algebras as optimal expanders.","one_line_summary":"Expander evolution algebras are nonassociative algebras whose graphs are expanders, proven connected and simple with Cheeger constant controlling subalgebra structure and spectral gaps over C.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The underlying undirected loopless graph of the algebra, in the sense of Kowalski, is an expander graph in the classical sense of Cheeger.","pith_extraction_headline":"Expander evolution algebras connect Cheeger graph expansion to algebraic connectivity and achieve the sharp Alon-Boppana eigenvalue bound over the complex numbers."},"references":{"count":15,"sample":[{"doi":"","year":1985,"title":"N. Alon and V.D. Milman, λ1, isoperimetric inequalities for graphs, and superconcentrators,J. Combin. Theory Ser. B38(1985), no. 1, 73–88","work_id":"32bde0b8-312e-4774-bed7-bc77471ceab7","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2008,"title":"J. Bourgain and A. Gamburd, Uniform expansion bounds for Cayley graphs of SL2(Fp),Ann. of Math. (2)167(2008), no. 2, 625–642","work_id":"2d1c7752-8589-4d07-9129-e771d939db21","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"On the connection between evolution algebras, random walks and graphs","work_id":"a6de9097-07cd-4f82-b029-707ba62670a5","ref_index":3,"cited_arxiv_id":"1707.05897","is_internal_anchor":true},{"doi":"","year":2013,"title":"Some properties of evolution algebras","work_id":"6fe14bf0-93df-49bf-adec-41509855afec","ref_index":4,"cited_arxiv_id":"1004.1987","is_internal_anchor":true},{"doi":"","year":2014,"title":"On evolution algebras","work_id":"603991fe-ac42-42fd-a607-db20cd0e9f5e","ref_index":5,"cited_arxiv_id":"1004.1050","is_internal_anchor":true}],"resolved_work":15,"snapshot_sha256":"4deb5cdc60b5c3c71b0a91acc00dbc3e187ffe19089e8b85070a3afb278fd750","internal_anchors":5},"formal_canon":{"evidence_count":2,"snapshot_sha256":"208a3255f553b9557975002a2a005f19c3ea2d186cfc2d6f217896dc1849c918"},"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":"2605.12672","created_at":"2026-05-18T03:09:50.163238+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.12672v1","created_at":"2026-05-18T03:09:50.163238+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.12672","created_at":"2026-05-18T03:09:50.163238+00:00"},{"alias_kind":"pith_short_12","alias_value":"NEFBUFTA7DGP","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"NEFBUFTA7DGPVRLV","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"NEFBUFTA","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NEFBUFTA7DGPVRLVGTURLACLVQ","json":"https://pith.science/pith/NEFBUFTA7DGPVRLVGTURLACLVQ.json","graph_json":"https://pith.science/api/pith-number/NEFBUFTA7DGPVRLVGTURLACLVQ/graph.json","events_json":"https://pith.science/api/pith-number/NEFBUFTA7DGPVRLVGTURLACLVQ/events.json","paper":"https://pith.science/paper/NEFBUFTA"},"agent_actions":{"view_html":"https://pith.science/pith/NEFBUFTA7DGPVRLVGTURLACLVQ","download_json":"https://pith.science/pith/NEFBUFTA7DGPVRLVGTURLACLVQ.json","view_paper":"https://pith.science/paper/NEFBUFTA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.12672&json=true","fetch_graph":"https://pith.science/api/pith-number/NEFBUFTA7DGPVRLVGTURLACLVQ/graph.json","fetch_events":"https://pith.science/api/pith-number/NEFBUFTA7DGPVRLVGTURLACLVQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NEFBUFTA7DGPVRLVGTURLACLVQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NEFBUFTA7DGPVRLVGTURLACLVQ/action/storage_attestation","attest_author":"https://pith.science/pith/NEFBUFTA7DGPVRLVGTURLACLVQ/action/author_attestation","sign_citation":"https://pith.science/pith/NEFBUFTA7DGPVRLVGTURLACLVQ/action/citation_signature","submit_replication":"https://pith.science/pith/NEFBUFTA7DGPVRLVGTURLACLVQ/action/replication_record"}},"created_at":"2026-05-18T03:09:50.163238+00:00","updated_at":"2026-05-18T03:09:50.163238+00:00"}