{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:GPQEWABDZLARRDLVIP62KMFMMA","short_pith_number":"pith:GPQEWABD","schema_version":"1.0","canonical_sha256":"33e04b0023cac1188d7543fda530ac60082e58b487a7c7c9e1412ee12aa5fcfc","source":{"kind":"arxiv","id":"1103.4672","version":1},"attestation_state":"computed","paper":{"title":"On the arithmetic of the BC-system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.QA","authors_text":"Alain Connes, Caterina Consani","submitted_at":"2011-03-24T02:51:44Z","abstract_excerpt":"For each prime p and each embedding of the multiplicative group of an algebraic closure of F_p as complex roots of unity, we construct a p-adic indecomposable representation of the integral BC-system as additive endomorphisms of the big Witt ring of an algebraic closure of F_p. The obtained representations are the p-adic analogues of the complex, extremal KMS states at zero temperature of the BC-system. The role of the Riemann zeta function, as partition function of the BC-system over complex numbers is replaced, in the p-adic case, by the p-adic L-functions and the polylogarithms whose values"},"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":"1103.4672","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-03-24T02:51:44Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"a8a0df8bc8c566d83dfef4bbc2d093b1aeadc6de50ea32881d54eaf2bdb1c5bd","abstract_canon_sha256":"eb7bedf193ebaa7aa72e722e91f7c8826149c83cbf9d910bbfa7c07937f77eb6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:01.114504Z","signature_b64":"YO3yD+nsOZV5eq1Vk+qgdz7bBo0jL0SzvMLbm68txEaLyubve1ICm1NegjTWdb/Ysv5k6hrifLi0y8nr3ExPBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33e04b0023cac1188d7543fda530ac60082e58b487a7c7c9e1412ee12aa5fcfc","last_reissued_at":"2026-05-18T04:26:01.114076Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:01.114076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the arithmetic of the BC-system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.QA","authors_text":"Alain Connes, Caterina Consani","submitted_at":"2011-03-24T02:51:44Z","abstract_excerpt":"For each prime p and each embedding of the multiplicative group of an algebraic closure of F_p as complex roots of unity, we construct a p-adic indecomposable representation of the integral BC-system as additive endomorphisms of the big Witt ring of an algebraic closure of F_p. The obtained representations are the p-adic analogues of the complex, extremal KMS states at zero temperature of the BC-system. The role of the Riemann zeta function, as partition function of the BC-system over complex numbers is replaced, in the p-adic case, by the p-adic L-functions and the polylogarithms whose values"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4672","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":"1103.4672","created_at":"2026-05-18T04:26:01.114142+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.4672v1","created_at":"2026-05-18T04:26:01.114142+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4672","created_at":"2026-05-18T04:26:01.114142+00:00"},{"alias_kind":"pith_short_12","alias_value":"GPQEWABDZLAR","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"GPQEWABDZLARRDLV","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"GPQEWABD","created_at":"2026-05-18T12:26:30.835961+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/GPQEWABDZLARRDLVIP62KMFMMA","json":"https://pith.science/pith/GPQEWABDZLARRDLVIP62KMFMMA.json","graph_json":"https://pith.science/api/pith-number/GPQEWABDZLARRDLVIP62KMFMMA/graph.json","events_json":"https://pith.science/api/pith-number/GPQEWABDZLARRDLVIP62KMFMMA/events.json","paper":"https://pith.science/paper/GPQEWABD"},"agent_actions":{"view_html":"https://pith.science/pith/GPQEWABDZLARRDLVIP62KMFMMA","download_json":"https://pith.science/pith/GPQEWABDZLARRDLVIP62KMFMMA.json","view_paper":"https://pith.science/paper/GPQEWABD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.4672&json=true","fetch_graph":"https://pith.science/api/pith-number/GPQEWABDZLARRDLVIP62KMFMMA/graph.json","fetch_events":"https://pith.science/api/pith-number/GPQEWABDZLARRDLVIP62KMFMMA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GPQEWABDZLARRDLVIP62KMFMMA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GPQEWABDZLARRDLVIP62KMFMMA/action/storage_attestation","attest_author":"https://pith.science/pith/GPQEWABDZLARRDLVIP62KMFMMA/action/author_attestation","sign_citation":"https://pith.science/pith/GPQEWABDZLARRDLVIP62KMFMMA/action/citation_signature","submit_replication":"https://pith.science/pith/GPQEWABDZLARRDLVIP62KMFMMA/action/replication_record"}},"created_at":"2026-05-18T04:26:01.114142+00:00","updated_at":"2026-05-18T04:26:01.114142+00:00"}