{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:IZOEEDNZNQXZIECNPDLDZMBNMV","short_pith_number":"pith:IZOEEDNZ","schema_version":"1.0","canonical_sha256":"465c420db96c2f94104d78d63cb02d6578637ecc8c29dfd0014ec4e8644af4ee","source":{"kind":"arxiv","id":"1210.2431","version":1},"attestation_state":"computed","paper":{"title":"Modular lattices from finite projective planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Tathagata Basak","submitted_at":"2012-10-08T22:04:25Z","abstract_excerpt":"Using the geometry of the projective plane over the finite field F_q, we construct a Hermitian Lorentzian lattice L_q of dimension (q^2 + q + 2) defined over a certain number ring $\\cO$ that depends on q. We show that infinitely many of these lattices are p-modular, that is, p L'_q = L_q, where p is some prime in $\\cO$ such that |p|^2 = q. The reflection group of the Lorentzian lattice obtained for q = 3 seems to be closely related to the monster simple group via the presentation of the bimonster as a quotient of the Coxeter group on the incidence graph of P^2(F_3). The Lorentzian lattices L_q"},"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":"1210.2431","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-08T22:04:25Z","cross_cats_sorted":[],"title_canon_sha256":"a8979c41876154d7497d57711b0243edc54b36a9ddeb4b5e52bedbb03cdc888e","abstract_canon_sha256":"22f401233a7c662747642afab69d2734c9aa11c28d45415412e8234ca6dd448f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:41.562581Z","signature_b64":"wJO6hJNII5czs0SzdRrlpNLw3Ij/nWET86GeWOo0otcAOu497BWgVar00RdXvhNtXk0zHZvG8vLYzah4QcRAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"465c420db96c2f94104d78d63cb02d6578637ecc8c29dfd0014ec4e8644af4ee","last_reissued_at":"2026-05-18T03:43:41.562080Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:41.562080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modular lattices from finite projective planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Tathagata Basak","submitted_at":"2012-10-08T22:04:25Z","abstract_excerpt":"Using the geometry of the projective plane over the finite field F_q, we construct a Hermitian Lorentzian lattice L_q of dimension (q^2 + q + 2) defined over a certain number ring $\\cO$ that depends on q. We show that infinitely many of these lattices are p-modular, that is, p L'_q = L_q, where p is some prime in $\\cO$ such that |p|^2 = q. The reflection group of the Lorentzian lattice obtained for q = 3 seems to be closely related to the monster simple group via the presentation of the bimonster as a quotient of the Coxeter group on the incidence graph of P^2(F_3). The Lorentzian lattices L_q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2431","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":"1210.2431","created_at":"2026-05-18T03:43:41.562169+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.2431v1","created_at":"2026-05-18T03:43:41.562169+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2431","created_at":"2026-05-18T03:43:41.562169+00:00"},{"alias_kind":"pith_short_12","alias_value":"IZOEEDNZNQXZ","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"IZOEEDNZNQXZIECN","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"IZOEEDNZ","created_at":"2026-05-18T12:27:09.501522+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/IZOEEDNZNQXZIECNPDLDZMBNMV","json":"https://pith.science/pith/IZOEEDNZNQXZIECNPDLDZMBNMV.json","graph_json":"https://pith.science/api/pith-number/IZOEEDNZNQXZIECNPDLDZMBNMV/graph.json","events_json":"https://pith.science/api/pith-number/IZOEEDNZNQXZIECNPDLDZMBNMV/events.json","paper":"https://pith.science/paper/IZOEEDNZ"},"agent_actions":{"view_html":"https://pith.science/pith/IZOEEDNZNQXZIECNPDLDZMBNMV","download_json":"https://pith.science/pith/IZOEEDNZNQXZIECNPDLDZMBNMV.json","view_paper":"https://pith.science/paper/IZOEEDNZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.2431&json=true","fetch_graph":"https://pith.science/api/pith-number/IZOEEDNZNQXZIECNPDLDZMBNMV/graph.json","fetch_events":"https://pith.science/api/pith-number/IZOEEDNZNQXZIECNPDLDZMBNMV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IZOEEDNZNQXZIECNPDLDZMBNMV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IZOEEDNZNQXZIECNPDLDZMBNMV/action/storage_attestation","attest_author":"https://pith.science/pith/IZOEEDNZNQXZIECNPDLDZMBNMV/action/author_attestation","sign_citation":"https://pith.science/pith/IZOEEDNZNQXZIECNPDLDZMBNMV/action/citation_signature","submit_replication":"https://pith.science/pith/IZOEEDNZNQXZIECNPDLDZMBNMV/action/replication_record"}},"created_at":"2026-05-18T03:43:41.562169+00:00","updated_at":"2026-05-18T03:43:41.562169+00:00"}