{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SQJH62PQ3OK5J7XLAER4MCQC5U","short_pith_number":"pith:SQJH62PQ","canonical_record":{"source":{"id":"1301.7622","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-01-31T14:26:48Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"ae76af3ee24cd980d91314236b146ba3658014e1ca49514489737e8a19cbc0eb","abstract_canon_sha256":"15023787cc7b3b14c3235c253e79281e53e7474c88cc80ed0d53509f2fbe2a74"},"schema_version":"1.0"},"canonical_sha256":"94127f69f0db95d4feeb0123c60a02ed14febbd540e2a48f56d061ca9355b3ca","source":{"kind":"arxiv","id":"1301.7622","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.7622","created_at":"2026-05-18T03:34:49Z"},{"alias_kind":"arxiv_version","alias_value":"1301.7622v1","created_at":"2026-05-18T03:34:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7622","created_at":"2026-05-18T03:34:49Z"},{"alias_kind":"pith_short_12","alias_value":"SQJH62PQ3OK5","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SQJH62PQ3OK5J7XL","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SQJH62PQ","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SQJH62PQ3OK5J7XLAER4MCQC5U","target":"record","payload":{"canonical_record":{"source":{"id":"1301.7622","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-01-31T14:26:48Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"ae76af3ee24cd980d91314236b146ba3658014e1ca49514489737e8a19cbc0eb","abstract_canon_sha256":"15023787cc7b3b14c3235c253e79281e53e7474c88cc80ed0d53509f2fbe2a74"},"schema_version":"1.0"},"canonical_sha256":"94127f69f0db95d4feeb0123c60a02ed14febbd540e2a48f56d061ca9355b3ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:49.099378Z","signature_b64":"4xtNvM5sVyazUP401SGdBvhYNJFTx95YtFPNabs3eIXVUthF2ou0ymGiRBY0inXgqhYjIdRQnSjGcRWk3fC9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94127f69f0db95d4feeb0123c60a02ed14febbd540e2a48f56d061ca9355b3ca","last_reissued_at":"2026-05-18T03:34:49.098719Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:49.098719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.7622","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:34:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7pYHDECi3lqHtnwcqBXY6wkXO8f3sDw4Bsx2qEw8mTQ4P/vf0VKK8VyqbEZFw0sDXH6l3gzTHSOwUqjUN9RJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:21:08.689165Z"},"content_sha256":"3d1595bf75ea99448375b689a1b92bb1ea530186277c460f41e1febe61ee3d68","schema_version":"1.0","event_id":"sha256:3d1595bf75ea99448375b689a1b92bb1ea530186277c460f41e1febe61ee3d68"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SQJH62PQ3OK5J7XLAER4MCQC5U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The p-adic group ring of SL_2(p^f)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Florian Eisele","submitted_at":"2013-01-31T14:26:48Z","abstract_excerpt":"In this article we show that the $\\Z_p[\\zeta_{p^f-1}]$-order $\\Z_p[\\zeta_{p^f-1}]\\SL_2(p^f)$ can be recognized among those orders whose reduction modulo $p$ is isomorphic to $\\F_{p^f}\\SL_2(p^f)$ using only ring-theoretic properties (in other words we show that $\\F_{p^f}\\SL_2(p^f)$ lifts uniquely to a $\\Z_p[\\zeta_{p^f-1}]$-order, provided certain reasonable conditions are imposed on the lift). This proves a conjecture made by Nebe concerning the basic order of $\\Z_p[\\zeta_{p^f-1}]\\SL_2(p^f)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7622","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:34:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aeS8Aa+nJmnBdvlJYBH2gSKAzmOsTV+rTxsp2N0Y71DZASVzUzIL1J+Qeb9QuTYABRiLMPLW6M3NNIj+Ieb/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:21:08.689522Z"},"content_sha256":"c5cf07418ee3d82af9c1e249dbe12299e9d8f7255a0410eecfb7bcd37e3277fc","schema_version":"1.0","event_id":"sha256:c5cf07418ee3d82af9c1e249dbe12299e9d8f7255a0410eecfb7bcd37e3277fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SQJH62PQ3OK5J7XLAER4MCQC5U/bundle.json","state_url":"https://pith.science/pith/SQJH62PQ3OK5J7XLAER4MCQC5U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SQJH62PQ3OK5J7XLAER4MCQC5U/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T19:21:08Z","links":{"resolver":"https://pith.science/pith/SQJH62PQ3OK5J7XLAER4MCQC5U","bundle":"https://pith.science/pith/SQJH62PQ3OK5J7XLAER4MCQC5U/bundle.json","state":"https://pith.science/pith/SQJH62PQ3OK5J7XLAER4MCQC5U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SQJH62PQ3OK5J7XLAER4MCQC5U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SQJH62PQ3OK5J7XLAER4MCQC5U","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"15023787cc7b3b14c3235c253e79281e53e7474c88cc80ed0d53509f2fbe2a74","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-01-31T14:26:48Z","title_canon_sha256":"ae76af3ee24cd980d91314236b146ba3658014e1ca49514489737e8a19cbc0eb"},"schema_version":"1.0","source":{"id":"1301.7622","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.7622","created_at":"2026-05-18T03:34:49Z"},{"alias_kind":"arxiv_version","alias_value":"1301.7622v1","created_at":"2026-05-18T03:34:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7622","created_at":"2026-05-18T03:34:49Z"},{"alias_kind":"pith_short_12","alias_value":"SQJH62PQ3OK5","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SQJH62PQ3OK5J7XL","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SQJH62PQ","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:c5cf07418ee3d82af9c1e249dbe12299e9d8f7255a0410eecfb7bcd37e3277fc","target":"graph","created_at":"2026-05-18T03:34:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this article we show that the $\\Z_p[\\zeta_{p^f-1}]$-order $\\Z_p[\\zeta_{p^f-1}]\\SL_2(p^f)$ can be recognized among those orders whose reduction modulo $p$ is isomorphic to $\\F_{p^f}\\SL_2(p^f)$ using only ring-theoretic properties (in other words we show that $\\F_{p^f}\\SL_2(p^f)$ lifts uniquely to a $\\Z_p[\\zeta_{p^f-1}]$-order, provided certain reasonable conditions are imposed on the lift). This proves a conjecture made by Nebe concerning the basic order of $\\Z_p[\\zeta_{p^f-1}]\\SL_2(p^f)$.","authors_text":"Florian Eisele","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-01-31T14:26:48Z","title":"The p-adic group ring of SL_2(p^f)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7622","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3d1595bf75ea99448375b689a1b92bb1ea530186277c460f41e1febe61ee3d68","target":"record","created_at":"2026-05-18T03:34:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"15023787cc7b3b14c3235c253e79281e53e7474c88cc80ed0d53509f2fbe2a74","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-01-31T14:26:48Z","title_canon_sha256":"ae76af3ee24cd980d91314236b146ba3658014e1ca49514489737e8a19cbc0eb"},"schema_version":"1.0","source":{"id":"1301.7622","kind":"arxiv","version":1}},"canonical_sha256":"94127f69f0db95d4feeb0123c60a02ed14febbd540e2a48f56d061ca9355b3ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94127f69f0db95d4feeb0123c60a02ed14febbd540e2a48f56d061ca9355b3ca","first_computed_at":"2026-05-18T03:34:49.098719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:49.098719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4xtNvM5sVyazUP401SGdBvhYNJFTx95YtFPNabs3eIXVUthF2ou0ymGiRBY0inXgqhYjIdRQnSjGcRWk3fC9DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:49.099378Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.7622","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d1595bf75ea99448375b689a1b92bb1ea530186277c460f41e1febe61ee3d68","sha256:c5cf07418ee3d82af9c1e249dbe12299e9d8f7255a0410eecfb7bcd37e3277fc"],"state_sha256":"d9a4137ef174cb7c023bc768ab9cad5ca713f245d164068f85e33cde95ebba33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ygPe4iecLo2diibJMMkPRNHN8o9xPDJbU1bAqmYmESfP90IQBPXOpC4eBXucEPflDBYJV6P21j29YB5mjiTbAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:21:08.691380Z","bundle_sha256":"22c8996901598064e206e69967f72a379946f081ce327cb72de76436531df223"}}