{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UEOYRC2E2RFZQKQZRN6TYDRWDM","short_pith_number":"pith:UEOYRC2E","canonical_record":{"source":{"id":"1402.6788","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-27T04:41:44Z","cross_cats_sorted":[],"title_canon_sha256":"bf8b4acca9bd80ec8a29c01ca932903199c1b26a63e9d0a0a34c03b17911ed06","abstract_canon_sha256":"ed0ba6f4f974e6a8a59f89e4a31b207a9551755029a254c744ae08c433723ea0"},"schema_version":"1.0"},"canonical_sha256":"a11d888b44d44b982a198b7d3c0e361b2a1fd12424bd4d4e859411fd9da4b20b","source":{"kind":"arxiv","id":"1402.6788","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6788","created_at":"2026-05-18T02:57:37Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6788v1","created_at":"2026-05-18T02:57:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6788","created_at":"2026-05-18T02:57:37Z"},{"alias_kind":"pith_short_12","alias_value":"UEOYRC2E2RFZ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UEOYRC2E2RFZQKQZ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UEOYRC2E","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UEOYRC2E2RFZQKQZRN6TYDRWDM","target":"record","payload":{"canonical_record":{"source":{"id":"1402.6788","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-27T04:41:44Z","cross_cats_sorted":[],"title_canon_sha256":"bf8b4acca9bd80ec8a29c01ca932903199c1b26a63e9d0a0a34c03b17911ed06","abstract_canon_sha256":"ed0ba6f4f974e6a8a59f89e4a31b207a9551755029a254c744ae08c433723ea0"},"schema_version":"1.0"},"canonical_sha256":"a11d888b44d44b982a198b7d3c0e361b2a1fd12424bd4d4e859411fd9da4b20b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:37.033253Z","signature_b64":"K4VFmMNe/coIOsCP2jA26r1zvER+V4Ksdp50QoHrqcAb31TecQ1Vft6rHA7dd8C6F5rQzvRk9R0Ivycxgc6MCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a11d888b44d44b982a198b7d3c0e361b2a1fd12424bd4d4e859411fd9da4b20b","last_reissued_at":"2026-05-18T02:57:37.032491Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:37.032491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.6788","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":"2026-05-18T02:57:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/2RODvVHkek+G3re+su7+Fsye8tGoPsrnuG3BGo8uuMmY9QNAvNY7oW/8NZ3/cjdRSAFXhLa2JlQPlm135cxBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:40:53.688629Z"},"content_sha256":"1fce8a359b95b7b89bdafb24ebd740c886a6fd199737700ae23619d72faea500","schema_version":"1.0","event_id":"sha256:1fce8a359b95b7b89bdafb24ebd740c886a6fd199737700ae23619d72faea500"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UEOYRC2E2RFZQKQZRN6TYDRWDM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An L2-quotient algorithm for finitely presented groups on arbitrarily many generators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Sebastian Jambor","submitted_at":"2014-02-27T04:41:44Z","abstract_excerpt":"We generalize the Plesken-Fabia\\'nska $\\mathrm{L}_2$-quotient algorithm for finitely presented groups on two or three generators to allow an arbitrary number of generators. The main difficulty lies in a constructive description of the invariant ring of $\\mathrm{GL}(2, K)$ on $m$ copies of $\\mathrm{SL}(2, K)$ by simultaneous conjugation. By giving this description, we generalize and simplify some of the known results in invariant theory. An implementation of the algorithm is available in the computer algebra system Magma."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6788","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":"2026-05-18T02:57:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hGkZrkM76hR2Zz4F4E2hHUpt/3/JSUrkDyMGjtEfURMiEXV7/FkZVSPfIq9S8pAo/tDREcR4G3EI5VAkcucvDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:40:53.689204Z"},"content_sha256":"f78b6b23bce93d5f8e8ada2a5121650c115dda19e8b7871b40fda21c5b412bcc","schema_version":"1.0","event_id":"sha256:f78b6b23bce93d5f8e8ada2a5121650c115dda19e8b7871b40fda21c5b412bcc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UEOYRC2E2RFZQKQZRN6TYDRWDM/bundle.json","state_url":"https://pith.science/pith/UEOYRC2E2RFZQKQZRN6TYDRWDM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UEOYRC2E2RFZQKQZRN6TYDRWDM/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":"2026-05-27T17:40:53Z","links":{"resolver":"https://pith.science/pith/UEOYRC2E2RFZQKQZRN6TYDRWDM","bundle":"https://pith.science/pith/UEOYRC2E2RFZQKQZRN6TYDRWDM/bundle.json","state":"https://pith.science/pith/UEOYRC2E2RFZQKQZRN6TYDRWDM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UEOYRC2E2RFZQKQZRN6TYDRWDM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UEOYRC2E2RFZQKQZRN6TYDRWDM","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":"ed0ba6f4f974e6a8a59f89e4a31b207a9551755029a254c744ae08c433723ea0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-27T04:41:44Z","title_canon_sha256":"bf8b4acca9bd80ec8a29c01ca932903199c1b26a63e9d0a0a34c03b17911ed06"},"schema_version":"1.0","source":{"id":"1402.6788","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6788","created_at":"2026-05-18T02:57:37Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6788v1","created_at":"2026-05-18T02:57:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6788","created_at":"2026-05-18T02:57:37Z"},{"alias_kind":"pith_short_12","alias_value":"UEOYRC2E2RFZ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UEOYRC2E2RFZQKQZ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UEOYRC2E","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:f78b6b23bce93d5f8e8ada2a5121650c115dda19e8b7871b40fda21c5b412bcc","target":"graph","created_at":"2026-05-18T02:57:37Z","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":"We generalize the Plesken-Fabia\\'nska $\\mathrm{L}_2$-quotient algorithm for finitely presented groups on two or three generators to allow an arbitrary number of generators. The main difficulty lies in a constructive description of the invariant ring of $\\mathrm{GL}(2, K)$ on $m$ copies of $\\mathrm{SL}(2, K)$ by simultaneous conjugation. By giving this description, we generalize and simplify some of the known results in invariant theory. An implementation of the algorithm is available in the computer algebra system Magma.","authors_text":"Sebastian Jambor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-27T04:41:44Z","title":"An L2-quotient algorithm for finitely presented groups on arbitrarily many generators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6788","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":"sha256:1fce8a359b95b7b89bdafb24ebd740c886a6fd199737700ae23619d72faea500","target":"record","created_at":"2026-05-18T02:57:37Z","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":"ed0ba6f4f974e6a8a59f89e4a31b207a9551755029a254c744ae08c433723ea0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-27T04:41:44Z","title_canon_sha256":"bf8b4acca9bd80ec8a29c01ca932903199c1b26a63e9d0a0a34c03b17911ed06"},"schema_version":"1.0","source":{"id":"1402.6788","kind":"arxiv","version":1}},"canonical_sha256":"a11d888b44d44b982a198b7d3c0e361b2a1fd12424bd4d4e859411fd9da4b20b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a11d888b44d44b982a198b7d3c0e361b2a1fd12424bd4d4e859411fd9da4b20b","first_computed_at":"2026-05-18T02:57:37.032491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:37.032491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K4VFmMNe/coIOsCP2jA26r1zvER+V4Ksdp50QoHrqcAb31TecQ1Vft6rHA7dd8C6F5rQzvRk9R0Ivycxgc6MCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:37.033253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.6788","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fce8a359b95b7b89bdafb24ebd740c886a6fd199737700ae23619d72faea500","sha256:f78b6b23bce93d5f8e8ada2a5121650c115dda19e8b7871b40fda21c5b412bcc"],"state_sha256":"bb1f12739a482d2ea8ab799cbbcd05101e39cc40f3d0c10d54331748368b89d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YFQ49tHuCRrCFXcHUUqSbqGXDAEE1/8uSXWgHWdRvxY4oM4UX82CYkFWZzFAfeDKQICxmyHSXW1kUT7TpHStDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T17:40:53.692373Z","bundle_sha256":"a6ef090b7121cb80680ef3ce68f49e33d0e545341851b75af7fb4eb7b3e37d97"}}