{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BAXPDEB4DDC7ZEFLUV4HE6WNZW","short_pith_number":"pith:BAXPDEB4","canonical_record":{"source":{"id":"1502.05896","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-02-20T15:14:32Z","cross_cats_sorted":[],"title_canon_sha256":"b01a193f05b99e66fed8de6c04d584723d9487574b72cbef40ae89c8298debc9","abstract_canon_sha256":"12497600111bb2bf9debd1dffb540b0047263c0bb047f18b109afb2c1df06710"},"schema_version":"1.0"},"canonical_sha256":"082ef1903c18c5fc90aba578727acdcdaa82196f799e5d56b19328320d9008ff","source":{"kind":"arxiv","id":"1502.05896","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05896","created_at":"2026-05-18T02:20:28Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05896v2","created_at":"2026-05-18T02:20:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05896","created_at":"2026-05-18T02:20:28Z"},{"alias_kind":"pith_short_12","alias_value":"BAXPDEB4DDC7","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BAXPDEB4DDC7ZEFL","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BAXPDEB4","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BAXPDEB4DDC7ZEFLUV4HE6WNZW","target":"record","payload":{"canonical_record":{"source":{"id":"1502.05896","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-02-20T15:14:32Z","cross_cats_sorted":[],"title_canon_sha256":"b01a193f05b99e66fed8de6c04d584723d9487574b72cbef40ae89c8298debc9","abstract_canon_sha256":"12497600111bb2bf9debd1dffb540b0047263c0bb047f18b109afb2c1df06710"},"schema_version":"1.0"},"canonical_sha256":"082ef1903c18c5fc90aba578727acdcdaa82196f799e5d56b19328320d9008ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:28.263942Z","signature_b64":"2jGH+EqRDNFt5CB6mSwTkUIStVPWUXGufj+MHW2NIGvZwdy7g2ARN+EjTqJD8tRDY/mRoLNMZ/O7plLzsQiRDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"082ef1903c18c5fc90aba578727acdcdaa82196f799e5d56b19328320d9008ff","last_reissued_at":"2026-05-18T02:20:28.263466Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:28.263466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.05896","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:20:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HTZTgN9gCZFXAp77ODD1jnzWWqT+tz31S/KG2NGnAjHOzU57II08/iBxkuTkm+7AePYtVs5wMpy/S0/mZgiUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:52:17.626887Z"},"content_sha256":"bb74b5bc3e26f302119df22d5216a005fd1aabf5d108c64e0faee7ada4cf4f1d","schema_version":"1.0","event_id":"sha256:bb74b5bc3e26f302119df22d5216a005fd1aabf5d108c64e0faee7ada4cf4f1d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BAXPDEB4DDC7ZEFLUV4HE6WNZW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Endotrivial modules for the sporadic simple groups and their covers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Caroline Lassueur, Nadia Mazza","submitted_at":"2015-02-20T15:14:32Z","abstract_excerpt":"In a step towards the classification of endotrivial modules for quasi-simple groups, we investigate endotrivial modules for the sporadic simple groups and their covers. A main outcome of our study is the existence of torsion endotrivial modules with dimension greater than one for several sporadic groups with $p$-rank greater than one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05896","kind":"arxiv","version":2},"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":"2026-05-18T02:20:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jLejOFstDoHbiA7x3+DTGui0QgL3C8R8+TDQCJVX+uYONA3hsOBly/0D/OPWbB8DN9ob1EdD7oTxbs0DOhzUBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:52:17.627341Z"},"content_sha256":"bb85c0f0787196a85cdcd06e8aff069812928c59ae2731d2109b35dd549c1d5f","schema_version":"1.0","event_id":"sha256:bb85c0f0787196a85cdcd06e8aff069812928c59ae2731d2109b35dd549c1d5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BAXPDEB4DDC7ZEFLUV4HE6WNZW/bundle.json","state_url":"https://pith.science/pith/BAXPDEB4DDC7ZEFLUV4HE6WNZW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BAXPDEB4DDC7ZEFLUV4HE6WNZW/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":"2026-05-30T11:52:17Z","links":{"resolver":"https://pith.science/pith/BAXPDEB4DDC7ZEFLUV4HE6WNZW","bundle":"https://pith.science/pith/BAXPDEB4DDC7ZEFLUV4HE6WNZW/bundle.json","state":"https://pith.science/pith/BAXPDEB4DDC7ZEFLUV4HE6WNZW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BAXPDEB4DDC7ZEFLUV4HE6WNZW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BAXPDEB4DDC7ZEFLUV4HE6WNZW","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":"12497600111bb2bf9debd1dffb540b0047263c0bb047f18b109afb2c1df06710","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-02-20T15:14:32Z","title_canon_sha256":"b01a193f05b99e66fed8de6c04d584723d9487574b72cbef40ae89c8298debc9"},"schema_version":"1.0","source":{"id":"1502.05896","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05896","created_at":"2026-05-18T02:20:28Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05896v2","created_at":"2026-05-18T02:20:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05896","created_at":"2026-05-18T02:20:28Z"},{"alias_kind":"pith_short_12","alias_value":"BAXPDEB4DDC7","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BAXPDEB4DDC7ZEFL","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BAXPDEB4","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:bb85c0f0787196a85cdcd06e8aff069812928c59ae2731d2109b35dd549c1d5f","target":"graph","created_at":"2026-05-18T02:20:28Z","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 a step towards the classification of endotrivial modules for quasi-simple groups, we investigate endotrivial modules for the sporadic simple groups and their covers. A main outcome of our study is the existence of torsion endotrivial modules with dimension greater than one for several sporadic groups with $p$-rank greater than one.","authors_text":"Caroline Lassueur, Nadia Mazza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-02-20T15:14:32Z","title":"Endotrivial modules for the sporadic simple groups and their covers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05896","kind":"arxiv","version":2},"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:bb74b5bc3e26f302119df22d5216a005fd1aabf5d108c64e0faee7ada4cf4f1d","target":"record","created_at":"2026-05-18T02:20:28Z","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":"12497600111bb2bf9debd1dffb540b0047263c0bb047f18b109afb2c1df06710","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-02-20T15:14:32Z","title_canon_sha256":"b01a193f05b99e66fed8de6c04d584723d9487574b72cbef40ae89c8298debc9"},"schema_version":"1.0","source":{"id":"1502.05896","kind":"arxiv","version":2}},"canonical_sha256":"082ef1903c18c5fc90aba578727acdcdaa82196f799e5d56b19328320d9008ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"082ef1903c18c5fc90aba578727acdcdaa82196f799e5d56b19328320d9008ff","first_computed_at":"2026-05-18T02:20:28.263466Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:28.263466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2jGH+EqRDNFt5CB6mSwTkUIStVPWUXGufj+MHW2NIGvZwdy7g2ARN+EjTqJD8tRDY/mRoLNMZ/O7plLzsQiRDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:28.263942Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.05896","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb74b5bc3e26f302119df22d5216a005fd1aabf5d108c64e0faee7ada4cf4f1d","sha256:bb85c0f0787196a85cdcd06e8aff069812928c59ae2731d2109b35dd549c1d5f"],"state_sha256":"e940d758dc4179dbe3aef7375aaea30b8f3fd1d006080e790338754e51b039f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iWt7ciMmlegA+rrTQMeOUjhiKSZl9VtqM2nAZ9tDe3OuXQexwSpWkMMCnF1/GC5Md/8MwNL0iI5+qP27YBMdDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T11:52:17.631016Z","bundle_sha256":"ac763b0d56fea8feed0d7f2be70ad52c3d7537f6fc6837d56370ecad96ad5ddc"}}