{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FWOBE35W652KRGEH75YH6UEUEP","short_pith_number":"pith:FWOBE35W","canonical_record":{"source":{"id":"1406.0069","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-31T11:18:55Z","cross_cats_sorted":[],"title_canon_sha256":"e316c6897726784f2ce4f50b832102901c5e02a17797d7fb3bf321a7baadc8c4","abstract_canon_sha256":"16a6bad7209405fd5beb2a9451dd9a067c258f8a39ceb3b08b1573e3a7ee3e9a"},"schema_version":"1.0"},"canonical_sha256":"2d9c126fb6f774a89887ff707f509423efe47000a170874d1244f2e703a53aaf","source":{"kind":"arxiv","id":"1406.0069","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.0069","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"arxiv_version","alias_value":"1406.0069v1","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0069","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"pith_short_12","alias_value":"FWOBE35W652K","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FWOBE35W652KRGEH","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FWOBE35W","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FWOBE35W652KRGEH75YH6UEUEP","target":"record","payload":{"canonical_record":{"source":{"id":"1406.0069","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-31T11:18:55Z","cross_cats_sorted":[],"title_canon_sha256":"e316c6897726784f2ce4f50b832102901c5e02a17797d7fb3bf321a7baadc8c4","abstract_canon_sha256":"16a6bad7209405fd5beb2a9451dd9a067c258f8a39ceb3b08b1573e3a7ee3e9a"},"schema_version":"1.0"},"canonical_sha256":"2d9c126fb6f774a89887ff707f509423efe47000a170874d1244f2e703a53aaf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:41.872289Z","signature_b64":"zF7BtCL7Q0knfCCKpFLpWwh59tLaSArt/WViLaFjlUDMm5ApzjpXa/jmV7+j+hGQNJ6415olw3iXTzaSP5ClBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d9c126fb6f774a89887ff707f509423efe47000a170874d1244f2e703a53aaf","last_reissued_at":"2026-05-18T02:50:41.871670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:41.871670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.0069","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":"2026-05-18T02:50:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fm8T4aurdYDZcY75wf+WGyQkKnuiWt2hbq18yB3Fh7xtNheAPlZxFwhIoMvNASdKvLMMlcOwZD0WU++/UQyhBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T11:11:52.360246Z"},"content_sha256":"413153192b6a9130dbf8d10f0cfe670037119dbb670c764381bd6471da19e8e1","schema_version":"1.0","event_id":"sha256:413153192b6a9130dbf8d10f0cfe670037119dbb670c764381bd6471da19e8e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FWOBE35W652KRGEH75YH6UEUEP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$p$-Central Subspaces of Central Simple Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Adam Chapman","submitted_at":"2014-05-31T11:18:55Z","abstract_excerpt":"We study central simple algebras in various ways, focusing on the role of $p$-central subspaces. The first part of my thesis is dedicated to the study of Clifford algebras. The standard Clifford algebra of a given form is the generic associative algebra containing a $p$-central subspace whose exponentiation form is equal to the given form. There is an old question as for whether these algebras have representations of finite rank over the center, and jointly with Daniel Krashen and Max Lieblich we managed to provide a positive answer. Different generalizations of the structure of the Clifford a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0069","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":"2026-05-18T02:50:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S7FE22vgutndL0DBTXZCClIvqtRC3XfcggcXfAyuNBVvX01IVFs2ry9k+JTZuA7zSe0A6CQgJO3LnrIn9InxBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T11:11:52.360612Z"},"content_sha256":"77bb69df1fc443e039fd26026e87516dde45eb4cbdb093911038170038f860bb","schema_version":"1.0","event_id":"sha256:77bb69df1fc443e039fd26026e87516dde45eb4cbdb093911038170038f860bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FWOBE35W652KRGEH75YH6UEUEP/bundle.json","state_url":"https://pith.science/pith/FWOBE35W652KRGEH75YH6UEUEP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FWOBE35W652KRGEH75YH6UEUEP/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":"2026-06-04T11:11:52Z","links":{"resolver":"https://pith.science/pith/FWOBE35W652KRGEH75YH6UEUEP","bundle":"https://pith.science/pith/FWOBE35W652KRGEH75YH6UEUEP/bundle.json","state":"https://pith.science/pith/FWOBE35W652KRGEH75YH6UEUEP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FWOBE35W652KRGEH75YH6UEUEP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FWOBE35W652KRGEH75YH6UEUEP","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":"16a6bad7209405fd5beb2a9451dd9a067c258f8a39ceb3b08b1573e3a7ee3e9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-31T11:18:55Z","title_canon_sha256":"e316c6897726784f2ce4f50b832102901c5e02a17797d7fb3bf321a7baadc8c4"},"schema_version":"1.0","source":{"id":"1406.0069","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.0069","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"arxiv_version","alias_value":"1406.0069v1","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0069","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"pith_short_12","alias_value":"FWOBE35W652K","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FWOBE35W652KRGEH","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FWOBE35W","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:77bb69df1fc443e039fd26026e87516dde45eb4cbdb093911038170038f860bb","target":"graph","created_at":"2026-05-18T02:50:41Z","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 study central simple algebras in various ways, focusing on the role of $p$-central subspaces. The first part of my thesis is dedicated to the study of Clifford algebras. The standard Clifford algebra of a given form is the generic associative algebra containing a $p$-central subspace whose exponentiation form is equal to the given form. There is an old question as for whether these algebras have representations of finite rank over the center, and jointly with Daniel Krashen and Max Lieblich we managed to provide a positive answer. Different generalizations of the structure of the Clifford a","authors_text":"Adam Chapman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-31T11:18:55Z","title":"$p$-Central Subspaces of Central Simple Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0069","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":"sha256:413153192b6a9130dbf8d10f0cfe670037119dbb670c764381bd6471da19e8e1","target":"record","created_at":"2026-05-18T02:50:41Z","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":"16a6bad7209405fd5beb2a9451dd9a067c258f8a39ceb3b08b1573e3a7ee3e9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-05-31T11:18:55Z","title_canon_sha256":"e316c6897726784f2ce4f50b832102901c5e02a17797d7fb3bf321a7baadc8c4"},"schema_version":"1.0","source":{"id":"1406.0069","kind":"arxiv","version":1}},"canonical_sha256":"2d9c126fb6f774a89887ff707f509423efe47000a170874d1244f2e703a53aaf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d9c126fb6f774a89887ff707f509423efe47000a170874d1244f2e703a53aaf","first_computed_at":"2026-05-18T02:50:41.871670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:41.871670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zF7BtCL7Q0knfCCKpFLpWwh59tLaSArt/WViLaFjlUDMm5ApzjpXa/jmV7+j+hGQNJ6415olw3iXTzaSP5ClBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:41.872289Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.0069","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:413153192b6a9130dbf8d10f0cfe670037119dbb670c764381bd6471da19e8e1","sha256:77bb69df1fc443e039fd26026e87516dde45eb4cbdb093911038170038f860bb"],"state_sha256":"f598717b9353e56ca98ba98d4db832ccd715d40c0c4fb69e8aecb50485d4379f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OlSFbQmIKi6SthxkQ1V3RNeifBqnZbiMiNCkxEo2mCoyI8vbTQUL1mBWMcCMn2mZ+Fz61ctifL4PZ9xhYI6JAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T11:11:52.362684Z","bundle_sha256":"d5f3a6dd65d02312b918b1226108e276a9fbbf942f99bb6305761b4052d3afe6"}}