{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:U7SKZF2XMOWHRPY7TWZQNSUVC6","short_pith_number":"pith:U7SKZF2X","canonical_record":{"source":{"id":"1312.4167","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-12-15T17:00:06Z","cross_cats_sorted":[],"title_canon_sha256":"e6e5226cfb362a78d018d6d1fc39363947252c6ba7dea278e67bbf12ce6eff98","abstract_canon_sha256":"680f6655d4e7a943b49576947ec1194cc8a31acfe3aa54bef7d396070c135c4f"},"schema_version":"1.0"},"canonical_sha256":"a7e4ac975763ac78bf1f9db306ca9517a7dade89e8251e2f6e47107ca628f8ee","source":{"kind":"arxiv","id":"1312.4167","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4167","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4167v2","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4167","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"pith_short_12","alias_value":"U7SKZF2XMOWH","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U7SKZF2XMOWHRPY7","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U7SKZF2X","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:U7SKZF2XMOWHRPY7TWZQNSUVC6","target":"record","payload":{"canonical_record":{"source":{"id":"1312.4167","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-12-15T17:00:06Z","cross_cats_sorted":[],"title_canon_sha256":"e6e5226cfb362a78d018d6d1fc39363947252c6ba7dea278e67bbf12ce6eff98","abstract_canon_sha256":"680f6655d4e7a943b49576947ec1194cc8a31acfe3aa54bef7d396070c135c4f"},"schema_version":"1.0"},"canonical_sha256":"a7e4ac975763ac78bf1f9db306ca9517a7dade89e8251e2f6e47107ca628f8ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:31.021995Z","signature_b64":"pw1U3FEpB4IGSzi5Y+ZpY804INpEQC0b37rArpESAMyw8IMt53no/9kVIOi0NgeYbH2MqLfhm+VUZVDx/F0SCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7e4ac975763ac78bf1f9db306ca9517a7dade89e8251e2f6e47107ca628f8ee","last_reissued_at":"2026-05-18T01:34:31.021554Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:31.021554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.4167","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":"2026-05-18T01:34:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KbR11obAdDGaZ5V4/1BFg0/ciWukzENamTLSR8sGF37IRntyTBldUxCj9B1yJqRnFdk1WOSbg7Ji+Hu4M6S0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T07:24:33.004350Z"},"content_sha256":"4e8e4938db7a5b9dedb2b520cc2f86c73448867443e66bf9341fcee6177ad371","schema_version":"1.0","event_id":"sha256:4e8e4938db7a5b9dedb2b520cc2f86c73448867443e66bf9341fcee6177ad371"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:U7SKZF2XMOWHRPY7TWZQNSUVC6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Codimension Sequence of G-Simple Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Yaakov Karasik, Yuval Shpigelman","submitted_at":"2013-12-15T17:00:06Z","abstract_excerpt":"In the 80's, Regev, using results of Formanek, Procesi and Razmyslov in invariant theory and Hilbert series', determined asymptotically the codimension sequence of mXm matrices over an algebraically closed field of characteristic zero. Inspired by Regev's ideas, we found that the asymptotics of $c_{n}^{G}(A)$, the G graded codimension sequence of a finite dimensional G simple algebra A, is equal to $\\alpha n^{\\frac{1-\\dim(A_{e})}{2}}(\\dim(A)^{n}\n  $ (this was conjectured by E.Aljadeff, D.Haile and M. Natapov), where \\alpha is not yet determined number. Moreover, in the case where A is the alge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4167","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":"2026-05-18T01:34:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LWIuI88IT7t+CqKavayDzbOKjgluiwKxz+D0eRykz3ifBZUuTUxQ/VcKc+KTG+BOUCABs+q9DiHqJmAMg9lCBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T07:24:33.005075Z"},"content_sha256":"76d38c5df7c6c09670488b894bb24a765d65d9d7e26ebe158c3c1457d1b04963","schema_version":"1.0","event_id":"sha256:76d38c5df7c6c09670488b894bb24a765d65d9d7e26ebe158c3c1457d1b04963"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U7SKZF2XMOWHRPY7TWZQNSUVC6/bundle.json","state_url":"https://pith.science/pith/U7SKZF2XMOWHRPY7TWZQNSUVC6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U7SKZF2XMOWHRPY7TWZQNSUVC6/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":"2026-06-04T07:24:33Z","links":{"resolver":"https://pith.science/pith/U7SKZF2XMOWHRPY7TWZQNSUVC6","bundle":"https://pith.science/pith/U7SKZF2XMOWHRPY7TWZQNSUVC6/bundle.json","state":"https://pith.science/pith/U7SKZF2XMOWHRPY7TWZQNSUVC6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U7SKZF2XMOWHRPY7TWZQNSUVC6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:U7SKZF2XMOWHRPY7TWZQNSUVC6","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":"680f6655d4e7a943b49576947ec1194cc8a31acfe3aa54bef7d396070c135c4f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-12-15T17:00:06Z","title_canon_sha256":"e6e5226cfb362a78d018d6d1fc39363947252c6ba7dea278e67bbf12ce6eff98"},"schema_version":"1.0","source":{"id":"1312.4167","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4167","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4167v2","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4167","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"pith_short_12","alias_value":"U7SKZF2XMOWH","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U7SKZF2XMOWHRPY7","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U7SKZF2X","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:76d38c5df7c6c09670488b894bb24a765d65d9d7e26ebe158c3c1457d1b04963","target":"graph","created_at":"2026-05-18T01:34:31Z","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 the 80's, Regev, using results of Formanek, Procesi and Razmyslov in invariant theory and Hilbert series', determined asymptotically the codimension sequence of mXm matrices over an algebraically closed field of characteristic zero. Inspired by Regev's ideas, we found that the asymptotics of $c_{n}^{G}(A)$, the G graded codimension sequence of a finite dimensional G simple algebra A, is equal to $\\alpha n^{\\frac{1-\\dim(A_{e})}{2}}(\\dim(A)^{n}\n  $ (this was conjectured by E.Aljadeff, D.Haile and M. Natapov), where \\alpha is not yet determined number. Moreover, in the case where A is the alge","authors_text":"Yaakov Karasik, Yuval Shpigelman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-12-15T17:00:06Z","title":"On the Codimension Sequence of G-Simple Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4167","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":"sha256:4e8e4938db7a5b9dedb2b520cc2f86c73448867443e66bf9341fcee6177ad371","target":"record","created_at":"2026-05-18T01:34:31Z","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":"680f6655d4e7a943b49576947ec1194cc8a31acfe3aa54bef7d396070c135c4f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-12-15T17:00:06Z","title_canon_sha256":"e6e5226cfb362a78d018d6d1fc39363947252c6ba7dea278e67bbf12ce6eff98"},"schema_version":"1.0","source":{"id":"1312.4167","kind":"arxiv","version":2}},"canonical_sha256":"a7e4ac975763ac78bf1f9db306ca9517a7dade89e8251e2f6e47107ca628f8ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7e4ac975763ac78bf1f9db306ca9517a7dade89e8251e2f6e47107ca628f8ee","first_computed_at":"2026-05-18T01:34:31.021554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:31.021554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pw1U3FEpB4IGSzi5Y+ZpY804INpEQC0b37rArpESAMyw8IMt53no/9kVIOi0NgeYbH2MqLfhm+VUZVDx/F0SCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:31.021995Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.4167","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e8e4938db7a5b9dedb2b520cc2f86c73448867443e66bf9341fcee6177ad371","sha256:76d38c5df7c6c09670488b894bb24a765d65d9d7e26ebe158c3c1457d1b04963"],"state_sha256":"120b18d89285965727aec0d2dce19006687d7b2308e271ed7cd444254eb662dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E4N64v5RfUSA4D+GdIB8PMWVj+dNQEea0Of671C8dqMH95ym5j54Je0Q8b1MwYX2xZWmbmAq6ehqMhcW/3uDBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T07:24:33.009669Z","bundle_sha256":"13cc8c59d8cd6d5dcfec9d75626c2083fed84a779810d1abdf8aab6c1514c12a"}}