{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NTAYW7I66LESRICVLW5CFBIYOR","short_pith_number":"pith:NTAYW7I6","canonical_record":{"source":{"id":"1304.7719","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-29T17:35:30Z","cross_cats_sorted":[],"title_canon_sha256":"024410ac9b1002db19eea021821a1cba3052b57bed15a86b1855b295ce19ce84","abstract_canon_sha256":"d8ed1c5e8f4133195d21b0e424504cf9019375636a670ccd956ba4c1d0c4c71a"},"schema_version":"1.0"},"canonical_sha256":"6cc18b7d1ef2c928a0555dba228518745ab1cd526bbf807afaf8ec67c8f63152","source":{"kind":"arxiv","id":"1304.7719","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7719","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7719v3","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7719","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"NTAYW7I66LES","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NTAYW7I66LESRICV","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NTAYW7I6","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NTAYW7I66LESRICVLW5CFBIYOR","target":"record","payload":{"canonical_record":{"source":{"id":"1304.7719","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-29T17:35:30Z","cross_cats_sorted":[],"title_canon_sha256":"024410ac9b1002db19eea021821a1cba3052b57bed15a86b1855b295ce19ce84","abstract_canon_sha256":"d8ed1c5e8f4133195d21b0e424504cf9019375636a670ccd956ba4c1d0c4c71a"},"schema_version":"1.0"},"canonical_sha256":"6cc18b7d1ef2c928a0555dba228518745ab1cd526bbf807afaf8ec67c8f63152","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:17.569152Z","signature_b64":"HzkOsKOP043BTAdtQfNYPXisUixwGRamW4nvwSU6F5zreopL6iuE1vKR/VGERFvGXxvFLs9wAryiy7GsSBz+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cc18b7d1ef2c928a0555dba228518745ab1cd526bbf807afaf8ec67c8f63152","last_reissued_at":"2026-05-17T23:53:17.568500Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:17.568500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.7719","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YPhhcmIkYsDqPMrtZNOI4Fzovsh2wb7epzvTSK7ryfhd4/8pJ73MQFhzhZoBrFPCZZa/YDS9aE1yUw2TZb6NAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T23:55:49.474109Z"},"content_sha256":"b51c485b9e01c0f42ffac734a6618b5686662155178d94d3391cfeec4ecddef9","schema_version":"1.0","event_id":"sha256:b51c485b9e01c0f42ffac734a6618b5686662155178d94d3391cfeec4ecddef9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NTAYW7I66LESRICVLW5CFBIYOR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Popov-Pommerening conjecture for linear algebraic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Gergely B\\'erczi","submitted_at":"2013-04-29T17:35:30Z","abstract_excerpt":"Let $G$ be a reductive group over an algebraically closed subfield $k$ of $\\mathbb{C}$ of characteristic zero, $H \\subseteq G$ an observable subgroup normalized by a maximal torus of $G$ and $X$ an affine $k$-variety acted on by $G$. Popov and Pommerening conjectured in the late 70's that the invariant algebra $k[X]^H$ is finitely generated. We prove the conjecture for 1) subgroups of $\\mathrm{SL}_n(k)$ closed under left (or right) Borel action and for 2) a class of Borel regular subgroups of classical groups. We give a partial affirmative answer to the conjecture for general regular subgroups"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7719","kind":"arxiv","version":3},"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":"2026-05-17T23:53:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5iujOm4lsB67237xvcaU7Nka4dl5o+DQ4rteDMNCXkQrK2vZtfvSolZfikG8rLv9DyyIS8YeKkvG33IELIhVAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T23:55:49.474771Z"},"content_sha256":"c2c06b16e1356f38f8e420064ec1b5c20f2e6fd5ee38c8511733bb29712817b9","schema_version":"1.0","event_id":"sha256:c2c06b16e1356f38f8e420064ec1b5c20f2e6fd5ee38c8511733bb29712817b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NTAYW7I66LESRICVLW5CFBIYOR/bundle.json","state_url":"https://pith.science/pith/NTAYW7I66LESRICVLW5CFBIYOR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NTAYW7I66LESRICVLW5CFBIYOR/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":"2026-05-22T23:55:49Z","links":{"resolver":"https://pith.science/pith/NTAYW7I66LESRICVLW5CFBIYOR","bundle":"https://pith.science/pith/NTAYW7I66LESRICVLW5CFBIYOR/bundle.json","state":"https://pith.science/pith/NTAYW7I66LESRICVLW5CFBIYOR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NTAYW7I66LESRICVLW5CFBIYOR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NTAYW7I66LESRICVLW5CFBIYOR","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":"d8ed1c5e8f4133195d21b0e424504cf9019375636a670ccd956ba4c1d0c4c71a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-29T17:35:30Z","title_canon_sha256":"024410ac9b1002db19eea021821a1cba3052b57bed15a86b1855b295ce19ce84"},"schema_version":"1.0","source":{"id":"1304.7719","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7719","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7719v3","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7719","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"NTAYW7I66LES","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NTAYW7I66LESRICV","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NTAYW7I6","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:c2c06b16e1356f38f8e420064ec1b5c20f2e6fd5ee38c8511733bb29712817b9","target":"graph","created_at":"2026-05-17T23:53:17Z","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":"Let $G$ be a reductive group over an algebraically closed subfield $k$ of $\\mathbb{C}$ of characteristic zero, $H \\subseteq G$ an observable subgroup normalized by a maximal torus of $G$ and $X$ an affine $k$-variety acted on by $G$. Popov and Pommerening conjectured in the late 70's that the invariant algebra $k[X]^H$ is finitely generated. We prove the conjecture for 1) subgroups of $\\mathrm{SL}_n(k)$ closed under left (or right) Borel action and for 2) a class of Borel regular subgroups of classical groups. We give a partial affirmative answer to the conjecture for general regular subgroups","authors_text":"Gergely B\\'erczi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-29T17:35:30Z","title":"On the Popov-Pommerening conjecture for linear algebraic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7719","kind":"arxiv","version":3},"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:b51c485b9e01c0f42ffac734a6618b5686662155178d94d3391cfeec4ecddef9","target":"record","created_at":"2026-05-17T23:53:17Z","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":"d8ed1c5e8f4133195d21b0e424504cf9019375636a670ccd956ba4c1d0c4c71a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-04-29T17:35:30Z","title_canon_sha256":"024410ac9b1002db19eea021821a1cba3052b57bed15a86b1855b295ce19ce84"},"schema_version":"1.0","source":{"id":"1304.7719","kind":"arxiv","version":3}},"canonical_sha256":"6cc18b7d1ef2c928a0555dba228518745ab1cd526bbf807afaf8ec67c8f63152","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cc18b7d1ef2c928a0555dba228518745ab1cd526bbf807afaf8ec67c8f63152","first_computed_at":"2026-05-17T23:53:17.568500Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:17.568500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HzkOsKOP043BTAdtQfNYPXisUixwGRamW4nvwSU6F5zreopL6iuE1vKR/VGERFvGXxvFLs9wAryiy7GsSBz+CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:17.569152Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.7719","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b51c485b9e01c0f42ffac734a6618b5686662155178d94d3391cfeec4ecddef9","sha256:c2c06b16e1356f38f8e420064ec1b5c20f2e6fd5ee38c8511733bb29712817b9"],"state_sha256":"5734a0a3bbf5cad855440b7a6d0be3a2ef7aa0fdd527397435e3b6547e11bddd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1sXm9/JEDGytEFTj4MzXzu6PYwALBw4tYJULZ55kYm4JfswgbtUEGhAiwJMzy1KO53F0YjSdTg0FVmiM+hyFBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T23:55:49.478658Z","bundle_sha256":"a6518c94dd040b07070a4bcc5351a5591e5b8605ad10dd5731eb1d9a1641baf6"}}