{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:TPJVHY7T52EPTJI6V6QY6QJV6Y","short_pith_number":"pith:TPJVHY7T","schema_version":"1.0","canonical_sha256":"9bd353e3f3ee88f9a51eafa18f4135f60fd944ad6573b19f25b4be2c9730028e","source":{"kind":"arxiv","id":"1501.05528","version":2},"attestation_state":"computed","paper":{"title":"Permanent versus determinant: not via saturations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"cs.CC","authors_text":"Christian Ikenmeyer, Jesko H\\\"uttenhain, Peter B\\\"urgisser","submitted_at":"2015-01-22T15:11:40Z","abstract_excerpt":"Let Det_n denote the closure of the GL_{n^2}(C)-orbit of the determinant polynomial det_n with respect to linear substitution. The highest weights (partitions) of irreducible GL_{n^2}(C)-representations occurring in the coordinate ring of Det_n form a finitely generated monoid S(Det_n). We prove that the saturation of S(Det_n) contains all partitions lambda with length at most n and size divisible by n. This implies that representation theoretic obstructions for the permanent versus determinant problem must be holes of the monoid S(Det_n)."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1501.05528","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-01-22T15:11:40Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"da504ecbb172d7ad5e12251bb0c81dd02d662116630fb79789c241715bb4ae79","abstract_canon_sha256":"214a3e095a30b7131ecc4629d15e421a9eab7f424821755c9d4837a5cf3f9418"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:52.760239Z","signature_b64":"tK4h9u3k7FTeHa7jVzDBhDpAQzRHkPxMtDXpmSDanenlVuyRkHvDofj82eTmtx5nmLJEpnUmnWlTusdSGKpLAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bd353e3f3ee88f9a51eafa18f4135f60fd944ad6573b19f25b4be2c9730028e","last_reissued_at":"2026-05-18T00:49:52.759710Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:52.759710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Permanent versus determinant: not via saturations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"cs.CC","authors_text":"Christian Ikenmeyer, Jesko H\\\"uttenhain, Peter B\\\"urgisser","submitted_at":"2015-01-22T15:11:40Z","abstract_excerpt":"Let Det_n denote the closure of the GL_{n^2}(C)-orbit of the determinant polynomial det_n with respect to linear substitution. The highest weights (partitions) of irreducible GL_{n^2}(C)-representations occurring in the coordinate ring of Det_n form a finitely generated monoid S(Det_n). We prove that the saturation of S(Det_n) contains all partitions lambda with length at most n and size divisible by n. This implies that representation theoretic obstructions for the permanent versus determinant problem must be holes of the monoid S(Det_n)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05528","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1501.05528","created_at":"2026-05-18T00:49:52.759788+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.05528v2","created_at":"2026-05-18T00:49:52.759788+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05528","created_at":"2026-05-18T00:49:52.759788+00:00"},{"alias_kind":"pith_short_12","alias_value":"TPJVHY7T52EP","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"TPJVHY7T52EPTJI6","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"TPJVHY7T","created_at":"2026-05-18T12:29:42.218222+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TPJVHY7T52EPTJI6V6QY6QJV6Y","json":"https://pith.science/pith/TPJVHY7T52EPTJI6V6QY6QJV6Y.json","graph_json":"https://pith.science/api/pith-number/TPJVHY7T52EPTJI6V6QY6QJV6Y/graph.json","events_json":"https://pith.science/api/pith-number/TPJVHY7T52EPTJI6V6QY6QJV6Y/events.json","paper":"https://pith.science/paper/TPJVHY7T"},"agent_actions":{"view_html":"https://pith.science/pith/TPJVHY7T52EPTJI6V6QY6QJV6Y","download_json":"https://pith.science/pith/TPJVHY7T52EPTJI6V6QY6QJV6Y.json","view_paper":"https://pith.science/paper/TPJVHY7T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.05528&json=true","fetch_graph":"https://pith.science/api/pith-number/TPJVHY7T52EPTJI6V6QY6QJV6Y/graph.json","fetch_events":"https://pith.science/api/pith-number/TPJVHY7T52EPTJI6V6QY6QJV6Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TPJVHY7T52EPTJI6V6QY6QJV6Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TPJVHY7T52EPTJI6V6QY6QJV6Y/action/storage_attestation","attest_author":"https://pith.science/pith/TPJVHY7T52EPTJI6V6QY6QJV6Y/action/author_attestation","sign_citation":"https://pith.science/pith/TPJVHY7T52EPTJI6V6QY6QJV6Y/action/citation_signature","submit_replication":"https://pith.science/pith/TPJVHY7T52EPTJI6V6QY6QJV6Y/action/replication_record"}},"created_at":"2026-05-18T00:49:52.759788+00:00","updated_at":"2026-05-18T00:49:52.759788+00:00"}