{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:R6NLSISYV73AFZ74CKR37P5ELA","short_pith_number":"pith:R6NLSISY","schema_version":"1.0","canonical_sha256":"8f9ab92258aff602e7fc12a3bfbfa45828e5799ffed2bd65da4948c118cc94c2","source":{"kind":"arxiv","id":"1902.10773","version":1},"attestation_state":"computed","paper":{"title":"An exponential lower bound for the degrees of invariants of cubic forms and tensor actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.AC","math.RA"],"primary_cat":"math.RT","authors_text":"Harm Derksen, Visu Makam","submitted_at":"2019-02-27T20:35:31Z","abstract_excerpt":"Using the Grosshans Principle, we develop a method for proving lower bounds for the maximal degree of a system of generators of an invariant ring. This method also gives lower bounds for the maximal degree of a set of invariants that define Hilbert's null cone. We consider two actions: The first is the action of ${\\rm SL}(V)$ on ${\\rm Sym}^3(V)^{\\oplus 4}$, the space of $4$-tuples of cubic forms, and the second is the action of ${\\rm SL}(V) \\times {\\rm SL}(W) \\times {\\rm SL}(Z)$ on the tensor space $(V \\otimes W \\otimes Z)^{\\oplus 9}$. In both these cases, we prove an exponential lower degree "},"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":"1902.10773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-27T20:35:31Z","cross_cats_sorted":["cs.CC","math.AC","math.RA"],"title_canon_sha256":"e0dbd185a5666ff59d5f87b6378d81e91c766764f70e2d71c9db2e846018f4ef","abstract_canon_sha256":"92604df5a0b6ecc5b1d0d855ae15a6ee906a91159e754f993e45f8d372f96d52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:29.764558Z","signature_b64":"w3Y71HSdM/LSce9iVDzTRFGfNFWpG+CRyZr5jBb27WGiCQ64RNjIWIcZf1w6v++VjpWIGuoq1Ny/W4eZkDZqAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f9ab92258aff602e7fc12a3bfbfa45828e5799ffed2bd65da4948c118cc94c2","last_reissued_at":"2026-05-17T23:52:29.764120Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:29.764120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An exponential lower bound for the degrees of invariants of cubic forms and tensor actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.AC","math.RA"],"primary_cat":"math.RT","authors_text":"Harm Derksen, Visu Makam","submitted_at":"2019-02-27T20:35:31Z","abstract_excerpt":"Using the Grosshans Principle, we develop a method for proving lower bounds for the maximal degree of a system of generators of an invariant ring. This method also gives lower bounds for the maximal degree of a set of invariants that define Hilbert's null cone. We consider two actions: The first is the action of ${\\rm SL}(V)$ on ${\\rm Sym}^3(V)^{\\oplus 4}$, the space of $4$-tuples of cubic forms, and the second is the action of ${\\rm SL}(V) \\times {\\rm SL}(W) \\times {\\rm SL}(Z)$ on the tensor space $(V \\otimes W \\otimes Z)^{\\oplus 9}$. In both these cases, we prove an exponential lower degree "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10773","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1902.10773","created_at":"2026-05-17T23:52:29.764189+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.10773v1","created_at":"2026-05-17T23:52:29.764189+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.10773","created_at":"2026-05-17T23:52:29.764189+00:00"},{"alias_kind":"pith_short_12","alias_value":"R6NLSISYV73A","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"R6NLSISYV73AFZ74","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"R6NLSISY","created_at":"2026-05-18T12:33:27.125529+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/R6NLSISYV73AFZ74CKR37P5ELA","json":"https://pith.science/pith/R6NLSISYV73AFZ74CKR37P5ELA.json","graph_json":"https://pith.science/api/pith-number/R6NLSISYV73AFZ74CKR37P5ELA/graph.json","events_json":"https://pith.science/api/pith-number/R6NLSISYV73AFZ74CKR37P5ELA/events.json","paper":"https://pith.science/paper/R6NLSISY"},"agent_actions":{"view_html":"https://pith.science/pith/R6NLSISYV73AFZ74CKR37P5ELA","download_json":"https://pith.science/pith/R6NLSISYV73AFZ74CKR37P5ELA.json","view_paper":"https://pith.science/paper/R6NLSISY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.10773&json=true","fetch_graph":"https://pith.science/api/pith-number/R6NLSISYV73AFZ74CKR37P5ELA/graph.json","fetch_events":"https://pith.science/api/pith-number/R6NLSISYV73AFZ74CKR37P5ELA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R6NLSISYV73AFZ74CKR37P5ELA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R6NLSISYV73AFZ74CKR37P5ELA/action/storage_attestation","attest_author":"https://pith.science/pith/R6NLSISYV73AFZ74CKR37P5ELA/action/author_attestation","sign_citation":"https://pith.science/pith/R6NLSISYV73AFZ74CKR37P5ELA/action/citation_signature","submit_replication":"https://pith.science/pith/R6NLSISYV73AFZ74CKR37P5ELA/action/replication_record"}},"created_at":"2026-05-17T23:52:29.764189+00:00","updated_at":"2026-05-17T23:52:29.764189+00:00"}