{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:T3JWAGRBRXE72CSMWLHLWP34MZ","short_pith_number":"pith:T3JWAGRB","canonical_record":{"source":{"id":"1701.01849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-07T16:14:51Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"db6ee9ff6231a9d03c19964b7d3a4616679bc2d1ef0b297fbe4aff1a9bc5bc10","abstract_canon_sha256":"4ff5ddc2c9a778d3346490353f0f254da8b830e7fde153851abaa2546136178c"},"schema_version":"1.0"},"canonical_sha256":"9ed3601a218dc9fd0a4cb2cebb3f7c6642d82cb8f47438ddda4c89ce1d05c0b5","source":{"kind":"arxiv","id":"1701.01849","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01849","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01849v2","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01849","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"pith_short_12","alias_value":"T3JWAGRBRXE7","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"T3JWAGRBRXE72CSM","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"T3JWAGRB","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:T3JWAGRBRXE72CSMWLHLWP34MZ","target":"record","payload":{"canonical_record":{"source":{"id":"1701.01849","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-07T16:14:51Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"db6ee9ff6231a9d03c19964b7d3a4616679bc2d1ef0b297fbe4aff1a9bc5bc10","abstract_canon_sha256":"4ff5ddc2c9a778d3346490353f0f254da8b830e7fde153851abaa2546136178c"},"schema_version":"1.0"},"canonical_sha256":"9ed3601a218dc9fd0a4cb2cebb3f7c6642d82cb8f47438ddda4c89ce1d05c0b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:56.818929Z","signature_b64":"yKLqk/U7YrTxzWl43XdQlKLkDfsR8iHGtFGr9RVjNpn2Rx1wan7K1D4Gjkn4u6dTSllzbVgXSFL+tD4wCvStBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ed3601a218dc9fd0a4cb2cebb3f7c6642d82cb8f47438ddda4c89ce1d05c0b5","last_reissued_at":"2026-05-18T00:20:56.818351Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:56.818351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.01849","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":"2026-05-18T00:20:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3r6RKRF4COcYBGsz0vM7OLMSeQzCO4Fz/tjO7eNBzw1kepa17826Ql9wRLduWOOqs4tCxTC1oaLzFysdCQ7YDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:06:31.844398Z"},"content_sha256":"f722e97d10f3fc5bb4423df45aac0805d16cd6373be6f16fc85bb1d5e155d514","schema_version":"1.0","event_id":"sha256:f722e97d10f3fc5bb4423df45aac0805d16cd6373be6f16fc85bb1d5e155d514"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:T3JWAGRBRXE72CSMWLHLWP34MZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological noetherianity for cubic polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Andrew Snowden, Harm Derksen, Rob H. Eggermont","submitted_at":"2017-01-07T16:14:51Z","abstract_excerpt":"Let $P_3(\\mathbf{C}^{\\infty})$ be the space of complex cubic polynomials in infinitely many variables. We show that this space is $\\mathbf{GL}_{\\infty}$-noetherian, meaning that any $\\mathbf{GL}_{\\infty}$-stable Zariski closed subset is cut out by finitely many orbits of equations. Our method relies on a careful analysis of an invariant of cubics introduced here called q-rank. This result is motivated by recent work in representation stability, especially the theory of twisted commutative algebras. It is also connected to certain stability problems in commutative algebra, such as Stillman's co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01849","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":"2026-05-18T00:20:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EK1mF3xDeEsnDBMlwtrTv6wk/o6khW70BtR5oH6j9hgl+vXoVK9Y4qNv770N2r4nAHKl4VBWOEWC1SLePGbvAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:06:31.844752Z"},"content_sha256":"9620d2c3103ca1d6c850a232ad585dd52a0b2db5b03f7638a5d9c3e125196409","schema_version":"1.0","event_id":"sha256:9620d2c3103ca1d6c850a232ad585dd52a0b2db5b03f7638a5d9c3e125196409"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T3JWAGRBRXE72CSMWLHLWP34MZ/bundle.json","state_url":"https://pith.science/pith/T3JWAGRBRXE72CSMWLHLWP34MZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T3JWAGRBRXE72CSMWLHLWP34MZ/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":"2026-06-04T06:06:31Z","links":{"resolver":"https://pith.science/pith/T3JWAGRBRXE72CSMWLHLWP34MZ","bundle":"https://pith.science/pith/T3JWAGRBRXE72CSMWLHLWP34MZ/bundle.json","state":"https://pith.science/pith/T3JWAGRBRXE72CSMWLHLWP34MZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T3JWAGRBRXE72CSMWLHLWP34MZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:T3JWAGRBRXE72CSMWLHLWP34MZ","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":"4ff5ddc2c9a778d3346490353f0f254da8b830e7fde153851abaa2546136178c","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-07T16:14:51Z","title_canon_sha256":"db6ee9ff6231a9d03c19964b7d3a4616679bc2d1ef0b297fbe4aff1a9bc5bc10"},"schema_version":"1.0","source":{"id":"1701.01849","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01849","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01849v2","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01849","created_at":"2026-05-18T00:20:56Z"},{"alias_kind":"pith_short_12","alias_value":"T3JWAGRBRXE7","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"T3JWAGRBRXE72CSM","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"T3JWAGRB","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:9620d2c3103ca1d6c850a232ad585dd52a0b2db5b03f7638a5d9c3e125196409","target":"graph","created_at":"2026-05-18T00:20:56Z","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 $P_3(\\mathbf{C}^{\\infty})$ be the space of complex cubic polynomials in infinitely many variables. We show that this space is $\\mathbf{GL}_{\\infty}$-noetherian, meaning that any $\\mathbf{GL}_{\\infty}$-stable Zariski closed subset is cut out by finitely many orbits of equations. Our method relies on a careful analysis of an invariant of cubics introduced here called q-rank. This result is motivated by recent work in representation stability, especially the theory of twisted commutative algebras. It is also connected to certain stability problems in commutative algebra, such as Stillman's co","authors_text":"Andrew Snowden, Harm Derksen, Rob H. Eggermont","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-07T16:14:51Z","title":"Topological noetherianity for cubic polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01849","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:f722e97d10f3fc5bb4423df45aac0805d16cd6373be6f16fc85bb1d5e155d514","target":"record","created_at":"2026-05-18T00:20:56Z","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":"4ff5ddc2c9a778d3346490353f0f254da8b830e7fde153851abaa2546136178c","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-07T16:14:51Z","title_canon_sha256":"db6ee9ff6231a9d03c19964b7d3a4616679bc2d1ef0b297fbe4aff1a9bc5bc10"},"schema_version":"1.0","source":{"id":"1701.01849","kind":"arxiv","version":2}},"canonical_sha256":"9ed3601a218dc9fd0a4cb2cebb3f7c6642d82cb8f47438ddda4c89ce1d05c0b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ed3601a218dc9fd0a4cb2cebb3f7c6642d82cb8f47438ddda4c89ce1d05c0b5","first_computed_at":"2026-05-18T00:20:56.818351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:56.818351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yKLqk/U7YrTxzWl43XdQlKLkDfsR8iHGtFGr9RVjNpn2Rx1wan7K1D4Gjkn4u6dTSllzbVgXSFL+tD4wCvStBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:56.818929Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.01849","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f722e97d10f3fc5bb4423df45aac0805d16cd6373be6f16fc85bb1d5e155d514","sha256:9620d2c3103ca1d6c850a232ad585dd52a0b2db5b03f7638a5d9c3e125196409"],"state_sha256":"228f85790b3d539c8eaa295b6b17bf2b7626214a7c8ae9f7306cb75358cde92f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8sPZ1Kodvvw7Dj4QHBwphE53jUw+q1H07zDZvTPnafUtS4ADZMP+STNFy69yLFNKdc5Sp0LrkHRDNBHVDxI9Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:06:31.846640Z","bundle_sha256":"1f9e214a9b7fd7e4a27c2874d061c5dffc01475370467aee5982517800bdfc18"}}