{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WJVKVVJOY3ZFTLGTCRYTAFDPX7","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":"b84ab34c78d9796c41f0336e4e858de6990e94fc59330ca706c9bfeff6cacb06","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2024-08-13T06:41:40Z","title_canon_sha256":"5cda3e2625995990e7c89069decb9df57c6e89f30879309510e9dc2e9f21efc7"},"schema_version":"1.0","source":{"id":"2408.06669","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.06669","created_at":"2026-07-05T08:59:11Z"},{"alias_kind":"arxiv_version","alias_value":"2408.06669v2","created_at":"2026-07-05T08:59:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.06669","created_at":"2026-07-05T08:59:11Z"},{"alias_kind":"pith_short_12","alias_value":"WJVKVVJOY3ZF","created_at":"2026-07-05T08:59:11Z"},{"alias_kind":"pith_short_16","alias_value":"WJVKVVJOY3ZFTLGT","created_at":"2026-07-05T08:59:11Z"},{"alias_kind":"pith_short_8","alias_value":"WJVKVVJO","created_at":"2026-07-05T08:59:11Z"}],"graph_snapshots":[{"event_id":"sha256:533410ba437f1a7074c51c7ac69830cd8ca40136d1f7c8e990b856bb34955291","target":"graph","created_at":"2026-07-05T08:59:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2408.06669/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Write $P_k:= \\mathbb F_2[x_1,x_2,\\ldots ,x_k]$ for the polynomial algebra over the prime field $\\mathbb F_2$ with two elements, in $k$ generators $x_1, x_2, \\ldots , x_k$, each of degree 1. The polynomial algebra $P_k$ is considered as a module over the mod-2 Steenrod algebra, $\\mathcal A$. Let $GL_k$ be the general linear group over the field $\\mathbb F_2$. This group acts naturally on $P_k$ by matrix substitution. Since the two actions of $\\mathcal A$ and $GL_k$ upon $P_k$ commute with each other, there is an inherit action of $GL_k$ on $\\mathbb F_2{\\otimes}_{\\mathcal A}P_k$. Denote by $(\\ma","authors_text":"Nguyen Sum","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2024-08-13T06:41:40Z","title":"A counter-example to Singer's conjecture for the algebraic transfer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.06669","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:e64a9450da25922919fe823d02e36b9813f40b338d5b29239477ac9e66bec412","target":"record","created_at":"2026-07-05T08:59:11Z","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":"b84ab34c78d9796c41f0336e4e858de6990e94fc59330ca706c9bfeff6cacb06","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2024-08-13T06:41:40Z","title_canon_sha256":"5cda3e2625995990e7c89069decb9df57c6e89f30879309510e9dc2e9f21efc7"},"schema_version":"1.0","source":{"id":"2408.06669","kind":"arxiv","version":2}},"canonical_sha256":"b26aaad52ec6f259acd3147130146fbfe54ab388f7c4eda2309df0365832075f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b26aaad52ec6f259acd3147130146fbfe54ab388f7c4eda2309df0365832075f","first_computed_at":"2026-07-05T08:59:11.519612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:59:11.519612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dSoiaZsxqtOMPHrYjUkFy6w72pQ80GhmqcmBg4pjS1qJJm8vERvk+1dWVqquOSHQdIUFQDKs3laRSK6ZajugCw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:59:11.520056Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.06669","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e64a9450da25922919fe823d02e36b9813f40b338d5b29239477ac9e66bec412","sha256:533410ba437f1a7074c51c7ac69830cd8ca40136d1f7c8e990b856bb34955291"],"state_sha256":"7da059b0856e1b864f3118eeda835153f4e4d1d8a83ad8b7f6af654342206c4f"}