{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:LRTHLOQGC42CTOHSRUU4OMFQBN","short_pith_number":"pith:LRTHLOQG","schema_version":"1.0","canonical_sha256":"5c6675ba06173429b8f28d29c730b00b451831ff921fb5d5a470f576013f278f","source":{"kind":"arxiv","id":"2607.22844","version":1},"attestation_state":"computed","paper":{"title":"Carlsson's Conjecture and the Generalized Total Rank Conjecture in Characteristic Two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.RT"],"primary_cat":"math.AC","authors_text":"Keller VandeBogert","submitted_at":"2026-07-24T18:35:29Z","abstract_excerpt":"We prove the generalized total rank conjecture over regular rings in characteristic $2$: if $R$ is\n  a regular Noetherian\n  domain of characteristic $2$ and $P$ is a differential $R$-module admitting a finite projective\n  flag and having nonzero homology $H(P)$, then $\\rank_R(P)\\ge2^{\\codim_RH(P)}$. In particular, we\n  prove Carlsson's conjecture for elementary abelian $2$-groups in every rank. We also\n  obtain sharp homology bounds for arbitrary continuous actions of such groups and for perfect complexes\n  over finite group algebras; the sphere rank conjecture follows. The proof identifies th"},"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":"2607.22844","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-07-24T18:35:29Z","cross_cats_sorted":["math.AT","math.RT"],"title_canon_sha256":"c5020a2575acec0400490378758f0955ff35f565300803963e930a501d33039f","abstract_canon_sha256":"f5519df8a14844c034b21ff8874523a941e8b4c1ca2399a3d9c97d59bf3ce725"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T00:21:58.068144Z","signature_b64":"r/zd5HyZbDB8Geohf42CRFgi3oAG/9xAYarO0ClScI0YwY+nib91hXMXAiHfywkWYkxG8Yv9s1BemtOTC90LCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c6675ba06173429b8f28d29c730b00b451831ff921fb5d5a470f576013f278f","last_reissued_at":"2026-07-28T00:21:58.067279Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T00:21:58.067279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Carlsson's Conjecture and the Generalized Total Rank Conjecture in Characteristic Two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.RT"],"primary_cat":"math.AC","authors_text":"Keller VandeBogert","submitted_at":"2026-07-24T18:35:29Z","abstract_excerpt":"We prove the generalized total rank conjecture over regular rings in characteristic $2$: if $R$ is\n  a regular Noetherian\n  domain of characteristic $2$ and $P$ is a differential $R$-module admitting a finite projective\n  flag and having nonzero homology $H(P)$, then $\\rank_R(P)\\ge2^{\\codim_RH(P)}$. In particular, we\n  prove Carlsson's conjecture for elementary abelian $2$-groups in every rank. We also\n  obtain sharp homology bounds for arbitrary continuous actions of such groups and for perfect complexes\n  over finite group algebras; the sphere rank conjecture follows. The proof identifies th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22844","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.22844/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2607.22844","created_at":"2026-07-28T00:21:58.067732+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.22844v1","created_at":"2026-07-28T00:21:58.067732+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.22844","created_at":"2026-07-28T00:21:58.067732+00:00"},{"alias_kind":"pith_short_12","alias_value":"LRTHLOQGC42C","created_at":"2026-07-28T00:21:58.067732+00:00"},{"alias_kind":"pith_short_16","alias_value":"LRTHLOQGC42CTOHS","created_at":"2026-07-28T00:21:58.067732+00:00"},{"alias_kind":"pith_short_8","alias_value":"LRTHLOQG","created_at":"2026-07-28T00:21:58.067732+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/LRTHLOQGC42CTOHSRUU4OMFQBN","json":"https://pith.science/pith/LRTHLOQGC42CTOHSRUU4OMFQBN.json","graph_json":"https://pith.science/api/pith-number/LRTHLOQGC42CTOHSRUU4OMFQBN/graph.json","events_json":"https://pith.science/api/pith-number/LRTHLOQGC42CTOHSRUU4OMFQBN/events.json","paper":"https://pith.science/paper/LRTHLOQG"},"agent_actions":{"view_html":"https://pith.science/pith/LRTHLOQGC42CTOHSRUU4OMFQBN","download_json":"https://pith.science/pith/LRTHLOQGC42CTOHSRUU4OMFQBN.json","view_paper":"https://pith.science/paper/LRTHLOQG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.22844&json=true","fetch_graph":"https://pith.science/api/pith-number/LRTHLOQGC42CTOHSRUU4OMFQBN/graph.json","fetch_events":"https://pith.science/api/pith-number/LRTHLOQGC42CTOHSRUU4OMFQBN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LRTHLOQGC42CTOHSRUU4OMFQBN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LRTHLOQGC42CTOHSRUU4OMFQBN/action/storage_attestation","attest_author":"https://pith.science/pith/LRTHLOQGC42CTOHSRUU4OMFQBN/action/author_attestation","sign_citation":"https://pith.science/pith/LRTHLOQGC42CTOHSRUU4OMFQBN/action/citation_signature","submit_replication":"https://pith.science/pith/LRTHLOQGC42CTOHSRUU4OMFQBN/action/replication_record"}},"created_at":"2026-07-28T00:21:58.067732+00:00","updated_at":"2026-07-28T00:21:58.067732+00:00"}