{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:CQU5H7XUH35MZ72LURKIRQHJNA","short_pith_number":"pith:CQU5H7XU","schema_version":"1.0","canonical_sha256":"1429d3fef43efaccff4ba45488c0e968089fb5952038275cadb66111f5b0511b","source":{"kind":"arxiv","id":"2403.04733","version":1},"attestation_state":"computed","paper":{"title":"Enumerating stably trivial vector bundles with higher real $K$-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Hood Chatham, Morgan Opie, Yang Hu","submitted_at":"2024-03-07T18:36:21Z","abstract_excerpt":"Given positive integers $r$ and $c$, let $\\phi(r,c)$ denote the number of isomorphism classes of complex rank $r$ topological vector bundles on $\\mathbb{CP}^{r+c}$ that are stably trivial. We compute the $p$-adic valuation of the number $\\phi(r,c)$ for all pairs $r$ and $c$ such that $c \\leq \\operatorname{min}\\{r,2p-3\\}$. We also give some systematic lower bounds for $p$-divisibility of $\\phi(r,c)$ when $c<2p^2-p-2$, and detect some nontrivial $p$-divisibility for larger $c$. As an additional application of our methods, we find new $p$-torsion in unstable homotopy groups of unitary groups."},"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":"2403.04733","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-03-07T18:36:21Z","cross_cats_sorted":[],"title_canon_sha256":"47e941899fc95b434fcc3a6fbed45e9b4ddda58fd69b384ba760ddcc72e1e841","abstract_canon_sha256":"b010b917b9feb51c8120c7f96331986b6b00692ea1117e35e131f3a2e285251a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:53:27.203897Z","signature_b64":"PKHvYWSgBiN+y2tnBLgNZ6Am27uyP1aGcL4Poq3p49rnFlB8tE3cSzbmZqVAvDMk5spsFWlh4uF7fbbOHbjPAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1429d3fef43efaccff4ba45488c0e968089fb5952038275cadb66111f5b0511b","last_reissued_at":"2026-07-05T07:53:27.203523Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:53:27.203523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Enumerating stably trivial vector bundles with higher real $K$-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Hood Chatham, Morgan Opie, Yang Hu","submitted_at":"2024-03-07T18:36:21Z","abstract_excerpt":"Given positive integers $r$ and $c$, let $\\phi(r,c)$ denote the number of isomorphism classes of complex rank $r$ topological vector bundles on $\\mathbb{CP}^{r+c}$ that are stably trivial. We compute the $p$-adic valuation of the number $\\phi(r,c)$ for all pairs $r$ and $c$ such that $c \\leq \\operatorname{min}\\{r,2p-3\\}$. We also give some systematic lower bounds for $p$-divisibility of $\\phi(r,c)$ when $c<2p^2-p-2$, and detect some nontrivial $p$-divisibility for larger $c$. As an additional application of our methods, we find new $p$-torsion in unstable homotopy groups of unitary groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.04733","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/2403.04733/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":"2403.04733","created_at":"2026-07-05T07:53:27.203577+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.04733v1","created_at":"2026-07-05T07:53:27.203577+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.04733","created_at":"2026-07-05T07:53:27.203577+00:00"},{"alias_kind":"pith_short_12","alias_value":"CQU5H7XUH35M","created_at":"2026-07-05T07:53:27.203577+00:00"},{"alias_kind":"pith_short_16","alias_value":"CQU5H7XUH35MZ72L","created_at":"2026-07-05T07:53:27.203577+00:00"},{"alias_kind":"pith_short_8","alias_value":"CQU5H7XU","created_at":"2026-07-05T07:53:27.203577+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.26837","citing_title":"Realification of stably trivial vector bundles","ref_index":2,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CQU5H7XUH35MZ72LURKIRQHJNA","json":"https://pith.science/pith/CQU5H7XUH35MZ72LURKIRQHJNA.json","graph_json":"https://pith.science/api/pith-number/CQU5H7XUH35MZ72LURKIRQHJNA/graph.json","events_json":"https://pith.science/api/pith-number/CQU5H7XUH35MZ72LURKIRQHJNA/events.json","paper":"https://pith.science/paper/CQU5H7XU"},"agent_actions":{"view_html":"https://pith.science/pith/CQU5H7XUH35MZ72LURKIRQHJNA","download_json":"https://pith.science/pith/CQU5H7XUH35MZ72LURKIRQHJNA.json","view_paper":"https://pith.science/paper/CQU5H7XU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.04733&json=true","fetch_graph":"https://pith.science/api/pith-number/CQU5H7XUH35MZ72LURKIRQHJNA/graph.json","fetch_events":"https://pith.science/api/pith-number/CQU5H7XUH35MZ72LURKIRQHJNA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CQU5H7XUH35MZ72LURKIRQHJNA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CQU5H7XUH35MZ72LURKIRQHJNA/action/storage_attestation","attest_author":"https://pith.science/pith/CQU5H7XUH35MZ72LURKIRQHJNA/action/author_attestation","sign_citation":"https://pith.science/pith/CQU5H7XUH35MZ72LURKIRQHJNA/action/citation_signature","submit_replication":"https://pith.science/pith/CQU5H7XUH35MZ72LURKIRQHJNA/action/replication_record"}},"created_at":"2026-07-05T07:53:27.203577+00:00","updated_at":"2026-07-05T07:53:27.203577+00:00"}