{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:7ZF5CD76ATUXWPSOK2PJRPWUPC","short_pith_number":"pith:7ZF5CD76","schema_version":"1.0","canonical_sha256":"fe4bd10ffe04e97b3e4e569e98bed478a555ce38043be08c3a8d00e74e0bfda0","source":{"kind":"arxiv","id":"1707.06840","version":1},"attestation_state":"computed","paper":{"title":"Intersection multiplicity one for classical groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Ivan Dimitrov, Mike Roth","submitted_at":"2017-07-21T10:57:48Z","abstract_excerpt":"In this paper we show that when $\\mathrm{G}$ is a classical semi-simple algebraic group, $\\mathrm{B}\\subset\\mathrm{G}$ a Borel subgroup, and $\\mathrm{X} = \\mathrm{G}/\\mathrm{B}$, then the structure coefficients of the Belkale-Kumar product $\\odot_{0}$ on $\\mathrm{H}^{*}(\\mathrm{X}, \\mathbf{Z})$ are all either $0$ or $1$."},"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":"1707.06840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-21T10:57:48Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"5c354a6b78d1c0a4126e7602844e363b8853437fb2dd81d7c9cb97734a0c64d8","abstract_canon_sha256":"f276f49e2594618a8cddbfabefc01ee7feea2fdd2b032843f7411e8be1e2d2e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:51.417145Z","signature_b64":"YO9wVmOcfKLnC0EslgWBXZOBsjl44ZyeVPO4eYG4hM8HHwNZCbFqANotLQpnIlp7emjnPfbtBGsuKlSJF45GAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe4bd10ffe04e97b3e4e569e98bed478a555ce38043be08c3a8d00e74e0bfda0","last_reissued_at":"2026-05-18T00:39:51.416538Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:51.416538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intersection multiplicity one for classical groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Ivan Dimitrov, Mike Roth","submitted_at":"2017-07-21T10:57:48Z","abstract_excerpt":"In this paper we show that when $\\mathrm{G}$ is a classical semi-simple algebraic group, $\\mathrm{B}\\subset\\mathrm{G}$ a Borel subgroup, and $\\mathrm{X} = \\mathrm{G}/\\mathrm{B}$, then the structure coefficients of the Belkale-Kumar product $\\odot_{0}$ on $\\mathrm{H}^{*}(\\mathrm{X}, \\mathbf{Z})$ are all either $0$ or $1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06840","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":"1707.06840","created_at":"2026-05-18T00:39:51.416621+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.06840v1","created_at":"2026-05-18T00:39:51.416621+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06840","created_at":"2026-05-18T00:39:51.416621+00:00"},{"alias_kind":"pith_short_12","alias_value":"7ZF5CD76ATUX","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"7ZF5CD76ATUXWPSO","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"7ZF5CD76","created_at":"2026-05-18T12:31:05.417338+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/7ZF5CD76ATUXWPSOK2PJRPWUPC","json":"https://pith.science/pith/7ZF5CD76ATUXWPSOK2PJRPWUPC.json","graph_json":"https://pith.science/api/pith-number/7ZF5CD76ATUXWPSOK2PJRPWUPC/graph.json","events_json":"https://pith.science/api/pith-number/7ZF5CD76ATUXWPSOK2PJRPWUPC/events.json","paper":"https://pith.science/paper/7ZF5CD76"},"agent_actions":{"view_html":"https://pith.science/pith/7ZF5CD76ATUXWPSOK2PJRPWUPC","download_json":"https://pith.science/pith/7ZF5CD76ATUXWPSOK2PJRPWUPC.json","view_paper":"https://pith.science/paper/7ZF5CD76","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.06840&json=true","fetch_graph":"https://pith.science/api/pith-number/7ZF5CD76ATUXWPSOK2PJRPWUPC/graph.json","fetch_events":"https://pith.science/api/pith-number/7ZF5CD76ATUXWPSOK2PJRPWUPC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7ZF5CD76ATUXWPSOK2PJRPWUPC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7ZF5CD76ATUXWPSOK2PJRPWUPC/action/storage_attestation","attest_author":"https://pith.science/pith/7ZF5CD76ATUXWPSOK2PJRPWUPC/action/author_attestation","sign_citation":"https://pith.science/pith/7ZF5CD76ATUXWPSOK2PJRPWUPC/action/citation_signature","submit_replication":"https://pith.science/pith/7ZF5CD76ATUXWPSOK2PJRPWUPC/action/replication_record"}},"created_at":"2026-05-18T00:39:51.416621+00:00","updated_at":"2026-05-18T00:39:51.416621+00:00"}