{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:O54BBYZTMVCADCST7VR5AVGMJK","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":"801b7c0d8727a819d5705c4504e6eae7bc2c9252dfbd30572d3b92a13006d898","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-06-23T12:02:18Z","title_canon_sha256":"eda7dfc544513a9a40f94be5e17547db86f1693e6074eb73f2a9c7a8a37ed29e"},"schema_version":"1.0","source":{"id":"1706.07651","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07651","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07651v1","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07651","created_at":"2026-05-18T00:41:48Z"},{"alias_kind":"pith_short_12","alias_value":"O54BBYZTMVCA","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"O54BBYZTMVCADCST","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"O54BBYZT","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:67c7657f3eac5d8e56a3b15db9c83401304a434ef9a485e07c91af47b5092ded","target":"graph","created_at":"2026-05-18T00:41:48Z","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":"Flag measures are descriptors of convex bodies $K$ in $d$-dimensional Euclidean space generalizing the classical area measures. They have been used to provide general integral formulas for mixed volumes (see Hug, Rataj and Weil (2017)). Here, we consider an image measure $\\gamma_j(K,\\cdot)$ of flag measures, defined on the Grassmannian $G(d,j)$ of affine $j$-spaces, $1\\le j\\le d-1$, and show that it determines centrally symmetric bodies $K$ of dimension $\\geq j+1$ uniquely. We then explain that Grassmann measures appear in the representation of smooth, translation invariant, continuous and eve","authors_text":"Wolfgang Weil","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-06-23T12:02:18Z","title":"Grassmann measures of convex bodies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07651","kind":"arxiv","version":1},"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:e50164194d8e6a8cc93799daedd77b5e4aca946115d85de1cec50e62bd1b1079","target":"record","created_at":"2026-05-18T00:41:48Z","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":"801b7c0d8727a819d5705c4504e6eae7bc2c9252dfbd30572d3b92a13006d898","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-06-23T12:02:18Z","title_canon_sha256":"eda7dfc544513a9a40f94be5e17547db86f1693e6074eb73f2a9c7a8a37ed29e"},"schema_version":"1.0","source":{"id":"1706.07651","kind":"arxiv","version":1}},"canonical_sha256":"777810e3336544018a53fd63d054cc4a81af3e73dc1895c21ea53cc435c852c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"777810e3336544018a53fd63d054cc4a81af3e73dc1895c21ea53cc435c852c0","first_computed_at":"2026-05-18T00:41:48.544189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:48.544189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z7YdQ11NDwWq7TDCZ9WdJIFg9pnEKXBHF1UmRi28oGhW3GbwnLzGTdVJ0D84UgmTpzeJMO86B70hjopyeFmnCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:48.544658Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07651","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e50164194d8e6a8cc93799daedd77b5e4aca946115d85de1cec50e62bd1b1079","sha256:67c7657f3eac5d8e56a3b15db9c83401304a434ef9a485e07c91af47b5092ded"],"state_sha256":"aeb5c7520f93dd3aa7793b5a05fdf9ba3ffcdebc83731ce2eb61c751b5ab9dd9"}