{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AKIR3SJRVVLQY5G57H4KRJO27Q","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":"66381636eeb814a20c85a11f3abd08571471ebae9a0ab3911bc79b7d447df6c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-20T21:48:56Z","title_canon_sha256":"0fd411ce1de471365075805b9cc79fcc5d8d10023018f9a23a2d6539f8208ea2"},"schema_version":"1.0","source":{"id":"1612.06893","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06893","created_at":"2026-05-18T00:25:34Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06893v3","created_at":"2026-05-18T00:25:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06893","created_at":"2026-05-18T00:25:34Z"},{"alias_kind":"pith_short_12","alias_value":"AKIR3SJRVVLQ","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AKIR3SJRVVLQY5G5","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AKIR3SJR","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:e4da76796326bf8e5d1657fb533447d898b505b5ec269132e0cabbc81ea2a43d","target":"graph","created_at":"2026-05-18T00:25:34Z","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":"We initiate the study of average intersection theory in real Grassmannians. We define the expected degree $\\textrm{edeg} G(k,n)$ of the real Grassmannian $G(k,n)$ as the average number of real $k$-planes meeting nontrivially $k(n-k)$ random subspaces of $\\mathbb{R}^n$, all of dimension $n-k$, where these subspaces are sampled uniformly and independently from $G(n-k,n)$. We express $\\textrm{edeg} G(k,n)$ in terms of the volume of an invariant convex body in the tangent space to the Grassmanian, and prove that for fixed $k\\ge 2$ and $n\\to\\infty$, $$ \\textrm{edeg} G(k,n) = \\textrm{deg} G_\\mathbb{","authors_text":"Antonio Lerario, Peter B\\\"urgisser","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-20T21:48:56Z","title":"Probabilistic Schubert Calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06893","kind":"arxiv","version":3},"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:b93fc5eb48623d90e6c3010708afb88f9af32e30250a1e98e518821ec2709bae","target":"record","created_at":"2026-05-18T00:25:34Z","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":"66381636eeb814a20c85a11f3abd08571471ebae9a0ab3911bc79b7d447df6c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-20T21:48:56Z","title_canon_sha256":"0fd411ce1de471365075805b9cc79fcc5d8d10023018f9a23a2d6539f8208ea2"},"schema_version":"1.0","source":{"id":"1612.06893","kind":"arxiv","version":3}},"canonical_sha256":"02911dc931ad570c74ddf9f8a8a5dafc00a210478fdc401e6fc85d7bfc505396","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02911dc931ad570c74ddf9f8a8a5dafc00a210478fdc401e6fc85d7bfc505396","first_computed_at":"2026-05-18T00:25:34.722631Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:34.722631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7bwHNRI0ZXZg7VthVR04tC/+Df416SUTA9UjnzFeV/nLXoaxPKE61Udk3vdqmjQeH9DgLqR0LKZTrirvfjxwAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:34.723395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06893","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b93fc5eb48623d90e6c3010708afb88f9af32e30250a1e98e518821ec2709bae","sha256:e4da76796326bf8e5d1657fb533447d898b505b5ec269132e0cabbc81ea2a43d"],"state_sha256":"0c39510c7e9161a92b103b40c2b7b1754082133ad9e6699499eb5235839b7e61"}