{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:H2VLNQ5ZQJKTH2AZYTRSLIX5P6","short_pith_number":"pith:H2VLNQ5Z","canonical_record":{"source":{"id":"1507.05054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-17T17:49:47Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"88be3dfdcba5b7fe5261e7803829eddd81cf956fb1919e3cffc89c4940128e36","abstract_canon_sha256":"aae49bbc2cfdf65f57668055482a5a3070c33395456a7e68cd6c435db6171e93"},"schema_version":"1.0"},"canonical_sha256":"3eaab6c3b9825533e819c4e325a2fd7f88aaf7c75e920b9a4f00a717466105ee","source":{"kind":"arxiv","id":"1507.05054","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05054","created_at":"2026-05-18T01:04:22Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05054v1","created_at":"2026-05-18T01:04:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05054","created_at":"2026-05-18T01:04:22Z"},{"alias_kind":"pith_short_12","alias_value":"H2VLNQ5ZQJKT","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"H2VLNQ5ZQJKTH2AZ","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"H2VLNQ5Z","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:H2VLNQ5ZQJKTH2AZYTRSLIX5P6","target":"record","payload":{"canonical_record":{"source":{"id":"1507.05054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-17T17:49:47Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"88be3dfdcba5b7fe5261e7803829eddd81cf956fb1919e3cffc89c4940128e36","abstract_canon_sha256":"aae49bbc2cfdf65f57668055482a5a3070c33395456a7e68cd6c435db6171e93"},"schema_version":"1.0"},"canonical_sha256":"3eaab6c3b9825533e819c4e325a2fd7f88aaf7c75e920b9a4f00a717466105ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:22.659958Z","signature_b64":"gCK+bdPCvCSvz54Kb7B38SqmS7XeZYNQ9lzWNQ1H/prOr3JSQFPcOScDPk0Z8fbY7GkBrzeW6ycsrWiAQyRQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3eaab6c3b9825533e819c4e325a2fd7f88aaf7c75e920b9a4f00a717466105ee","last_reissued_at":"2026-05-18T01:04:22.659374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:22.659374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.05054","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dBRAArscJCu+jzVDdL4CMpcXZRR0K8vpn3vPZ6a81LkSXr9rE40r03/ujU2OFTTJ2b/L4aXnmT/KdmW1WFolDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T10:59:59.452351Z"},"content_sha256":"54bbfb551a78c180607a3cf6d808d6b6684a5a9084363dd800ed7bebc552da29","schema_version":"1.0","event_id":"sha256:54bbfb551a78c180607a3cf6d808d6b6684a5a9084363dd800ed7bebc552da29"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:H2VLNQ5ZQJKTH2AZYTRSLIX5P6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivariant Chow classes of matrix orbit closures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Alex Fink, Andrew Berget","submitted_at":"2015-07-17T17:49:47Z","abstract_excerpt":"Let $G$ be the product $GL_r(C) \\times (C^\\times)^n$. We show that the $G$-equivariant Chow class of a $G$ orbit closure in the space of $r$-by-$n$ matrices is determined by a matroid. To do this, we split the natural surjective map from the $G$ equvariant Chow ring of the space of matrices to the torus equivariant Chow ring of the Grassmannian. The splitting takes the class of a Schubert variety to the corresponding factorial Schur polynomial, and also has the property that the class of a subvariety of the Grassmannian is mapped to the class of the closure of those matrices whose row span is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05054","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"afcJ6YpFE6WAARl6785Nj9I8XdRnr5EWVbeIobG8jw5d341PQQx5n7I3uxx4X8NbZnZ7GrT2IgRMHy47jhRlBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T10:59:59.453039Z"},"content_sha256":"5f778c3edc6748a9c81aa691c16aca31666159bc8fde22962d09afe692d7e04f","schema_version":"1.0","event_id":"sha256:5f778c3edc6748a9c81aa691c16aca31666159bc8fde22962d09afe692d7e04f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H2VLNQ5ZQJKTH2AZYTRSLIX5P6/bundle.json","state_url":"https://pith.science/pith/H2VLNQ5ZQJKTH2AZYTRSLIX5P6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H2VLNQ5ZQJKTH2AZYTRSLIX5P6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T10:59:59Z","links":{"resolver":"https://pith.science/pith/H2VLNQ5ZQJKTH2AZYTRSLIX5P6","bundle":"https://pith.science/pith/H2VLNQ5ZQJKTH2AZYTRSLIX5P6/bundle.json","state":"https://pith.science/pith/H2VLNQ5ZQJKTH2AZYTRSLIX5P6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H2VLNQ5ZQJKTH2AZYTRSLIX5P6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:H2VLNQ5ZQJKTH2AZYTRSLIX5P6","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":"aae49bbc2cfdf65f57668055482a5a3070c33395456a7e68cd6c435db6171e93","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-17T17:49:47Z","title_canon_sha256":"88be3dfdcba5b7fe5261e7803829eddd81cf956fb1919e3cffc89c4940128e36"},"schema_version":"1.0","source":{"id":"1507.05054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05054","created_at":"2026-05-18T01:04:22Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05054v1","created_at":"2026-05-18T01:04:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05054","created_at":"2026-05-18T01:04:22Z"},{"alias_kind":"pith_short_12","alias_value":"H2VLNQ5ZQJKT","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"H2VLNQ5ZQJKTH2AZ","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"H2VLNQ5Z","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:5f778c3edc6748a9c81aa691c16aca31666159bc8fde22962d09afe692d7e04f","target":"graph","created_at":"2026-05-18T01:04:22Z","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":"Let $G$ be the product $GL_r(C) \\times (C^\\times)^n$. We show that the $G$-equivariant Chow class of a $G$ orbit closure in the space of $r$-by-$n$ matrices is determined by a matroid. To do this, we split the natural surjective map from the $G$ equvariant Chow ring of the space of matrices to the torus equivariant Chow ring of the Grassmannian. The splitting takes the class of a Schubert variety to the corresponding factorial Schur polynomial, and also has the property that the class of a subvariety of the Grassmannian is mapped to the class of the closure of those matrices whose row span is ","authors_text":"Alex Fink, Andrew Berget","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-17T17:49:47Z","title":"Equivariant Chow classes of matrix orbit closures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05054","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":"sha256:54bbfb551a78c180607a3cf6d808d6b6684a5a9084363dd800ed7bebc552da29","target":"record","created_at":"2026-05-18T01:04:22Z","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":"aae49bbc2cfdf65f57668055482a5a3070c33395456a7e68cd6c435db6171e93","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-17T17:49:47Z","title_canon_sha256":"88be3dfdcba5b7fe5261e7803829eddd81cf956fb1919e3cffc89c4940128e36"},"schema_version":"1.0","source":{"id":"1507.05054","kind":"arxiv","version":1}},"canonical_sha256":"3eaab6c3b9825533e819c4e325a2fd7f88aaf7c75e920b9a4f00a717466105ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3eaab6c3b9825533e819c4e325a2fd7f88aaf7c75e920b9a4f00a717466105ee","first_computed_at":"2026-05-18T01:04:22.659374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:22.659374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gCK+bdPCvCSvz54Kb7B38SqmS7XeZYNQ9lzWNQ1H/prOr3JSQFPcOScDPk0Z8fbY7GkBrzeW6ycsrWiAQyRQAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:22.659958Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54bbfb551a78c180607a3cf6d808d6b6684a5a9084363dd800ed7bebc552da29","sha256:5f778c3edc6748a9c81aa691c16aca31666159bc8fde22962d09afe692d7e04f"],"state_sha256":"a8ef959da61d874876ed35a1faea2155440e6ea541ef088864ca9f27401e8046"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r8FMxtsLELil5g8yLoYBDG8NcyqMrSTSOeCzI0pXkbX/w02FBO0uN3EWTm/N8UvBy1aNPMIuz1PiJczoEAzFAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T10:59:59.456589Z","bundle_sha256":"1602bf906146553a9373d1f7c01809ca9c98aec3714cd39dd7d8e1c497ca64b3"}}