{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BJ7U2NQ7JI436644K4HNCRU2RG","short_pith_number":"pith:BJ7U2NQ7","canonical_record":{"source":{"id":"1305.6329","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-27T21:13:17Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"db3b0b5b93aca10f27e47d49673061f1221861fc7a772d2b803a6c744ed97455","abstract_canon_sha256":"c4fbeae4a8d073fcd043df4fba6f24876833e40e5d2b3bc05d88dfaba14497ae"},"schema_version":"1.0"},"canonical_sha256":"0a7f4d361f4a39bf7b9c570ed1469a89be1c3c5b6b1b78774063a004ba4dcbbe","source":{"kind":"arxiv","id":"1305.6329","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6329","created_at":"2026-05-18T01:59:59Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6329v3","created_at":"2026-05-18T01:59:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6329","created_at":"2026-05-18T01:59:59Z"},{"alias_kind":"pith_short_12","alias_value":"BJ7U2NQ7JI43","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BJ7U2NQ7JI436644","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BJ7U2NQ7","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BJ7U2NQ7JI436644K4HNCRU2RG","target":"record","payload":{"canonical_record":{"source":{"id":"1305.6329","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-27T21:13:17Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"db3b0b5b93aca10f27e47d49673061f1221861fc7a772d2b803a6c744ed97455","abstract_canon_sha256":"c4fbeae4a8d073fcd043df4fba6f24876833e40e5d2b3bc05d88dfaba14497ae"},"schema_version":"1.0"},"canonical_sha256":"0a7f4d361f4a39bf7b9c570ed1469a89be1c3c5b6b1b78774063a004ba4dcbbe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:59.095543Z","signature_b64":"Av5IhY2jqZC67zCDx9SwnrNBDeLexCJulR6/cR9DQQKEerqqk6MHVq2iRTjZSOM7iaGdbQCvNulyDPRJZOuRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a7f4d361f4a39bf7b9c570ed1469a89be1c3c5b6b1b78774063a004ba4dcbbe","last_reissued_at":"2026-05-18T01:59:59.094993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:59.094993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.6329","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:59:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4HOeDT7RtYx4R3pvLIhkBgfH73nNiJfwhStb00M3Pa9O2+q6l0dCN83TTh73uAPGxZJh+b6XU92RkDkPbkeLCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:39:08.573429Z"},"content_sha256":"b17a57f04d912f5ae0fac4d8fc7014b27430fb96d422860c2c2583dae9c98c08","schema_version":"1.0","event_id":"sha256:b17a57f04d912f5ae0fac4d8fc7014b27430fb96d422860c2c2583dae9c98c08"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BJ7U2NQ7JI436644K4HNCRU2RG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stiefel tropical linear spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Alex Fink, Felipe Rinc\\'on","submitted_at":"2013-05-27T21:13:17Z","abstract_excerpt":"The tropical Stiefel map associates to a tropical matrix A its tropical Pluecker vector of maximal minors, and thus a tropical linear space L(A). We call the L(A)s obtained in this way Stiefel tropical linear spaces. We prove that they are dual to certain matroid subdivisions of polytopes of transversal matroids, and we relate their combinatorics to a canonically associated tropical hyperplane arrangement. We also explore a broad connection with the secondary fan of the Newton polytope of the product of all maximal minors of a matrix. In addition, we investigate the natural parametrization of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6329","kind":"arxiv","version":3},"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":"2026-05-18T01:59:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PW/ZbfUFTJRN4TYkF/wJORbypO45x8JX5HnDMx5HqiBlA05Y5O898l/XMQvR6vHa+SFakIougz/aoWwoOn9DBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:39:08.574031Z"},"content_sha256":"068e4fc3547cf513cc7919e37fd5aac1bff7d37f3e14ea563bb2dadc97b495a6","schema_version":"1.0","event_id":"sha256:068e4fc3547cf513cc7919e37fd5aac1bff7d37f3e14ea563bb2dadc97b495a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BJ7U2NQ7JI436644K4HNCRU2RG/bundle.json","state_url":"https://pith.science/pith/BJ7U2NQ7JI436644K4HNCRU2RG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BJ7U2NQ7JI436644K4HNCRU2RG/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":"2026-05-26T19:39:08Z","links":{"resolver":"https://pith.science/pith/BJ7U2NQ7JI436644K4HNCRU2RG","bundle":"https://pith.science/pith/BJ7U2NQ7JI436644K4HNCRU2RG/bundle.json","state":"https://pith.science/pith/BJ7U2NQ7JI436644K4HNCRU2RG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BJ7U2NQ7JI436644K4HNCRU2RG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BJ7U2NQ7JI436644K4HNCRU2RG","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":"c4fbeae4a8d073fcd043df4fba6f24876833e40e5d2b3bc05d88dfaba14497ae","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-27T21:13:17Z","title_canon_sha256":"db3b0b5b93aca10f27e47d49673061f1221861fc7a772d2b803a6c744ed97455"},"schema_version":"1.0","source":{"id":"1305.6329","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6329","created_at":"2026-05-18T01:59:59Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6329v3","created_at":"2026-05-18T01:59:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6329","created_at":"2026-05-18T01:59:59Z"},{"alias_kind":"pith_short_12","alias_value":"BJ7U2NQ7JI43","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BJ7U2NQ7JI436644","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BJ7U2NQ7","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:068e4fc3547cf513cc7919e37fd5aac1bff7d37f3e14ea563bb2dadc97b495a6","target":"graph","created_at":"2026-05-18T01:59:59Z","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":"The tropical Stiefel map associates to a tropical matrix A its tropical Pluecker vector of maximal minors, and thus a tropical linear space L(A). We call the L(A)s obtained in this way Stiefel tropical linear spaces. We prove that they are dual to certain matroid subdivisions of polytopes of transversal matroids, and we relate their combinatorics to a canonically associated tropical hyperplane arrangement. We also explore a broad connection with the secondary fan of the Newton polytope of the product of all maximal minors of a matrix. In addition, we investigate the natural parametrization of ","authors_text":"Alex Fink, Felipe Rinc\\'on","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-27T21:13:17Z","title":"Stiefel tropical linear spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6329","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:b17a57f04d912f5ae0fac4d8fc7014b27430fb96d422860c2c2583dae9c98c08","target":"record","created_at":"2026-05-18T01:59:59Z","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":"c4fbeae4a8d073fcd043df4fba6f24876833e40e5d2b3bc05d88dfaba14497ae","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-27T21:13:17Z","title_canon_sha256":"db3b0b5b93aca10f27e47d49673061f1221861fc7a772d2b803a6c744ed97455"},"schema_version":"1.0","source":{"id":"1305.6329","kind":"arxiv","version":3}},"canonical_sha256":"0a7f4d361f4a39bf7b9c570ed1469a89be1c3c5b6b1b78774063a004ba4dcbbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a7f4d361f4a39bf7b9c570ed1469a89be1c3c5b6b1b78774063a004ba4dcbbe","first_computed_at":"2026-05-18T01:59:59.094993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:59.094993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Av5IhY2jqZC67zCDx9SwnrNBDeLexCJulR6/cR9DQQKEerqqk6MHVq2iRTjZSOM7iaGdbQCvNulyDPRJZOuRDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:59.095543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6329","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b17a57f04d912f5ae0fac4d8fc7014b27430fb96d422860c2c2583dae9c98c08","sha256:068e4fc3547cf513cc7919e37fd5aac1bff7d37f3e14ea563bb2dadc97b495a6"],"state_sha256":"33dc42ef4e7b3af307458537acd6b13fa5234eb8c8cd8ebcd5e40b0a6e674ddf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lyESS/EzmiYk59n0ALDzY0lARKhHHHanMLogk7BQ/0xl9CO9BWnLU5TSgJLHivchB97SrqhlO6gRxgjiXfp3BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:39:08.577197Z","bundle_sha256":"e2da97dfbfbda464b0c5b51fbd97b8c390089a0b4099d04f93e08973f290de40"}}