{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3PAY47FYVMASCBTF455SDGZHCT","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":"5212a3bac5157c4a0478279a0f19724b2014887745d5b38520beba581fe08322","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-23T11:47:32Z","title_canon_sha256":"952b4f8ee2fbcd4cd8cd0a252494721e013fd1cb03caa2a0fb2aa8301f750bc8"},"schema_version":"1.0","source":{"id":"1109.5040","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5040","created_at":"2026-05-18T04:10:23Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5040v2","created_at":"2026-05-18T04:10:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5040","created_at":"2026-05-18T04:10:23Z"},{"alias_kind":"pith_short_12","alias_value":"3PAY47FYVMAS","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3PAY47FYVMASCBTF","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3PAY47FY","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:64eec7a56876ae25f14bc9a82ac8107fe18ef420ff77cc41cb622e14ca551a5c","target":"graph","created_at":"2026-05-18T04:10:23Z","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 $P_n$ denote the $n$-th linear ordering polytope. We define projections from $P_n$ to the $n$-th permutahedron and to the $(n-1)$-st linear ordering polytope. Both projections are equivariant with respect to the natural $\\Sn$-action and they project to orthogonal subspaces. In particular the second projection defines an $S_n$-action in $P_{n-1}$.","authors_text":"Lukas Katth\\\"an","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-23T11:47:32Z","title":"The Linear Ordering Polytope via Representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5040","kind":"arxiv","version":2},"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:b2b46ab69bf63cb6bd29f87c9e4871d360b745882e0e7ee4404b31cd8a2c05a6","target":"record","created_at":"2026-05-18T04:10:23Z","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":"5212a3bac5157c4a0478279a0f19724b2014887745d5b38520beba581fe08322","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-23T11:47:32Z","title_canon_sha256":"952b4f8ee2fbcd4cd8cd0a252494721e013fd1cb03caa2a0fb2aa8301f750bc8"},"schema_version":"1.0","source":{"id":"1109.5040","kind":"arxiv","version":2}},"canonical_sha256":"dbc18e7cb8ab01210665e77b219b2714ef75a101b249e1219fef4b0093ce6672","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbc18e7cb8ab01210665e77b219b2714ef75a101b249e1219fef4b0093ce6672","first_computed_at":"2026-05-18T04:10:23.218161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:23.218161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XVIcdkdQvMOCACMHa1x/+RvVzdKyba9wmBp+5DvVptNj0WwWsmOcmklRyBu5rPqvHhtBJVB865nh7dfL1VvsBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:23.218872Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5040","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2b46ab69bf63cb6bd29f87c9e4871d360b745882e0e7ee4404b31cd8a2c05a6","sha256:64eec7a56876ae25f14bc9a82ac8107fe18ef420ff77cc41cb622e14ca551a5c"],"state_sha256":"82a5e7d2cbb5389bea9cf96af306f67a576e77ea4b25e0fa21c4ccf05cbca07e"}