{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6ZM3MUCX2ZUS4MZ2QIMRDMQLWT","short_pith_number":"pith:6ZM3MUCX","canonical_record":{"source":{"id":"1107.0371","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-07-02T11:19:04Z","cross_cats_sorted":["cs.CG","math.CO"],"title_canon_sha256":"56e1c4acc9f1c3f9f8f079d819e466004aefe9dde21d904f30608f42f66bfa44","abstract_canon_sha256":"bf1f98e0c06430c2d7aff0c700f247a20daa5d67adc88edc824b8a19947f4010"},"schema_version":"1.0"},"canonical_sha256":"f659b65057d6692e333a821911b20bb4c0be95816284c5581c1b634e1198d577","source":{"kind":"arxiv","id":"1107.0371","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0371","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0371v2","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0371","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"pith_short_12","alias_value":"6ZM3MUCX2ZUS","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6ZM3MUCX2ZUS4MZ2","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6ZM3MUCX","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6ZM3MUCX2ZUS4MZ2QIMRDMQLWT","target":"record","payload":{"canonical_record":{"source":{"id":"1107.0371","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-07-02T11:19:04Z","cross_cats_sorted":["cs.CG","math.CO"],"title_canon_sha256":"56e1c4acc9f1c3f9f8f079d819e466004aefe9dde21d904f30608f42f66bfa44","abstract_canon_sha256":"bf1f98e0c06430c2d7aff0c700f247a20daa5d67adc88edc824b8a19947f4010"},"schema_version":"1.0"},"canonical_sha256":"f659b65057d6692e333a821911b20bb4c0be95816284c5581c1b634e1198d577","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:14.509428Z","signature_b64":"KYfygeW5cJgjS6lZpTp9qQcwfeBSMjqlZvxr5swQZYUWcaGzXzdsOtu8jIxjOVKtKJlABB+4B1gFC5OeEwhdAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f659b65057d6692e333a821911b20bb4c0be95816284c5581c1b634e1198d577","last_reissued_at":"2026-05-18T03:40:14.508846Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:14.508846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.0371","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:40:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lmlROYVpWe6EIH8eDC9hBrh6I1WDRAoEPKISXc6SmabvUmfgUqev65BJEGuZBWuWKX4OiWVq/oLNrAnyQdC0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T00:35:35.814396Z"},"content_sha256":"088ceb0667b6ffd28b496c18ecb34c1508c49c68df5f16eb6486a80c16b11dff","schema_version":"1.0","event_id":"sha256:088ceb0667b6ffd28b496c18ecb34c1508c49c68df5f16eb6486a80c16b11dff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6ZM3MUCX2ZUS4MZ2QIMRDMQLWT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extended formulations for polygons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.CO"],"primary_cat":"cs.DM","authors_text":"Hans Raj Tiwary, Samuel Fiorini, Thomas Rothvo{\\ss}","submitted_at":"2011-07-02T11:19:04Z","abstract_excerpt":"The extension complexity of a polytope $P$ is the smallest integer $k$ such that $P$ is the projection of a polytope $Q$ with $k$ facets. We study the extension complexity of $n$-gons in the plane. First, we give a new proof that the extension complexity of regular $n$-gons is $O(\\log n)$, a result originating from work by Ben-Tal and Nemirovski (2001). Our proof easily generalizes to other permutahedra and simplifies proofs of recent results by Goemans (2009), and Kaibel and Pashkovich (2011). Second, we prove a lower bound of $\\sqrt{2n}$ on the extension complexity of generic $n$-gons. Final"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0371","kind":"arxiv","version":2},"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":"2026-05-18T03:40:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lNXn2qB/X7vPKi0wB5TNNYiqZdikDAWOCIiQ31vWoHalylHvG9un17rtsC+p+Sg7yDCsfzeh9b8ksPCO4cgfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T00:35:35.815075Z"},"content_sha256":"bcd3e16c2d8cfb5258c936e3ed0a2dbef51cc9b4d0c25671cba6e4e84d246fc5","schema_version":"1.0","event_id":"sha256:bcd3e16c2d8cfb5258c936e3ed0a2dbef51cc9b4d0c25671cba6e4e84d246fc5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6ZM3MUCX2ZUS4MZ2QIMRDMQLWT/bundle.json","state_url":"https://pith.science/pith/6ZM3MUCX2ZUS4MZ2QIMRDMQLWT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6ZM3MUCX2ZUS4MZ2QIMRDMQLWT/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":"2026-05-25T00:35:35Z","links":{"resolver":"https://pith.science/pith/6ZM3MUCX2ZUS4MZ2QIMRDMQLWT","bundle":"https://pith.science/pith/6ZM3MUCX2ZUS4MZ2QIMRDMQLWT/bundle.json","state":"https://pith.science/pith/6ZM3MUCX2ZUS4MZ2QIMRDMQLWT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6ZM3MUCX2ZUS4MZ2QIMRDMQLWT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6ZM3MUCX2ZUS4MZ2QIMRDMQLWT","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":"bf1f98e0c06430c2d7aff0c700f247a20daa5d67adc88edc824b8a19947f4010","cross_cats_sorted":["cs.CG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-07-02T11:19:04Z","title_canon_sha256":"56e1c4acc9f1c3f9f8f079d819e466004aefe9dde21d904f30608f42f66bfa44"},"schema_version":"1.0","source":{"id":"1107.0371","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0371","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0371v2","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0371","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"pith_short_12","alias_value":"6ZM3MUCX2ZUS","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6ZM3MUCX2ZUS4MZ2","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6ZM3MUCX","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:bcd3e16c2d8cfb5258c936e3ed0a2dbef51cc9b4d0c25671cba6e4e84d246fc5","target":"graph","created_at":"2026-05-18T03:40:14Z","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 extension complexity of a polytope $P$ is the smallest integer $k$ such that $P$ is the projection of a polytope $Q$ with $k$ facets. We study the extension complexity of $n$-gons in the plane. First, we give a new proof that the extension complexity of regular $n$-gons is $O(\\log n)$, a result originating from work by Ben-Tal and Nemirovski (2001). Our proof easily generalizes to other permutahedra and simplifies proofs of recent results by Goemans (2009), and Kaibel and Pashkovich (2011). Second, we prove a lower bound of $\\sqrt{2n}$ on the extension complexity of generic $n$-gons. Final","authors_text":"Hans Raj Tiwary, Samuel Fiorini, Thomas Rothvo{\\ss}","cross_cats":["cs.CG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-07-02T11:19:04Z","title":"Extended formulations for polygons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0371","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":"sha256:088ceb0667b6ffd28b496c18ecb34c1508c49c68df5f16eb6486a80c16b11dff","target":"record","created_at":"2026-05-18T03:40:14Z","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":"bf1f98e0c06430c2d7aff0c700f247a20daa5d67adc88edc824b8a19947f4010","cross_cats_sorted":["cs.CG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-07-02T11:19:04Z","title_canon_sha256":"56e1c4acc9f1c3f9f8f079d819e466004aefe9dde21d904f30608f42f66bfa44"},"schema_version":"1.0","source":{"id":"1107.0371","kind":"arxiv","version":2}},"canonical_sha256":"f659b65057d6692e333a821911b20bb4c0be95816284c5581c1b634e1198d577","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f659b65057d6692e333a821911b20bb4c0be95816284c5581c1b634e1198d577","first_computed_at":"2026-05-18T03:40:14.508846Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:14.508846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KYfygeW5cJgjS6lZpTp9qQcwfeBSMjqlZvxr5swQZYUWcaGzXzdsOtu8jIxjOVKtKJlABB+4B1gFC5OeEwhdAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:14.509428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0371","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:088ceb0667b6ffd28b496c18ecb34c1508c49c68df5f16eb6486a80c16b11dff","sha256:bcd3e16c2d8cfb5258c936e3ed0a2dbef51cc9b4d0c25671cba6e4e84d246fc5"],"state_sha256":"412d763f5b5933400bda1f38593eac70686a7ea64c5098753f045897b47e29d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QF80jJZFvcrJfOLZJefHMllF0S9WtKw6CeWvX8ruUJSBOPEaqtK351N7zw/jbYV23WK42VadIbW1XknKKHiEAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T00:35:35.818733Z","bundle_sha256":"fb97121ec46a57b6e6c864fb0e5aa5d0878b6c1e5a0bbf38009b203100c24b41"}}