{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6X5DCEXEIP7ICYOZZ3LMFAOBHF","short_pith_number":"pith:6X5DCEXE","canonical_record":{"source":{"id":"1805.10325","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-05-25T18:42:46Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"07fc26d0971d65f249b24ddc8f184cc4d4bc61a3d4340dd0df26b046df99b938","abstract_canon_sha256":"4a5c42c5b4bcfc15a75986c4141f192fa2b86f791192bd63fc460c53dac13447"},"schema_version":"1.0"},"canonical_sha256":"f5fa3112e443fe8161d9ced6c281c1394200f04bf1be79f4998cfd860f948ac8","source":{"kind":"arxiv","id":"1805.10325","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10325","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10325v1","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10325","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"pith_short_12","alias_value":"6X5DCEXEIP7I","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6X5DCEXEIP7ICYOZ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6X5DCEXE","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6X5DCEXEIP7ICYOZZ3LMFAOBHF","target":"record","payload":{"canonical_record":{"source":{"id":"1805.10325","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-05-25T18:42:46Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"07fc26d0971d65f249b24ddc8f184cc4d4bc61a3d4340dd0df26b046df99b938","abstract_canon_sha256":"4a5c42c5b4bcfc15a75986c4141f192fa2b86f791192bd63fc460c53dac13447"},"schema_version":"1.0"},"canonical_sha256":"f5fa3112e443fe8161d9ced6c281c1394200f04bf1be79f4998cfd860f948ac8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:52.928018Z","signature_b64":"CkLm4HRSD+z74Kv3SAJegFirbDR2RTAWaihX+6uzW9LDDNqEUIJI/bpcAbb/8KdWcCjoG0JzQX14A/j12MqDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5fa3112e443fe8161d9ced6c281c1394200f04bf1be79f4998cfd860f948ac8","last_reissued_at":"2026-05-18T00:14:52.927361Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:52.927361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.10325","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":"2026-05-18T00:14:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vagdA+a7ZZHAXdiNjtNBqX3sSOxTS2l47Q67CCv/odCV+bd/mlLl6MbN4zBPbhaWuCDlvV82zzOLgVe1PBhHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T06:18:14.637820Z"},"content_sha256":"6cd215764bc436987f296fb5df8638fdec18a25d99019fe9dc3a5f1fb6559795","schema_version":"1.0","event_id":"sha256:6cd215764bc436987f296fb5df8638fdec18a25d99019fe9dc3a5f1fb6559795"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6X5DCEXEIP7ICYOZZ3LMFAOBHF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extended Formulations for Radial Cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Matthias Walter, Stefan Weltge","submitted_at":"2018-05-25T18:42:46Z","abstract_excerpt":"This paper studies extended formulations for radial cones at vertices of polyhedra, where the radial cone of a polyhedron $ P $ at a vertex $ v \\in P $ is the polyhedron defined by the constraints of $ P $ that are active at $ v $. Given an extended formulation for $ P $, it is easy to obtain an extended formulation of comparable size for each its radial cones. On the contrary, it is possible that radial cones of $ P $ admit much smaller extended formulations than $ P $ itself. A prominent example of this type is the perfect-matching polytope, which cannot be described by subexponential-size e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10325","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":"2026-05-18T00:14:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hOp7UAxMxRMCkXkqAtkuRwLEdHYvdKSNRuZ5xfuvvIEWWagr2Es8jCDcMupo7zOG+UdxGgZsNGc9guOR1rSkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T06:18:14.638561Z"},"content_sha256":"db6d8cb1cd79b25debd82a464f865a37f761a66b9e53509f9f7b0bc4f1d979d8","schema_version":"1.0","event_id":"sha256:db6d8cb1cd79b25debd82a464f865a37f761a66b9e53509f9f7b0bc4f1d979d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6X5DCEXEIP7ICYOZZ3LMFAOBHF/bundle.json","state_url":"https://pith.science/pith/6X5DCEXEIP7ICYOZZ3LMFAOBHF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6X5DCEXEIP7ICYOZZ3LMFAOBHF/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":"2026-05-26T06:18:14Z","links":{"resolver":"https://pith.science/pith/6X5DCEXEIP7ICYOZZ3LMFAOBHF","bundle":"https://pith.science/pith/6X5DCEXEIP7ICYOZZ3LMFAOBHF/bundle.json","state":"https://pith.science/pith/6X5DCEXEIP7ICYOZZ3LMFAOBHF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6X5DCEXEIP7ICYOZZ3LMFAOBHF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6X5DCEXEIP7ICYOZZ3LMFAOBHF","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":"4a5c42c5b4bcfc15a75986c4141f192fa2b86f791192bd63fc460c53dac13447","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-05-25T18:42:46Z","title_canon_sha256":"07fc26d0971d65f249b24ddc8f184cc4d4bc61a3d4340dd0df26b046df99b938"},"schema_version":"1.0","source":{"id":"1805.10325","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10325","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10325v1","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10325","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"pith_short_12","alias_value":"6X5DCEXEIP7I","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6X5DCEXEIP7ICYOZ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6X5DCEXE","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:db6d8cb1cd79b25debd82a464f865a37f761a66b9e53509f9f7b0bc4f1d979d8","target":"graph","created_at":"2026-05-18T00:14:52Z","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":"This paper studies extended formulations for radial cones at vertices of polyhedra, where the radial cone of a polyhedron $ P $ at a vertex $ v \\in P $ is the polyhedron defined by the constraints of $ P $ that are active at $ v $. Given an extended formulation for $ P $, it is easy to obtain an extended formulation of comparable size for each its radial cones. On the contrary, it is possible that radial cones of $ P $ admit much smaller extended formulations than $ P $ itself. A prominent example of this type is the perfect-matching polytope, which cannot be described by subexponential-size e","authors_text":"Matthias Walter, Stefan Weltge","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-05-25T18:42:46Z","title":"Extended Formulations for Radial Cones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10325","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":"sha256:6cd215764bc436987f296fb5df8638fdec18a25d99019fe9dc3a5f1fb6559795","target":"record","created_at":"2026-05-18T00:14:52Z","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":"4a5c42c5b4bcfc15a75986c4141f192fa2b86f791192bd63fc460c53dac13447","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-05-25T18:42:46Z","title_canon_sha256":"07fc26d0971d65f249b24ddc8f184cc4d4bc61a3d4340dd0df26b046df99b938"},"schema_version":"1.0","source":{"id":"1805.10325","kind":"arxiv","version":1}},"canonical_sha256":"f5fa3112e443fe8161d9ced6c281c1394200f04bf1be79f4998cfd860f948ac8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5fa3112e443fe8161d9ced6c281c1394200f04bf1be79f4998cfd860f948ac8","first_computed_at":"2026-05-18T00:14:52.927361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:52.927361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CkLm4HRSD+z74Kv3SAJegFirbDR2RTAWaihX+6uzW9LDDNqEUIJI/bpcAbb/8KdWcCjoG0JzQX14A/j12MqDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:52.928018Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.10325","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cd215764bc436987f296fb5df8638fdec18a25d99019fe9dc3a5f1fb6559795","sha256:db6d8cb1cd79b25debd82a464f865a37f761a66b9e53509f9f7b0bc4f1d979d8"],"state_sha256":"ab8ca9bb90aa399c91f5da59e436d29b815d7f10a8adde2548c5cbd903ccc3a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0WWO4WpKd/HBR/1F5QKDKj4Yb8wo0JmiWb/itBfOQFR1pKhwXUeKPZHzNTLUsm89V7DywNT+gWU+KxN6ABvFBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T06:18:14.642435Z","bundle_sha256":"e18a87e92270d59960987a9a0b965e3c5dd6d8d315fa2cee51a26ef7835b928e"}}