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Using this we show that the extension complexity of the bond polytope of (K5 minus e)-minor-free graphs is linear.","weakest_assumption":"That the bond polytope of the summed graph is exactly obtainable from the polytopes of G1 and G2 via the described combination rules for 1-sums and 2-sums, without extra facets or vertices arising from the identification."}},"verdict_id":"bbd87635-7830-4374-b900-07813d01f3dd"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:65d87fbde0301074cb3461f76aec2c915e16ce979dbb3bb73560317d1f78c8ba","target":"record","created_at":"2026-05-20T01:05:06Z","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":"e1e6fe46d2908a72b4a1d26a1f93d1356cfa9ec68594b8e91a34af3f11144ef5","cross_cats_sorted":["cs.DM","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-01-16T09:26:38Z","title_canon_sha256":"f6a4bb11adcc89a8e6dd2740cdae6a97a53f114011bf83d5319b31d086c6b98a"},"schema_version":"1.0","source":{"id":"2601.11119","kind":"arxiv","version":2}},"canonical_sha256":"e47272f64601065e41c2c5972d76656b6f59064b1bbb5fadcea88bf683de2f96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e47272f64601065e41c2c5972d76656b6f59064b1bbb5fadcea88bf683de2f96","first_computed_at":"2026-05-20T01:05:06.049296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T01:05:06.049296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sjFnimedP8utyqnQ4WDK/AOuz9H+Pfzlby6pzPn72U7W3XSqwpeRhDHuKO1e1BUU4Go4j6sw9vpQLCIaFrpODA==","signature_status":"signed_v1","signed_at":"2026-05-20T01:05:06.050035Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.11119","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65d87fbde0301074cb3461f76aec2c915e16ce979dbb3bb73560317d1f78c8ba","sha256:b648f2f94b0aa3bcb83b9b5fa3409c8996853a74805108a15dcda5f4f0df2847"],"state_sha256":"9248af1808da358dd298a19266dae4ebbb01c71b3ececc8e9f71b35d3aff7d87"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WvssfVMg/CPCBF5sRIyadMofOjJKOZ9FyepwhvHRS7jtp0ZfGpwruHuC3pyXGG5Zyg470/AMz0SYk1ZJjKymDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T17:19:02.025384Z","bundle_sha256":"ccc153fa25adb82f4f4857a6e4f8fcfc4cdb52679f9c229764f5a6af00d661df"}}