{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:L7IR3LGTEJ5PFWNJDZDQX22E3X","short_pith_number":"pith:L7IR3LGT","canonical_record":{"source":{"id":"1806.06011","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-15T15:16:45Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"020612b247e54a10c3afb1aff92364804fc865860a69ca151a77fa0402f1bfee","abstract_canon_sha256":"760afb6e243f3400c419db2a80ac2d6d38830afa86646aab3abbe008deebc959"},"schema_version":"1.0"},"canonical_sha256":"5fd11dacd3227af2d9a91e470beb44ddc40bc1b6641e625f98ac45f47e817686","source":{"kind":"arxiv","id":"1806.06011","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.06011","created_at":"2026-05-18T00:13:08Z"},{"alias_kind":"arxiv_version","alias_value":"1806.06011v1","created_at":"2026-05-18T00:13:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06011","created_at":"2026-05-18T00:13:08Z"},{"alias_kind":"pith_short_12","alias_value":"L7IR3LGTEJ5P","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L7IR3LGTEJ5PFWNJ","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L7IR3LGT","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:L7IR3LGTEJ5PFWNJDZDQX22E3X","target":"record","payload":{"canonical_record":{"source":{"id":"1806.06011","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-15T15:16:45Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"020612b247e54a10c3afb1aff92364804fc865860a69ca151a77fa0402f1bfee","abstract_canon_sha256":"760afb6e243f3400c419db2a80ac2d6d38830afa86646aab3abbe008deebc959"},"schema_version":"1.0"},"canonical_sha256":"5fd11dacd3227af2d9a91e470beb44ddc40bc1b6641e625f98ac45f47e817686","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:08.699641Z","signature_b64":"MMDTN6zku7UQxplRgm8ROqqYSUVlEGaVil+5yT6JwzsqS6SsaKHWarTEf0K5YBnIFVYTi/yv/YbglydgKKUaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fd11dacd3227af2d9a91e470beb44ddc40bc1b6641e625f98ac45f47e817686","last_reissued_at":"2026-05-18T00:13:08.698950Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:08.698950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.06011","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":"2026-05-18T00:13:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D8KP9E9mcHHMUVHkHbP9H2Ay4k5AKAdeDLYzbPsaLVkeoQi4FG9M8LVMJlPCtSb4b07kPwwqNdMK2Cy9DOipDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:42:53.279352Z"},"content_sha256":"136bf939a152cdb60a13d33ac62dca8bcfc4b3bd890733e65635ecad740eed80","schema_version":"1.0","event_id":"sha256:136bf939a152cdb60a13d33ac62dca8bcfc4b3bd890733e65635ecad740eed80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:L7IR3LGTEJ5PFWNJDZDQX22E3X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounds on the number of 2-level polytopes, cones and configurations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Kanstantsin Pashkovich, Marco Macchia, Samuel Fiorini","submitted_at":"2018-06-15T15:16:45Z","abstract_excerpt":"We prove an upper bound of the form $2^{O(d^2 \\mathrm{polylog}\\,d)}$ on the number of affine (resp. linear) equivalence classes of, by increasing order of generality, 2-level d-polytopes, d-cones and d-configurations. This in particular answers positively a conjecture of Bohn et al. on 2-level polytopes. We obtain our upper bound by relating affine (resp. linear) equivalence classes of 2-level d-polytopes, d-cones and d-configurations to faces of the correlation cone. We complement this with a $2^{\\Omega(d^2)}$ lower bound, by estimating the number of nonequivalent stable set polytopes of bipa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06011","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":"2026-05-18T00:13:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vC7Tse/5kByyua2jDqcnUiiKqpm6jUxbZIzGcEn1H874yB21pfvEZyTSpOp+iB5CEHLcKIknYOB8SRXxCiuJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:42:53.279709Z"},"content_sha256":"e3af88b2d82434b2d5e3120c39d00221df09d9a0b5473739c7d617c0cb437628","schema_version":"1.0","event_id":"sha256:e3af88b2d82434b2d5e3120c39d00221df09d9a0b5473739c7d617c0cb437628"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L7IR3LGTEJ5PFWNJDZDQX22E3X/bundle.json","state_url":"https://pith.science/pith/L7IR3LGTEJ5PFWNJDZDQX22E3X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L7IR3LGTEJ5PFWNJDZDQX22E3X/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":"2026-05-28T02:42:53Z","links":{"resolver":"https://pith.science/pith/L7IR3LGTEJ5PFWNJDZDQX22E3X","bundle":"https://pith.science/pith/L7IR3LGTEJ5PFWNJDZDQX22E3X/bundle.json","state":"https://pith.science/pith/L7IR3LGTEJ5PFWNJDZDQX22E3X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L7IR3LGTEJ5PFWNJDZDQX22E3X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:L7IR3LGTEJ5PFWNJDZDQX22E3X","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":"760afb6e243f3400c419db2a80ac2d6d38830afa86646aab3abbe008deebc959","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-15T15:16:45Z","title_canon_sha256":"020612b247e54a10c3afb1aff92364804fc865860a69ca151a77fa0402f1bfee"},"schema_version":"1.0","source":{"id":"1806.06011","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.06011","created_at":"2026-05-18T00:13:08Z"},{"alias_kind":"arxiv_version","alias_value":"1806.06011v1","created_at":"2026-05-18T00:13:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06011","created_at":"2026-05-18T00:13:08Z"},{"alias_kind":"pith_short_12","alias_value":"L7IR3LGTEJ5P","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"L7IR3LGTEJ5PFWNJ","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"L7IR3LGT","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:e3af88b2d82434b2d5e3120c39d00221df09d9a0b5473739c7d617c0cb437628","target":"graph","created_at":"2026-05-18T00:13:08Z","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":"We prove an upper bound of the form $2^{O(d^2 \\mathrm{polylog}\\,d)}$ on the number of affine (resp. linear) equivalence classes of, by increasing order of generality, 2-level d-polytopes, d-cones and d-configurations. This in particular answers positively a conjecture of Bohn et al. on 2-level polytopes. We obtain our upper bound by relating affine (resp. linear) equivalence classes of 2-level d-polytopes, d-cones and d-configurations to faces of the correlation cone. We complement this with a $2^{\\Omega(d^2)}$ lower bound, by estimating the number of nonequivalent stable set polytopes of bipa","authors_text":"Kanstantsin Pashkovich, Marco Macchia, Samuel Fiorini","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-15T15:16:45Z","title":"Bounds on the number of 2-level polytopes, cones and configurations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06011","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":"sha256:136bf939a152cdb60a13d33ac62dca8bcfc4b3bd890733e65635ecad740eed80","target":"record","created_at":"2026-05-18T00:13:08Z","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":"760afb6e243f3400c419db2a80ac2d6d38830afa86646aab3abbe008deebc959","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-15T15:16:45Z","title_canon_sha256":"020612b247e54a10c3afb1aff92364804fc865860a69ca151a77fa0402f1bfee"},"schema_version":"1.0","source":{"id":"1806.06011","kind":"arxiv","version":1}},"canonical_sha256":"5fd11dacd3227af2d9a91e470beb44ddc40bc1b6641e625f98ac45f47e817686","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fd11dacd3227af2d9a91e470beb44ddc40bc1b6641e625f98ac45f47e817686","first_computed_at":"2026-05-18T00:13:08.698950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:08.698950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MMDTN6zku7UQxplRgm8ROqqYSUVlEGaVil+5yT6JwzsqS6SsaKHWarTEf0K5YBnIFVYTi/yv/YbglydgKKUaBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:08.699641Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.06011","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:136bf939a152cdb60a13d33ac62dca8bcfc4b3bd890733e65635ecad740eed80","sha256:e3af88b2d82434b2d5e3120c39d00221df09d9a0b5473739c7d617c0cb437628"],"state_sha256":"6207e8c4a1d282390233edb9f095def666f7f41a6f7f7c1876597a1ebca9dd1a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E1Kphlkdx1ShDSp82/o+mknmtTg6DknZmhIs3HuUp+GODQX9v0xaoTqRcZhdYVsAG8uXam3AGO9TA7sw6mB2DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:42:53.281810Z","bundle_sha256":"bb4ffa9b3b88ca4d18de90c39f9719d919c6fb2e8a550f2de6a01853a6e66e36"}}