{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BVCJEOIGRJXEHBDSLOC3GDB4NZ","short_pith_number":"pith:BVCJEOIG","canonical_record":{"source":{"id":"1702.01959","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-07T11:02:48Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"4cf279e255afe2de480b7ae8fe088f7b81d2384328003a64678deb90b7b3ef89","abstract_canon_sha256":"eb4ab051b63f5515e3b9bb1f437b2f84ff27c49cc6fb4e29f82e2685a780b55b"},"schema_version":"1.0"},"canonical_sha256":"0d449239068a6e4384725b85b30c3c6e6b32203c4db35e04955f0dde6bcd813a","source":{"kind":"arxiv","id":"1702.01959","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01959","created_at":"2026-05-18T00:51:10Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01959v1","created_at":"2026-05-18T00:51:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01959","created_at":"2026-05-18T00:51:10Z"},{"alias_kind":"pith_short_12","alias_value":"BVCJEOIGRJXE","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BVCJEOIGRJXEHBDS","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BVCJEOIG","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BVCJEOIGRJXEHBDSLOC3GDB4NZ","target":"record","payload":{"canonical_record":{"source":{"id":"1702.01959","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-07T11:02:48Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"4cf279e255afe2de480b7ae8fe088f7b81d2384328003a64678deb90b7b3ef89","abstract_canon_sha256":"eb4ab051b63f5515e3b9bb1f437b2f84ff27c49cc6fb4e29f82e2685a780b55b"},"schema_version":"1.0"},"canonical_sha256":"0d449239068a6e4384725b85b30c3c6e6b32203c4db35e04955f0dde6bcd813a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:10.740182Z","signature_b64":"vpBfk8YdEv6J6DL4F1IOud5tCklZvPh0vKct0w9vIBXiwWtItR58GjODC7T+KiBnAcLJ8/jUacAyzFlMm1BZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d449239068a6e4384725b85b30c3c6e6b32203c4db35e04955f0dde6bcd813a","last_reissued_at":"2026-05-18T00:51:10.739368Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:10.739368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.01959","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":"2026-05-18T00:51:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lA2k2dems/lI/0IbP7L19vHkdqGAKIt4c36OVJc0m5PQpJ13gVQZij44/aBO9elpXj26f+cpfhYyrjESw8HmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:56:34.905090Z"},"content_sha256":"64d05c85b889cf62219e1887ef31f4adc2fffe039e7b3cb0c67c6fdea1b1815c","schema_version":"1.0","event_id":"sha256:64d05c85b889cf62219e1887ef31f4adc2fffe039e7b3cb0c67c6fdea1b1815c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BVCJEOIGRJXEHBDSLOC3GDB4NZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extension complexities of Cartesian products involving a pyramid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.OC","authors_text":"Hans Raj Tiwary, Rico Zenklusen, Stefan Weltge","submitted_at":"2017-02-07T11:02:48Z","abstract_excerpt":"It is an open question whether the linear extension complexity of the Cartesian product of two polytopes P, Q is the sum of the extension complexities of P and Q. We give an affirmative answer to this question for the case that one of the two polytopes is a pyramid."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01959","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":"2026-05-18T00:51:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U3qf5qQjKqkEcKjJVnmHcIWE2j4bRmGokSpNwJoctecBo+4v5uw/gZDkSGMQhQdUFQdBxjJhsn6A0sIO740FAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:56:34.905841Z"},"content_sha256":"355e8ef79d58ea71a7a8cdaa9be82d32fdb4f259011154833377e243b51451d8","schema_version":"1.0","event_id":"sha256:355e8ef79d58ea71a7a8cdaa9be82d32fdb4f259011154833377e243b51451d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BVCJEOIGRJXEHBDSLOC3GDB4NZ/bundle.json","state_url":"https://pith.science/pith/BVCJEOIGRJXEHBDSLOC3GDB4NZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BVCJEOIGRJXEHBDSLOC3GDB4NZ/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":"2026-05-26T09:56:34Z","links":{"resolver":"https://pith.science/pith/BVCJEOIGRJXEHBDSLOC3GDB4NZ","bundle":"https://pith.science/pith/BVCJEOIGRJXEHBDSLOC3GDB4NZ/bundle.json","state":"https://pith.science/pith/BVCJEOIGRJXEHBDSLOC3GDB4NZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BVCJEOIGRJXEHBDSLOC3GDB4NZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BVCJEOIGRJXEHBDSLOC3GDB4NZ","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":"eb4ab051b63f5515e3b9bb1f437b2f84ff27c49cc6fb4e29f82e2685a780b55b","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-07T11:02:48Z","title_canon_sha256":"4cf279e255afe2de480b7ae8fe088f7b81d2384328003a64678deb90b7b3ef89"},"schema_version":"1.0","source":{"id":"1702.01959","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01959","created_at":"2026-05-18T00:51:10Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01959v1","created_at":"2026-05-18T00:51:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01959","created_at":"2026-05-18T00:51:10Z"},{"alias_kind":"pith_short_12","alias_value":"BVCJEOIGRJXE","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BVCJEOIGRJXEHBDS","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BVCJEOIG","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:355e8ef79d58ea71a7a8cdaa9be82d32fdb4f259011154833377e243b51451d8","target":"graph","created_at":"2026-05-18T00:51:10Z","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":"It is an open question whether the linear extension complexity of the Cartesian product of two polytopes P, Q is the sum of the extension complexities of P and Q. We give an affirmative answer to this question for the case that one of the two polytopes is a pyramid.","authors_text":"Hans Raj Tiwary, Rico Zenklusen, Stefan Weltge","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-07T11:02:48Z","title":"Extension complexities of Cartesian products involving a pyramid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01959","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":"sha256:64d05c85b889cf62219e1887ef31f4adc2fffe039e7b3cb0c67c6fdea1b1815c","target":"record","created_at":"2026-05-18T00:51:10Z","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":"eb4ab051b63f5515e3b9bb1f437b2f84ff27c49cc6fb4e29f82e2685a780b55b","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-07T11:02:48Z","title_canon_sha256":"4cf279e255afe2de480b7ae8fe088f7b81d2384328003a64678deb90b7b3ef89"},"schema_version":"1.0","source":{"id":"1702.01959","kind":"arxiv","version":1}},"canonical_sha256":"0d449239068a6e4384725b85b30c3c6e6b32203c4db35e04955f0dde6bcd813a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d449239068a6e4384725b85b30c3c6e6b32203c4db35e04955f0dde6bcd813a","first_computed_at":"2026-05-18T00:51:10.739368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:10.739368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vpBfk8YdEv6J6DL4F1IOud5tCklZvPh0vKct0w9vIBXiwWtItR58GjODC7T+KiBnAcLJ8/jUacAyzFlMm1BZCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:10.740182Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.01959","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64d05c85b889cf62219e1887ef31f4adc2fffe039e7b3cb0c67c6fdea1b1815c","sha256:355e8ef79d58ea71a7a8cdaa9be82d32fdb4f259011154833377e243b51451d8"],"state_sha256":"b1349aad3b7a4f9f4b161056628c88200288ac9d2c0799ad8bc897f9d03256e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5TBT1H78Q+5xLHE+1KLSptLoenFs3TLY3vlbZ/4S1g6p2d0nhAij0PreeBSY49Uj7B6/DSAXByaZvE7ldb2GDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T09:56:34.909930Z","bundle_sha256":"1286655ad7c3113db755b4f97a7528c651c188fcaaaf6e242e7b045e26f70db5"}}