{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:TIMED4QPUTYX4XRF6ZAROSJ75O","short_pith_number":"pith:TIMED4QP","canonical_record":{"source":{"id":"2101.09267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-01-22T18:39:29Z","cross_cats_sorted":[],"title_canon_sha256":"0319d2cb010ea1fd2efd05b9873eda98dc18cc880ac8be959cdfed0bc82f1b76","abstract_canon_sha256":"e9ea71ed2539e15c1fdb6f13e4ce0cbcf103079a780a6ef6b79bf56a3c705e15"},"schema_version":"1.0"},"canonical_sha256":"9a1841f20fa4f17e5e25f64117493feb913c7ac815ff007f6bb19f37900ac862","source":{"kind":"arxiv","id":"2101.09267","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.09267","created_at":"2026-07-05T03:14:33Z"},{"alias_kind":"arxiv_version","alias_value":"2101.09267v1","created_at":"2026-07-05T03:14:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.09267","created_at":"2026-07-05T03:14:33Z"},{"alias_kind":"pith_short_12","alias_value":"TIMED4QPUTYX","created_at":"2026-07-05T03:14:33Z"},{"alias_kind":"pith_short_16","alias_value":"TIMED4QPUTYX4XRF","created_at":"2026-07-05T03:14:33Z"},{"alias_kind":"pith_short_8","alias_value":"TIMED4QP","created_at":"2026-07-05T03:14:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:TIMED4QPUTYX4XRF6ZAROSJ75O","target":"record","payload":{"canonical_record":{"source":{"id":"2101.09267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-01-22T18:39:29Z","cross_cats_sorted":[],"title_canon_sha256":"0319d2cb010ea1fd2efd05b9873eda98dc18cc880ac8be959cdfed0bc82f1b76","abstract_canon_sha256":"e9ea71ed2539e15c1fdb6f13e4ce0cbcf103079a780a6ef6b79bf56a3c705e15"},"schema_version":"1.0"},"canonical_sha256":"9a1841f20fa4f17e5e25f64117493feb913c7ac815ff007f6bb19f37900ac862","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:14:33.238949Z","signature_b64":"VY0cJKZJeaH9mNLBj8GEBkBy0a9c5WZV+mn5Q/k6Azhy2NA6VH0y0gubL3Zp3b73poET06e/RWl5/7vSIgsQDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a1841f20fa4f17e5e25f64117493feb913c7ac815ff007f6bb19f37900ac862","last_reissued_at":"2026-07-05T03:14:33.238465Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:14:33.238465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2101.09267","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":"2026-07-05T03:14:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F7qKcgpDiQh0cjhUO62RkD7gir7Af9qXkdN5hv410mqvtjDFz+7v7AIT89OenXSy/EBpaGRfUhhsSvQsDsyQDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T18:48:41.039865Z"},"content_sha256":"e0e24fd4efa60ad7b9c87d0e6725dc8e3cdf8065c4c21a3713a34611d09031c1","schema_version":"1.0","event_id":"sha256:e0e24fd4efa60ad7b9c87d0e6725dc8e3cdf8065c4c21a3713a34611d09031c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:TIMED4QPUTYX4XRF6ZAROSJ75O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Set characterizations and convex extensions for geometric convex-hull proofs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andreas B\\\"armann, Oskar Schneider","submitted_at":"2021-01-22T18:39:29Z","abstract_excerpt":"In the present work, we consider Zuckerberg's method for geometric convex-hull proofs introduced in [Geometric proofs for convex hull defining formulations, Operations Research Letters 44(5), 625-629 (2016)]. It has only been scarcely adopted in the literature so far, despite the great flexibility in designing algorithmic proofs for the completeness of polyhedral descriptions that it offers. We suspect that this is partly due to the rather heavy algebraic framework its original statement entails. This is why we present a much more lightweight and accessible approach to Zuckerberg's proof techn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.09267","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2101.09267/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:14:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qurd94aeXTZndR7Pei7b175z5YXsrjEfxObwPcnbbOnn3NPiTsGMFgQTy5q9JB/YkQL0KMPiRJQAKuEeG4g5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T18:48:41.040338Z"},"content_sha256":"52cf5cd74e5e622fe1506f01ee0f7bb419cd8ff0ca986eeb12814bcee7b5b2b8","schema_version":"1.0","event_id":"sha256:52cf5cd74e5e622fe1506f01ee0f7bb419cd8ff0ca986eeb12814bcee7b5b2b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TIMED4QPUTYX4XRF6ZAROSJ75O/bundle.json","state_url":"https://pith.science/pith/TIMED4QPUTYX4XRF6ZAROSJ75O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TIMED4QPUTYX4XRF6ZAROSJ75O/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":"2026-08-03T18:48:41Z","links":{"resolver":"https://pith.science/pith/TIMED4QPUTYX4XRF6ZAROSJ75O","bundle":"https://pith.science/pith/TIMED4QPUTYX4XRF6ZAROSJ75O/bundle.json","state":"https://pith.science/pith/TIMED4QPUTYX4XRF6ZAROSJ75O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TIMED4QPUTYX4XRF6ZAROSJ75O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:TIMED4QPUTYX4XRF6ZAROSJ75O","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":"e9ea71ed2539e15c1fdb6f13e4ce0cbcf103079a780a6ef6b79bf56a3c705e15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-01-22T18:39:29Z","title_canon_sha256":"0319d2cb010ea1fd2efd05b9873eda98dc18cc880ac8be959cdfed0bc82f1b76"},"schema_version":"1.0","source":{"id":"2101.09267","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.09267","created_at":"2026-07-05T03:14:33Z"},{"alias_kind":"arxiv_version","alias_value":"2101.09267v1","created_at":"2026-07-05T03:14:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.09267","created_at":"2026-07-05T03:14:33Z"},{"alias_kind":"pith_short_12","alias_value":"TIMED4QPUTYX","created_at":"2026-07-05T03:14:33Z"},{"alias_kind":"pith_short_16","alias_value":"TIMED4QPUTYX4XRF","created_at":"2026-07-05T03:14:33Z"},{"alias_kind":"pith_short_8","alias_value":"TIMED4QP","created_at":"2026-07-05T03:14:33Z"}],"graph_snapshots":[{"event_id":"sha256:52cf5cd74e5e622fe1506f01ee0f7bb419cd8ff0ca986eeb12814bcee7b5b2b8","target":"graph","created_at":"2026-07-05T03:14:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2101.09267/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the present work, we consider Zuckerberg's method for geometric convex-hull proofs introduced in [Geometric proofs for convex hull defining formulations, Operations Research Letters 44(5), 625-629 (2016)]. It has only been scarcely adopted in the literature so far, despite the great flexibility in designing algorithmic proofs for the completeness of polyhedral descriptions that it offers. We suspect that this is partly due to the rather heavy algebraic framework its original statement entails. This is why we present a much more lightweight and accessible approach to Zuckerberg's proof techn","authors_text":"Andreas B\\\"armann, Oskar Schneider","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-01-22T18:39:29Z","title":"Set characterizations and convex extensions for geometric convex-hull proofs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.09267","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:e0e24fd4efa60ad7b9c87d0e6725dc8e3cdf8065c4c21a3713a34611d09031c1","target":"record","created_at":"2026-07-05T03:14:33Z","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":"e9ea71ed2539e15c1fdb6f13e4ce0cbcf103079a780a6ef6b79bf56a3c705e15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-01-22T18:39:29Z","title_canon_sha256":"0319d2cb010ea1fd2efd05b9873eda98dc18cc880ac8be959cdfed0bc82f1b76"},"schema_version":"1.0","source":{"id":"2101.09267","kind":"arxiv","version":1}},"canonical_sha256":"9a1841f20fa4f17e5e25f64117493feb913c7ac815ff007f6bb19f37900ac862","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a1841f20fa4f17e5e25f64117493feb913c7ac815ff007f6bb19f37900ac862","first_computed_at":"2026-07-05T03:14:33.238465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:14:33.238465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VY0cJKZJeaH9mNLBj8GEBkBy0a9c5WZV+mn5Q/k6Azhy2NA6VH0y0gubL3Zp3b73poET06e/RWl5/7vSIgsQDA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:14:33.238949Z","signed_message":"canonical_sha256_bytes"},"source_id":"2101.09267","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0e24fd4efa60ad7b9c87d0e6725dc8e3cdf8065c4c21a3713a34611d09031c1","sha256:52cf5cd74e5e622fe1506f01ee0f7bb419cd8ff0ca986eeb12814bcee7b5b2b8"],"state_sha256":"95164344f39d5c0c9386fbbc626bdd05075c60214f2cdca8d8ea7958459563de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jxZ381Gc81/XHeb2sjvb10iE9l/WsN9vKQ9oLHIUwZ6ZL1rFMwujGsfo0xcxDOPtARN4COg0/HjJeDiH8T1vCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T18:48:41.043546Z","bundle_sha256":"09330b1b78837348b58301c12c36e8a6945fbfa6bd9ce3a4bb2e6d51e5f3500d"}}