{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:4PEIJSCUUQC6A75TMGG4PCQI6C","short_pith_number":"pith:4PEIJSCU","canonical_record":{"source":{"id":"math/0202204","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2002-02-20T13:27:04Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"6e0f52467ab8fa14ebe0ec06f05ce71bfdc74dc74aafb0e1f793c13b69bf22d5","abstract_canon_sha256":"d6971f1500b82d0a995eb6dc40cbda084972f4d9d77a606db1bbbd892341b099"},"schema_version":"1.0"},"canonical_sha256":"e3c884c854a405e07fb3618dc78a08f0a6772c888f4fa193f214d602daf8c235","source":{"kind":"arxiv","id":"math/0202204","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0202204","created_at":"2026-07-04T14:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"math/0202204v1","created_at":"2026-07-04T14:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0202204","created_at":"2026-07-04T14:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"4PEIJSCUUQC6","created_at":"2026-07-04T14:35:55Z"},{"alias_kind":"pith_short_16","alias_value":"4PEIJSCUUQC6A75T","created_at":"2026-07-04T14:35:55Z"},{"alias_kind":"pith_short_8","alias_value":"4PEIJSCU","created_at":"2026-07-04T14:35:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:4PEIJSCUUQC6A75TMGG4PCQI6C","target":"record","payload":{"canonical_record":{"source":{"id":"math/0202204","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2002-02-20T13:27:04Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"6e0f52467ab8fa14ebe0ec06f05ce71bfdc74dc74aafb0e1f793c13b69bf22d5","abstract_canon_sha256":"d6971f1500b82d0a995eb6dc40cbda084972f4d9d77a606db1bbbd892341b099"},"schema_version":"1.0"},"canonical_sha256":"e3c884c854a405e07fb3618dc78a08f0a6772c888f4fa193f214d602daf8c235","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:35:55.913297Z","signature_b64":"NuQJqnaAZsJU29glxzn6w0+kmZ7mXXuSvSK+Utx3QrF61QGp60HWAd92UoC6vDUr2VNO5shI28YIDFP1jwATDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3c884c854a405e07fb3618dc78a08f0a6772c888f4fa193f214d602daf8c235","last_reissued_at":"2026-07-04T14:35:55.912940Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:35:55.912940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0202204","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":"2026-07-04T14:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GoQTxKs4/OyBhJZoIyZfF3f6iQN8XV/lV1J9xZggJ78oE53TItI/CzExLfyeLuV5MlXf4D7o4PzDptP6aK3xCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T12:11:16.641470Z"},"content_sha256":"939e7e07a4cc59823b8ef21f9991d4c6b1dd1295bb44caa522551ca8afbbada7","schema_version":"1.0","event_id":"sha256:939e7e07a4cc59823b8ef21f9991d4c6b1dd1295bb44caa522551ca8afbbada7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:4PEIJSCUUQC6A75TMGG4PCQI6C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some Algorithmic Problems in Polytope Theory","license":"","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Marc E. Pfetsch, Volker Kaibel","submitted_at":"2002-02-20T13:27:04Z","abstract_excerpt":"This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The problems are grouped into the sections ``Coordinate Descriptions'', ``Combinatorial Structure'', ``Isomorphism'', ``Optimization'', ``Realizability'', and ``Beyond Polytopes''."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0202204","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/math/0202204/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":"2026-07-04T14:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EuN62P+GTZnLSLswoU9dQT+eF93d7YoNrDriiNTxDlg7Eu5kAXa1fKa9Nwx4wHQp2xNXnj4mKjuvDGkaxpmSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T12:11:16.641838Z"},"content_sha256":"a21bfed4e322e82184abaade93c7313f9f4fbd8b57dca21b0899a16ee03c31a6","schema_version":"1.0","event_id":"sha256:a21bfed4e322e82184abaade93c7313f9f4fbd8b57dca21b0899a16ee03c31a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4PEIJSCUUQC6A75TMGG4PCQI6C/bundle.json","state_url":"https://pith.science/pith/4PEIJSCUUQC6A75TMGG4PCQI6C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4PEIJSCUUQC6A75TMGG4PCQI6C/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":"2026-07-07T12:11:16Z","links":{"resolver":"https://pith.science/pith/4PEIJSCUUQC6A75TMGG4PCQI6C","bundle":"https://pith.science/pith/4PEIJSCUUQC6A75TMGG4PCQI6C/bundle.json","state":"https://pith.science/pith/4PEIJSCUUQC6A75TMGG4PCQI6C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4PEIJSCUUQC6A75TMGG4PCQI6C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:4PEIJSCUUQC6A75TMGG4PCQI6C","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":"d6971f1500b82d0a995eb6dc40cbda084972f4d9d77a606db1bbbd892341b099","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"math.CO","submitted_at":"2002-02-20T13:27:04Z","title_canon_sha256":"6e0f52467ab8fa14ebe0ec06f05ce71bfdc74dc74aafb0e1f793c13b69bf22d5"},"schema_version":"1.0","source":{"id":"math/0202204","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0202204","created_at":"2026-07-04T14:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"math/0202204v1","created_at":"2026-07-04T14:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0202204","created_at":"2026-07-04T14:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"4PEIJSCUUQC6","created_at":"2026-07-04T14:35:55Z"},{"alias_kind":"pith_short_16","alias_value":"4PEIJSCUUQC6A75T","created_at":"2026-07-04T14:35:55Z"},{"alias_kind":"pith_short_8","alias_value":"4PEIJSCU","created_at":"2026-07-04T14:35:55Z"}],"graph_snapshots":[{"event_id":"sha256:a21bfed4e322e82184abaade93c7313f9f4fbd8b57dca21b0899a16ee03c31a6","target":"graph","created_at":"2026-07-04T14:35:55Z","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/math/0202204/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The problems are grouped into the sections ``Coordinate Descriptions'', ``Combinatorial Structure'', ``Isomorphism'', ``Optimization'', ``Realizability'', and ``Beyond Polytopes''.","authors_text":"Marc E. Pfetsch, Volker Kaibel","cross_cats":["math.MG"],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2002-02-20T13:27:04Z","title":"Some Algorithmic Problems in Polytope Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0202204","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":"sha256:939e7e07a4cc59823b8ef21f9991d4c6b1dd1295bb44caa522551ca8afbbada7","target":"record","created_at":"2026-07-04T14:35:55Z","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":"d6971f1500b82d0a995eb6dc40cbda084972f4d9d77a606db1bbbd892341b099","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"math.CO","submitted_at":"2002-02-20T13:27:04Z","title_canon_sha256":"6e0f52467ab8fa14ebe0ec06f05ce71bfdc74dc74aafb0e1f793c13b69bf22d5"},"schema_version":"1.0","source":{"id":"math/0202204","kind":"arxiv","version":1}},"canonical_sha256":"e3c884c854a405e07fb3618dc78a08f0a6772c888f4fa193f214d602daf8c235","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3c884c854a405e07fb3618dc78a08f0a6772c888f4fa193f214d602daf8c235","first_computed_at":"2026-07-04T14:35:55.912940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:35:55.912940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NuQJqnaAZsJU29glxzn6w0+kmZ7mXXuSvSK+Utx3QrF61QGp60HWAd92UoC6vDUr2VNO5shI28YIDFP1jwATDw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:35:55.913297Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0202204","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:939e7e07a4cc59823b8ef21f9991d4c6b1dd1295bb44caa522551ca8afbbada7","sha256:a21bfed4e322e82184abaade93c7313f9f4fbd8b57dca21b0899a16ee03c31a6"],"state_sha256":"c3ae6b014effea782874f7a2f916dbff20e9e3e00e32f98dc49b3f08adf5bbfa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wXpTJLVtKIMWziEixvuJeQDbUPpkKZTkQsrbKfFUFHHsjsb3+e5l1Ht67vDwy8Q5VeJo9RqIZrSMo8aiHg73Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T12:11:16.643779Z","bundle_sha256":"64d01bf69b200448ef28ca8ec3e8d040abe344895516f550f4c54e01cdc78256"}}