{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SYGO2F7T2Z7FCHZCMJCVICG22P","short_pith_number":"pith:SYGO2F7T","canonical_record":{"source":{"id":"1307.6414","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-07-24T13:36:15Z","cross_cats_sorted":["cs.CG","math.MG","math.OC"],"title_canon_sha256":"ba90b7ae8b74aebde847cfe8cf6d3ed027a04df1e026643efee6484477211bd8","abstract_canon_sha256":"1964f165929c05c27e75774ff87db61f3b133426bc7c7ccf18f49b17b2aff99d"},"schema_version":"1.0"},"canonical_sha256":"960ced17f3d67e511f2262455408dad3fb87338d43f019ecbc548edc920440e3","source":{"kind":"arxiv","id":"1307.6414","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6414","created_at":"2026-05-18T03:17:36Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6414v1","created_at":"2026-05-18T03:17:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6414","created_at":"2026-05-18T03:17:36Z"},{"alias_kind":"pith_short_12","alias_value":"SYGO2F7T2Z7F","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SYGO2F7T2Z7FCHZC","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SYGO2F7T","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SYGO2F7T2Z7FCHZCMJCVICG22P","target":"record","payload":{"canonical_record":{"source":{"id":"1307.6414","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-07-24T13:36:15Z","cross_cats_sorted":["cs.CG","math.MG","math.OC"],"title_canon_sha256":"ba90b7ae8b74aebde847cfe8cf6d3ed027a04df1e026643efee6484477211bd8","abstract_canon_sha256":"1964f165929c05c27e75774ff87db61f3b133426bc7c7ccf18f49b17b2aff99d"},"schema_version":"1.0"},"canonical_sha256":"960ced17f3d67e511f2262455408dad3fb87338d43f019ecbc548edc920440e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:36.585118Z","signature_b64":"vnLqCgxK2It5ezrMIrqr48eLgwZUa1DbJA7RWo9fXgiAZKhvZBnqpEHvf0yX87xIrR7lX5K1Ix4GEZFZ/4DfBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"960ced17f3d67e511f2262455408dad3fb87338d43f019ecbc548edc920440e3","last_reissued_at":"2026-05-18T03:17:36.584479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:36.584479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.6414","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":"2026-05-18T03:17:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WAEgzB5jLa99jQL/e2Wd72Vts8+u6EI8Z1+R3CVjx2wMOY+iyOaQHCWsXPWIDDd0PxnpFQ40OguBaWLForxBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:25:15.482062Z"},"content_sha256":"b163109cfc23ea624453e36abe944db5371a19ad3fa8055288db5e286629398f","schema_version":"1.0","event_id":"sha256:b163109cfc23ea624453e36abe944db5371a19ad3fa8055288db5e286629398f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SYGO2F7T2Z7FCHZCMJCVICG22P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fixed Parameter Complexity and Approximability of Norm Maximization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.MG","math.OC"],"primary_cat":"cs.CC","authors_text":"Christian Knauer, Daniel Werner, Stefan K\\\"onig","submitted_at":"2013-07-24T13:36:15Z","abstract_excerpt":"The problem of maximizing the $p$-th power of a $p$-norm over a halfspace-presented polytope in $\\R^d$ is a convex maximization problem which plays a fundamental role in computational convexity. It has been shown in 1986 that this problem is $\\NP$-hard for all values $p \\in \\mathbb{N}$, if the dimension $d$ of the ambient space is part of the input. In this paper, we use the theory of parametrized complexity to analyze how heavily the hardness of norm maximization relies on the parameter $d$.\n  More precisely, we show that for $p=1$ the problem is fixed parameter tractable but that for all $p "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6414","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":"2026-05-18T03:17:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z2V/uCMT+1J6THvgAsPT4YKp7Foaq4VptSQdqZIeKVj9OGeZ7kXMJKX3WCx6b1ssidvPi85d26p/BOHO6HniBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:25:15.482423Z"},"content_sha256":"7e2fd65dab2997e491004142f84a90fd8a3ab787bc9f3e2a3b444c61f68c35bb","schema_version":"1.0","event_id":"sha256:7e2fd65dab2997e491004142f84a90fd8a3ab787bc9f3e2a3b444c61f68c35bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SYGO2F7T2Z7FCHZCMJCVICG22P/bundle.json","state_url":"https://pith.science/pith/SYGO2F7T2Z7FCHZCMJCVICG22P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SYGO2F7T2Z7FCHZCMJCVICG22P/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":"2026-06-02T18:25:15Z","links":{"resolver":"https://pith.science/pith/SYGO2F7T2Z7FCHZCMJCVICG22P","bundle":"https://pith.science/pith/SYGO2F7T2Z7FCHZCMJCVICG22P/bundle.json","state":"https://pith.science/pith/SYGO2F7T2Z7FCHZCMJCVICG22P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SYGO2F7T2Z7FCHZCMJCVICG22P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SYGO2F7T2Z7FCHZCMJCVICG22P","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":"1964f165929c05c27e75774ff87db61f3b133426bc7c7ccf18f49b17b2aff99d","cross_cats_sorted":["cs.CG","math.MG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-07-24T13:36:15Z","title_canon_sha256":"ba90b7ae8b74aebde847cfe8cf6d3ed027a04df1e026643efee6484477211bd8"},"schema_version":"1.0","source":{"id":"1307.6414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6414","created_at":"2026-05-18T03:17:36Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6414v1","created_at":"2026-05-18T03:17:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6414","created_at":"2026-05-18T03:17:36Z"},{"alias_kind":"pith_short_12","alias_value":"SYGO2F7T2Z7F","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SYGO2F7T2Z7FCHZC","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SYGO2F7T","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:7e2fd65dab2997e491004142f84a90fd8a3ab787bc9f3e2a3b444c61f68c35bb","target":"graph","created_at":"2026-05-18T03:17:36Z","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":"The problem of maximizing the $p$-th power of a $p$-norm over a halfspace-presented polytope in $\\R^d$ is a convex maximization problem which plays a fundamental role in computational convexity. It has been shown in 1986 that this problem is $\\NP$-hard for all values $p \\in \\mathbb{N}$, if the dimension $d$ of the ambient space is part of the input. In this paper, we use the theory of parametrized complexity to analyze how heavily the hardness of norm maximization relies on the parameter $d$.\n  More precisely, we show that for $p=1$ the problem is fixed parameter tractable but that for all $p ","authors_text":"Christian Knauer, Daniel Werner, Stefan K\\\"onig","cross_cats":["cs.CG","math.MG","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-07-24T13:36:15Z","title":"Fixed Parameter Complexity and Approximability of Norm Maximization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6414","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:b163109cfc23ea624453e36abe944db5371a19ad3fa8055288db5e286629398f","target":"record","created_at":"2026-05-18T03:17:36Z","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":"1964f165929c05c27e75774ff87db61f3b133426bc7c7ccf18f49b17b2aff99d","cross_cats_sorted":["cs.CG","math.MG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-07-24T13:36:15Z","title_canon_sha256":"ba90b7ae8b74aebde847cfe8cf6d3ed027a04df1e026643efee6484477211bd8"},"schema_version":"1.0","source":{"id":"1307.6414","kind":"arxiv","version":1}},"canonical_sha256":"960ced17f3d67e511f2262455408dad3fb87338d43f019ecbc548edc920440e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"960ced17f3d67e511f2262455408dad3fb87338d43f019ecbc548edc920440e3","first_computed_at":"2026-05-18T03:17:36.584479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:36.584479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vnLqCgxK2It5ezrMIrqr48eLgwZUa1DbJA7RWo9fXgiAZKhvZBnqpEHvf0yX87xIrR7lX5K1Ix4GEZFZ/4DfBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:36.585118Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.6414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b163109cfc23ea624453e36abe944db5371a19ad3fa8055288db5e286629398f","sha256:7e2fd65dab2997e491004142f84a90fd8a3ab787bc9f3e2a3b444c61f68c35bb"],"state_sha256":"49c9f2bfa86f3f1caf257e8873339bb9ccd59da7688fba35dfd901db8f9f146e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QFdChyvFoCZrxxBk1zdUiU4Vh0ipB5VQhGfdSSSvv/Wi8rPiv1BKZ3XykHgUztLn6nwSoLv5WeC6Zi7ZFfFgAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T18:25:15.484360Z","bundle_sha256":"cbf555ebc806056fcb5d3d815831bb324d618659bb173f8fd9107a3899b9508f"}}