{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:XUNN4BBU7U4ZG5FUJQJ5V5K4AO","short_pith_number":"pith:XUNN4BBU","canonical_record":{"source":{"id":"2106.03724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2021-06-07T15:39:18Z","cross_cats_sorted":[],"title_canon_sha256":"06e756db3aa60b956ab1378bae7959b5b364fc8c5c2b08b86152f4047d9aca5e","abstract_canon_sha256":"88313b0386390d9e2bfc6d80a3f050b17c6316eef8faff6a9d0576818160b487"},"schema_version":"1.0"},"canonical_sha256":"bd1ade0434fd399374b44c13daf55c03ba792a14229232baa6ba7791f7581b42","source":{"kind":"arxiv","id":"2106.03724","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.03724","created_at":"2026-07-05T02:46:52Z"},{"alias_kind":"arxiv_version","alias_value":"2106.03724v1","created_at":"2026-07-05T02:46:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.03724","created_at":"2026-07-05T02:46:52Z"},{"alias_kind":"pith_short_12","alias_value":"XUNN4BBU7U4Z","created_at":"2026-07-05T02:46:52Z"},{"alias_kind":"pith_short_16","alias_value":"XUNN4BBU7U4ZG5FU","created_at":"2026-07-05T02:46:52Z"},{"alias_kind":"pith_short_8","alias_value":"XUNN4BBU","created_at":"2026-07-05T02:46:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:XUNN4BBU7U4ZG5FUJQJ5V5K4AO","target":"record","payload":{"canonical_record":{"source":{"id":"2106.03724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2021-06-07T15:39:18Z","cross_cats_sorted":[],"title_canon_sha256":"06e756db3aa60b956ab1378bae7959b5b364fc8c5c2b08b86152f4047d9aca5e","abstract_canon_sha256":"88313b0386390d9e2bfc6d80a3f050b17c6316eef8faff6a9d0576818160b487"},"schema_version":"1.0"},"canonical_sha256":"bd1ade0434fd399374b44c13daf55c03ba792a14229232baa6ba7791f7581b42","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:46:52.513081Z","signature_b64":"zQ8HJ0E5PfRkJDVODVRzH4DdN5VzTmcKzE8HuWIeZr5Bk4qqMmlNUo9581rMUHdtCYphtafipahYhHpdc1IzAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd1ade0434fd399374b44c13daf55c03ba792a14229232baa6ba7791f7581b42","last_reissued_at":"2026-07-05T02:46:52.512619Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:46:52.512619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.03724","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":"2026-07-05T02:46:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X2oaWDqHVyDLtYJMeXJwDtbCWZCV3PPN8XnGK0QmlHw317Nrtra43+VyuOkfJikjxhU/CH2Zn7r9sszs31gyCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T13:23:13.535300Z"},"content_sha256":"cc4d074411f916ae450a909735952e7c66ee3a7045adb14b211c87243a09b388","schema_version":"1.0","event_id":"sha256:cc4d074411f916ae450a909735952e7c66ee3a7045adb14b211c87243a09b388"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:XUNN4BBU7U4ZG5FUJQJ5V5K4AO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Truthful allocation in graphs and hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Annamaria Kovacs, Elias Koutsoupias, George Christodoulou","submitted_at":"2021-06-07T15:39:18Z","abstract_excerpt":"We study truthful mechanisms for allocation problems in graphs, both for the minimization (i.e., scheduling) and maximization (i.e., auctions) setting. The minimization problem is a special case of the well-studied unrelated machines scheduling problem, in which every given task can be executed only by two pre-specified machines in the case of graphs or a given subset of machines in the case of hypergraphs. This corresponds to a multigraph whose nodes are the machines and its hyperedges are the tasks. This class of problems belongs to multidimensional mechanism design, for which there are no k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.03724","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/2106.03724/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":"2026-07-05T02:46:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iOb6ay9ISOYQVJcdQtNG4idQSjTTBmCSln2kPDo1UHP6RXGG8o9d1I0F0reOu9fWub7duZbP0eItB3XRW/ToAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T13:23:13.535817Z"},"content_sha256":"9dd5213dda3752597bfe46d687549939759f779e3427fcf038e57697d3911604","schema_version":"1.0","event_id":"sha256:9dd5213dda3752597bfe46d687549939759f779e3427fcf038e57697d3911604"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XUNN4BBU7U4ZG5FUJQJ5V5K4AO/bundle.json","state_url":"https://pith.science/pith/XUNN4BBU7U4ZG5FUJQJ5V5K4AO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XUNN4BBU7U4ZG5FUJQJ5V5K4AO/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":"2026-08-15T13:23:13Z","links":{"resolver":"https://pith.science/pith/XUNN4BBU7U4ZG5FUJQJ5V5K4AO","bundle":"https://pith.science/pith/XUNN4BBU7U4ZG5FUJQJ5V5K4AO/bundle.json","state":"https://pith.science/pith/XUNN4BBU7U4ZG5FUJQJ5V5K4AO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XUNN4BBU7U4ZG5FUJQJ5V5K4AO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:XUNN4BBU7U4ZG5FUJQJ5V5K4AO","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":"88313b0386390d9e2bfc6d80a3f050b17c6316eef8faff6a9d0576818160b487","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2021-06-07T15:39:18Z","title_canon_sha256":"06e756db3aa60b956ab1378bae7959b5b364fc8c5c2b08b86152f4047d9aca5e"},"schema_version":"1.0","source":{"id":"2106.03724","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.03724","created_at":"2026-07-05T02:46:52Z"},{"alias_kind":"arxiv_version","alias_value":"2106.03724v1","created_at":"2026-07-05T02:46:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.03724","created_at":"2026-07-05T02:46:52Z"},{"alias_kind":"pith_short_12","alias_value":"XUNN4BBU7U4Z","created_at":"2026-07-05T02:46:52Z"},{"alias_kind":"pith_short_16","alias_value":"XUNN4BBU7U4ZG5FU","created_at":"2026-07-05T02:46:52Z"},{"alias_kind":"pith_short_8","alias_value":"XUNN4BBU","created_at":"2026-07-05T02:46:52Z"}],"graph_snapshots":[{"event_id":"sha256:9dd5213dda3752597bfe46d687549939759f779e3427fcf038e57697d3911604","target":"graph","created_at":"2026-07-05T02:46:52Z","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/2106.03724/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study truthful mechanisms for allocation problems in graphs, both for the minimization (i.e., scheduling) and maximization (i.e., auctions) setting. The minimization problem is a special case of the well-studied unrelated machines scheduling problem, in which every given task can be executed only by two pre-specified machines in the case of graphs or a given subset of machines in the case of hypergraphs. This corresponds to a multigraph whose nodes are the machines and its hyperedges are the tasks. This class of problems belongs to multidimensional mechanism design, for which there are no k","authors_text":"Annamaria Kovacs, Elias Koutsoupias, George Christodoulou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2021-06-07T15:39:18Z","title":"Truthful allocation in graphs and hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.03724","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:cc4d074411f916ae450a909735952e7c66ee3a7045adb14b211c87243a09b388","target":"record","created_at":"2026-07-05T02:46:52Z","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":"88313b0386390d9e2bfc6d80a3f050b17c6316eef8faff6a9d0576818160b487","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2021-06-07T15:39:18Z","title_canon_sha256":"06e756db3aa60b956ab1378bae7959b5b364fc8c5c2b08b86152f4047d9aca5e"},"schema_version":"1.0","source":{"id":"2106.03724","kind":"arxiv","version":1}},"canonical_sha256":"bd1ade0434fd399374b44c13daf55c03ba792a14229232baa6ba7791f7581b42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd1ade0434fd399374b44c13daf55c03ba792a14229232baa6ba7791f7581b42","first_computed_at":"2026-07-05T02:46:52.512619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:46:52.512619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zQ8HJ0E5PfRkJDVODVRzH4DdN5VzTmcKzE8HuWIeZr5Bk4qqMmlNUo9581rMUHdtCYphtafipahYhHpdc1IzAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:46:52.513081Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.03724","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc4d074411f916ae450a909735952e7c66ee3a7045adb14b211c87243a09b388","sha256:9dd5213dda3752597bfe46d687549939759f779e3427fcf038e57697d3911604"],"state_sha256":"38e36876f97c9e566331db5f5ed2f3e72f4564cd0435a38a0ef8c698d5bae7bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BrEpqVIvIrosVPXJgoKCBxiAIiZV4UpU8Z+OHo4b9RdPRgfREu6LdA3ecwQhgT98GVvGSETTcqyPXVTPnMADCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T13:23:13.541838Z","bundle_sha256":"9459a3734960b51be35c0d50899f081bfad6cbd9369eb9fcabcb9036a92561c0"}}