{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:V7FDK4LL7OUZZQ2RNGOH7GPM5N","short_pith_number":"pith:V7FDK4LL","canonical_record":{"source":{"id":"1603.07210","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-03-23T14:53:44Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"34bd1bc2021aca9e2ff6fed0fe2a2e1b311555e0d93c0cf4067811094f9dbdea","abstract_canon_sha256":"f0c801805c75762103522b267633e9962321967f4c3d152b75c63f3c84db2236"},"schema_version":"1.0"},"canonical_sha256":"afca35716bfba99cc351699c7f99eceb5216cdcf585aa41151096bb219ff69a4","source":{"kind":"arxiv","id":"1603.07210","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07210","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07210v2","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07210","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"V7FDK4LL7OUZ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"V7FDK4LL7OUZZQ2R","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"V7FDK4LL","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:V7FDK4LL7OUZZQ2RNGOH7GPM5N","target":"record","payload":{"canonical_record":{"source":{"id":"1603.07210","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-03-23T14:53:44Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"34bd1bc2021aca9e2ff6fed0fe2a2e1b311555e0d93c0cf4067811094f9dbdea","abstract_canon_sha256":"f0c801805c75762103522b267633e9962321967f4c3d152b75c63f3c84db2236"},"schema_version":"1.0"},"canonical_sha256":"afca35716bfba99cc351699c7f99eceb5216cdcf585aa41151096bb219ff69a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:57.358693Z","signature_b64":"ln2z/Qunuw3GBcQBYCW1apaQX9WRXCDOS6OE7mM2pMILCed2zBFDxaq729bc9eqKt/eKDsdi7L8+DwsIbiQsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afca35716bfba99cc351699c7f99eceb5216cdcf585aa41151096bb219ff69a4","last_reissued_at":"2026-05-18T01:15:57.357999Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:57.357999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.07210","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:15:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5k3Kl9qVtjZtLd6h7A3fdUszwrEhPEHrjM9Xtq7LGqyZcxgKdg9cFOI7zJjmMxkI2N3cERABcncRzN1usSkSCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T06:21:29.877300Z"},"content_sha256":"e6c50c60396e858edad2745bab59a71f7b64737117d5e178286ec74eb0aa1624","schema_version":"1.0","event_id":"sha256:e6c50c60396e858edad2745bab59a71f7b64737117d5e178286ec74eb0aa1624"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:V7FDK4LL7OUZZQ2RNGOH7GPM5N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing Equilibria in Markets with Budget-Additive Utilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.GT","authors_text":"Jugal Garg, Kurt Mehlhorn, Martin Hoefer, Xiaohui Bei","submitted_at":"2016-03-23T14:53:44Z","abstract_excerpt":"We present the first analysis of Fisher markets with buyers that have budget-additive utility functions. Budget-additive utilities are elementary concave functions with numerous applications in online adword markets and revenue optimization problems. They extend the standard case of linear utilities and have been studied in a variety of other market models. In contrast to the frequently studied CES utilities, they have a global satiation point which can imply multiple market equilibria with quite different characteristics. Our main result is an efficient combinatorial algorithm to compute a ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07210","kind":"arxiv","version":2},"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":"2026-05-18T01:15:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i7+NZDyMABquiZoRZXN3OjNbFYlqKIT4gPcNbroAOiSOjvrEOxXwxw+ojAcT7H2GqkOx55Ylv1ws7osdcVbnBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T06:21:29.878031Z"},"content_sha256":"449004897378f9a7be2715908bb3f3900c1e9f5651fe0cd5042892691edb9c02","schema_version":"1.0","event_id":"sha256:449004897378f9a7be2715908bb3f3900c1e9f5651fe0cd5042892691edb9c02"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V7FDK4LL7OUZZQ2RNGOH7GPM5N/bundle.json","state_url":"https://pith.science/pith/V7FDK4LL7OUZZQ2RNGOH7GPM5N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V7FDK4LL7OUZZQ2RNGOH7GPM5N/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":"2026-05-26T06:21:29Z","links":{"resolver":"https://pith.science/pith/V7FDK4LL7OUZZQ2RNGOH7GPM5N","bundle":"https://pith.science/pith/V7FDK4LL7OUZZQ2RNGOH7GPM5N/bundle.json","state":"https://pith.science/pith/V7FDK4LL7OUZZQ2RNGOH7GPM5N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V7FDK4LL7OUZZQ2RNGOH7GPM5N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:V7FDK4LL7OUZZQ2RNGOH7GPM5N","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":"f0c801805c75762103522b267633e9962321967f4c3d152b75c63f3c84db2236","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-03-23T14:53:44Z","title_canon_sha256":"34bd1bc2021aca9e2ff6fed0fe2a2e1b311555e0d93c0cf4067811094f9dbdea"},"schema_version":"1.0","source":{"id":"1603.07210","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07210","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07210v2","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07210","created_at":"2026-05-18T01:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"V7FDK4LL7OUZ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"V7FDK4LL7OUZZQ2R","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"V7FDK4LL","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:449004897378f9a7be2715908bb3f3900c1e9f5651fe0cd5042892691edb9c02","target":"graph","created_at":"2026-05-18T01:15:57Z","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":"We present the first analysis of Fisher markets with buyers that have budget-additive utility functions. Budget-additive utilities are elementary concave functions with numerous applications in online adword markets and revenue optimization problems. They extend the standard case of linear utilities and have been studied in a variety of other market models. In contrast to the frequently studied CES utilities, they have a global satiation point which can imply multiple market equilibria with quite different characteristics. Our main result is an efficient combinatorial algorithm to compute a ma","authors_text":"Jugal Garg, Kurt Mehlhorn, Martin Hoefer, Xiaohui Bei","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-03-23T14:53:44Z","title":"Computing Equilibria in Markets with Budget-Additive Utilities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07210","kind":"arxiv","version":2},"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:e6c50c60396e858edad2745bab59a71f7b64737117d5e178286ec74eb0aa1624","target":"record","created_at":"2026-05-18T01:15:57Z","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":"f0c801805c75762103522b267633e9962321967f4c3d152b75c63f3c84db2236","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-03-23T14:53:44Z","title_canon_sha256":"34bd1bc2021aca9e2ff6fed0fe2a2e1b311555e0d93c0cf4067811094f9dbdea"},"schema_version":"1.0","source":{"id":"1603.07210","kind":"arxiv","version":2}},"canonical_sha256":"afca35716bfba99cc351699c7f99eceb5216cdcf585aa41151096bb219ff69a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afca35716bfba99cc351699c7f99eceb5216cdcf585aa41151096bb219ff69a4","first_computed_at":"2026-05-18T01:15:57.357999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:57.357999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ln2z/Qunuw3GBcQBYCW1apaQX9WRXCDOS6OE7mM2pMILCed2zBFDxaq729bc9eqKt/eKDsdi7L8+DwsIbiQsCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:57.358693Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07210","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6c50c60396e858edad2745bab59a71f7b64737117d5e178286ec74eb0aa1624","sha256:449004897378f9a7be2715908bb3f3900c1e9f5651fe0cd5042892691edb9c02"],"state_sha256":"c70f06e124faa383a0786cfaf0b60e995a8df83c67afee09fd81d1cf05524468"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lPEY3V6sZ4FTuhZZymdamZbERfe5TAsFjTMccNYx8eHQsZyDMhKGm9sDYC0Bj1W9F13ajdyvZgYGczHsiA2zCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T06:21:29.881700Z","bundle_sha256":"fc01ac272fa83b824afbc3456e29c64198a26973ec6aca0fe5050bfec8b9e0d8"}}