{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OUY5D6SRGL6RDDWGNUSPEENSVJ","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":"f8a0a20d2e980c92358348e5245a78f67dea02e44cdd7a6a00ee906106cc753c","cross_cats_sorted":["cs.AI","cs.LG","cs.MA","econ.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2026-07-25T17:53:10Z","title_canon_sha256":"f50a2e4eacf7b02c92f8d43bd4575d1f86e0c1e8ca5c799ede4f31d8ce642636"},"schema_version":"1.0","source":{"id":"2607.23310","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23310","created_at":"2026-07-28T01:22:47Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23310v1","created_at":"2026-07-28T01:22:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23310","created_at":"2026-07-28T01:22:47Z"},{"alias_kind":"pith_short_12","alias_value":"OUY5D6SRGL6R","created_at":"2026-07-28T01:22:47Z"},{"alias_kind":"pith_short_16","alias_value":"OUY5D6SRGL6RDDWG","created_at":"2026-07-28T01:22:47Z"},{"alias_kind":"pith_short_8","alias_value":"OUY5D6SR","created_at":"2026-07-28T01:22:47Z"}],"graph_snapshots":[{"event_id":"sha256:3c1178a61f27123c601a2e59bf82f5bd3107f007a8d7b5e28bb20048297e4372","target":"graph","created_at":"2026-07-28T01:22:47Z","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/2607.23310/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study an online variant of discrete fair division under generalized assignment budget constraints. Goods arrive one at a time and must be assigned irrevocably to a feasible agent or to charity, which holds all unallocated goods, while fairness is evaluated only against budget-feasible subsets of every recipient's bundle. We first show that, without additional structure, no deterministic online algorithm can guarantee any fixed approximation to feasible envy-freeness, even in highly symmetric instances. We then identify bounded density spread as a structural condition that restores meaningfu","authors_text":"Michael J. Wooldridge, Nicholas Teh, Paul W. Goldberg, Saar Cohen","cross_cats":["cs.AI","cs.LG","cs.MA","econ.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2026-07-25T17:53:10Z","title":"Online Fair Division with Budget Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23310","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":"sha256:5dd2b499a3db7d6afa653393faf681478f943d12f9643c115db3ec2764828a21","target":"record","created_at":"2026-07-28T01:22:47Z","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":"f8a0a20d2e980c92358348e5245a78f67dea02e44cdd7a6a00ee906106cc753c","cross_cats_sorted":["cs.AI","cs.LG","cs.MA","econ.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2026-07-25T17:53:10Z","title_canon_sha256":"f50a2e4eacf7b02c92f8d43bd4575d1f86e0c1e8ca5c799ede4f31d8ce642636"},"schema_version":"1.0","source":{"id":"2607.23310","kind":"arxiv","version":1}},"canonical_sha256":"7531d1fa5132fd118ec66d24f211b2aa4ea76c667d44377e55f96222e85c2edf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7531d1fa5132fd118ec66d24f211b2aa4ea76c667d44377e55f96222e85c2edf","first_computed_at":"2026-07-28T01:22:47.144610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T01:22:47.144610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6BE1PtemyWZwl+3CF2+VTftdqYHC3SRm6FXjI4EXz4rGZRlAj/eko1FWG4jg9vpze8umAKRNsynknWZsIghKDg==","signature_status":"signed_v1","signed_at":"2026-07-28T01:22:47.145427Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.23310","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dd2b499a3db7d6afa653393faf681478f943d12f9643c115db3ec2764828a21","sha256:3c1178a61f27123c601a2e59bf82f5bd3107f007a8d7b5e28bb20048297e4372"],"state_sha256":"bade348e7e0df13e5d8cf4485639663018348298a3bd6fafee9fe6af91e64e25"}