{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:63NRELHFFN5IYRD4CHKJSYLPIL","short_pith_number":"pith:63NRELHF","canonical_record":{"source":{"id":"2605.13875","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2026-05-08T06:56:35Z","cross_cats_sorted":[],"title_canon_sha256":"ec01d02e8ddaea2090a0c9969382906a7bd8f682e5499ce7de30b309fee65ba3","abstract_canon_sha256":"0d7b2fceed870fc9915bb543fe1bc4aad71a2254498f74720408394b6965a165"},"schema_version":"1.0"},"canonical_sha256":"f6db122ce52b7a8c447c11d499616f42fbb5cdaaa2db7b6b45e455121da19756","source":{"kind":"arxiv","id":"2605.13875","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13875","created_at":"2026-05-17T23:39:19Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13875v1","created_at":"2026-05-17T23:39:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13875","created_at":"2026-05-17T23:39:19Z"},{"alias_kind":"pith_short_12","alias_value":"63NRELHFFN5I","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"63NRELHFFN5IYRD4","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"63NRELHF","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:63NRELHFFN5IYRD4CHKJSYLPIL","target":"record","payload":{"canonical_record":{"source":{"id":"2605.13875","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2026-05-08T06:56:35Z","cross_cats_sorted":[],"title_canon_sha256":"ec01d02e8ddaea2090a0c9969382906a7bd8f682e5499ce7de30b309fee65ba3","abstract_canon_sha256":"0d7b2fceed870fc9915bb543fe1bc4aad71a2254498f74720408394b6965a165"},"schema_version":"1.0"},"canonical_sha256":"f6db122ce52b7a8c447c11d499616f42fbb5cdaaa2db7b6b45e455121da19756","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:19.263731Z","signature_b64":"WzcrMuPSQSdee8hb6nNyW8rcTfw7z55U7gkmVVTJKWiizLKZ2B75LUGODvyhrGPG5dlzFtE7vWJh3HPZoiQvBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6db122ce52b7a8c447c11d499616f42fbb5cdaaa2db7b6b45e455121da19756","last_reissued_at":"2026-05-17T23:39:19.262842Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:19.262842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.13875","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":"2026-05-17T23:39:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iJc6+ut0FrgdLE0K6uXfPs10dv91sKXpRAPozo1R2L3NmpsRUWWHW21c0eGkzMKIPzfwNlESfL5vQyjSoHEVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:15:10.906496Z"},"content_sha256":"b7cf9e4885c957d4c2516545a097d1a414b8470e9dc293ad626183c79024ec7b","schema_version":"1.0","event_id":"sha256:b7cf9e4885c957d4c2516545a097d1a414b8470e9dc293ad626183c79024ec7b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:63NRELHFFN5IYRD4CHKJSYLPIL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Common-agency Games for Multi-Objective Test-Time Alignment","license":"http://creativecommons.org/licenses/by/4.0/","headline":"CAGE treats multiple conflicting alignment goals as strategic principals bidding token incentives to produce an equilibrium LLM policy at inference time.","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Baiting Chen, Rui Yu, Tong Zhu, Xiaowu Dai","submitted_at":"2026-05-08T06:56:35Z","abstract_excerpt":"Aligning large language models (LLMs) with human preferences is inherently multi-objective: different users and evaluation criteria impose heterogeneous and often conflicting requirements on model outputs. We propose CAGE (Common-Agency Games for Alignment), a training-free, game-theoretic framework for multi-objective test-time alignment. CAGE models alignment objectives as strategic principals that allocate token-level incentives to a shared LLM, inducing an equilibrium policy that captures the joint effect of competing objectives. We develop an efficient algorithm based on equilibrium probl"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"CAGE enables flexible and fine-grained trade-offs across objectives at inference time, consistently outperforming existing test-time alignment methods while requiring no retraining. It further supports weak-to-strong generalization, making multi-objective alignment practical in resource-constrained settings.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That modeling heterogeneous objectives as strategic principals allocating token-level incentives produces an equilibrium policy whose joint effect meaningfully captures real user preferences, and that the EPEC-based algorithm reliably computes this equilibrium with the claimed existence, uniqueness, convergence, and stability guarantees.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"CAGE uses common-agency games and an EPEC algorithm to compute equilibrium policies that balance multiple conflicting objectives for test-time LLM alignment.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"CAGE treats multiple conflicting alignment goals as strategic principals bidding token incentives to produce an equilibrium LLM policy at inference time.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ba3aeb72703cb6e24891c5dae8672767889a68094fa699046c184755d7700103"},"source":{"id":"2605.13875","kind":"arxiv","version":1},"verdict":{"id":"1c5a5ac2-e479-4d34-af9e-4253368271a2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T06:11:14.544441Z","strongest_claim":"CAGE enables flexible and fine-grained trade-offs across objectives at inference time, consistently outperforming existing test-time alignment methods while requiring no retraining. It further supports weak-to-strong generalization, making multi-objective alignment practical in resource-constrained settings.","one_line_summary":"CAGE uses common-agency games and an EPEC algorithm to compute equilibrium policies that balance multiple conflicting objectives for test-time LLM alignment.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That modeling heterogeneous objectives as strategic principals allocating token-level incentives produces an equilibrium policy whose joint effect meaningfully captures real user preferences, and that the EPEC-based algorithm reliably computes this equilibrium with the claimed existence, uniqueness, convergence, and stability guarantees.","pith_extraction_headline":"CAGE treats multiple conflicting alignment goals as strategic principals bidding token incentives to produce an equilibrium LLM policy at inference time."},"references":{"count":230,"sample":[{"doi":"","year":2024,"title":"TinyLlama: An Open-Source Small Language Model , author=. 2024 , eprint=","work_id":"4b2a85e5-7934-4e57-ba32-e7ac0a26d388","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"International Conference on Learning Representations , year=","work_id":"7d66a0d4-a1e1-4771-b0cd-ea8c424cb4bd","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"The Twelfth International Conference on Learning Representations , year=","work_id":"44d6bf99-5902-43da-b8fd-83297976c6e0","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"C hat D ev: Communicative agents for software development","work_id":"166b34d2-9477-4b53-b493-bcce91575006","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Encouraging divergent thinking in large language models through multi-agent debate","work_id":"5e657239-8ab5-4c3c-ac58-63b4c9d2e420","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":230,"snapshot_sha256":"0d6a0ec0b4c4362b2aaaab7e88e2dcbc27332505742a1851b0d20041ea2a4151","internal_anchors":19},"formal_canon":{"evidence_count":2,"snapshot_sha256":"aebd8280c17417da790c7bdeedd992a81e4524c1d32020d083c0fcbfb65b478e"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"1c5a5ac2-e479-4d34-af9e-4253368271a2"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wODFnmMWUvIE6kxMCslH4lf/U1U7LujLqZGZffodQzEgJB60yWizfMj8R5UXnrai2xNUZDKf+aDmbBWDYOTADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:15:10.907010Z"},"content_sha256":"ed136807ceb5e28b334e297753e4aa49cb1d33de084418e50e4a5291704965e8","schema_version":"1.0","event_id":"sha256:ed136807ceb5e28b334e297753e4aa49cb1d33de084418e50e4a5291704965e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/63NRELHFFN5IYRD4CHKJSYLPIL/bundle.json","state_url":"https://pith.science/pith/63NRELHFFN5IYRD4CHKJSYLPIL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/63NRELHFFN5IYRD4CHKJSYLPIL/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":"2026-06-02T16:15:10Z","links":{"resolver":"https://pith.science/pith/63NRELHFFN5IYRD4CHKJSYLPIL","bundle":"https://pith.science/pith/63NRELHFFN5IYRD4CHKJSYLPIL/bundle.json","state":"https://pith.science/pith/63NRELHFFN5IYRD4CHKJSYLPIL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/63NRELHFFN5IYRD4CHKJSYLPIL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:63NRELHFFN5IYRD4CHKJSYLPIL","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":"0d7b2fceed870fc9915bb543fe1bc4aad71a2254498f74720408394b6965a165","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2026-05-08T06:56:35Z","title_canon_sha256":"ec01d02e8ddaea2090a0c9969382906a7bd8f682e5499ce7de30b309fee65ba3"},"schema_version":"1.0","source":{"id":"2605.13875","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13875","created_at":"2026-05-17T23:39:19Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13875v1","created_at":"2026-05-17T23:39:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13875","created_at":"2026-05-17T23:39:19Z"},{"alias_kind":"pith_short_12","alias_value":"63NRELHFFN5I","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"63NRELHFFN5IYRD4","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"63NRELHF","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:ed136807ceb5e28b334e297753e4aa49cb1d33de084418e50e4a5291704965e8","target":"graph","created_at":"2026-05-17T23:39:19Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"CAGE enables flexible and fine-grained trade-offs across objectives at inference time, consistently outperforming existing test-time alignment methods while requiring no retraining. It further supports weak-to-strong generalization, making multi-objective alignment practical in resource-constrained settings."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That modeling heterogeneous objectives as strategic principals allocating token-level incentives produces an equilibrium policy whose joint effect meaningfully captures real user preferences, and that the EPEC-based algorithm reliably computes this equilibrium with the claimed existence, uniqueness, convergence, and stability guarantees."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"CAGE uses common-agency games and an EPEC algorithm to compute equilibrium policies that balance multiple conflicting objectives for test-time LLM alignment."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"CAGE treats multiple conflicting alignment goals as strategic principals bidding token incentives to produce an equilibrium LLM policy at inference time."}],"snapshot_sha256":"ba3aeb72703cb6e24891c5dae8672767889a68094fa699046c184755d7700103"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"aebd8280c17417da790c7bdeedd992a81e4524c1d32020d083c0fcbfb65b478e"},"paper":{"abstract_excerpt":"Aligning large language models (LLMs) with human preferences is inherently multi-objective: different users and evaluation criteria impose heterogeneous and often conflicting requirements on model outputs. We propose CAGE (Common-Agency Games for Alignment), a training-free, game-theoretic framework for multi-objective test-time alignment. CAGE models alignment objectives as strategic principals that allocate token-level incentives to a shared LLM, inducing an equilibrium policy that captures the joint effect of competing objectives. We develop an efficient algorithm based on equilibrium probl","authors_text":"Baiting Chen, Rui Yu, Tong Zhu, Xiaowu Dai","cross_cats":[],"headline":"CAGE treats multiple conflicting alignment goals as strategic principals bidding token incentives to produce an equilibrium LLM policy at inference time.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2026-05-08T06:56:35Z","title":"Common-agency Games for Multi-Objective Test-Time Alignment"},"references":{"count":230,"internal_anchors":19,"resolved_work":230,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"TinyLlama: An Open-Source Small Language Model , author=. 2024 , eprint=","work_id":"4b2a85e5-7934-4e57-ba32-e7ac0a26d388","year":2024},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"International Conference on Learning Representations , year=","work_id":"7d66a0d4-a1e1-4771-b0cd-ea8c424cb4bd","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"The Twelfth International Conference on Learning Representations , year=","work_id":"44d6bf99-5902-43da-b8fd-83297976c6e0","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"C hat D ev: Communicative agents for software development","work_id":"166b34d2-9477-4b53-b493-bcce91575006","year":2024},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Encouraging divergent thinking in large language models through multi-agent debate","work_id":"5e657239-8ab5-4c3c-ac58-63b4c9d2e420","year":2024}],"snapshot_sha256":"0d6a0ec0b4c4362b2aaaab7e88e2dcbc27332505742a1851b0d20041ea2a4151"},"source":{"id":"2605.13875","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-15T06:11:14.544441Z","id":"1c5a5ac2-e479-4d34-af9e-4253368271a2","model_set":{"reader":"grok-4.3"},"one_line_summary":"CAGE uses common-agency games and an EPEC algorithm to compute equilibrium policies that balance multiple conflicting objectives for test-time LLM alignment.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"CAGE treats multiple conflicting alignment goals as strategic principals bidding token incentives to produce an equilibrium LLM policy at inference time.","strongest_claim":"CAGE enables flexible and fine-grained trade-offs across objectives at inference time, consistently outperforming existing test-time alignment methods while requiring no retraining. It further supports weak-to-strong generalization, making multi-objective alignment practical in resource-constrained settings.","weakest_assumption":"That modeling heterogeneous objectives as strategic principals allocating token-level incentives produces an equilibrium policy whose joint effect meaningfully captures real user preferences, and that the EPEC-based algorithm reliably computes this equilibrium with the claimed existence, uniqueness, convergence, and stability guarantees."}},"verdict_id":"1c5a5ac2-e479-4d34-af9e-4253368271a2"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b7cf9e4885c957d4c2516545a097d1a414b8470e9dc293ad626183c79024ec7b","target":"record","created_at":"2026-05-17T23:39:19Z","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":"0d7b2fceed870fc9915bb543fe1bc4aad71a2254498f74720408394b6965a165","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2026-05-08T06:56:35Z","title_canon_sha256":"ec01d02e8ddaea2090a0c9969382906a7bd8f682e5499ce7de30b309fee65ba3"},"schema_version":"1.0","source":{"id":"2605.13875","kind":"arxiv","version":1}},"canonical_sha256":"f6db122ce52b7a8c447c11d499616f42fbb5cdaaa2db7b6b45e455121da19756","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6db122ce52b7a8c447c11d499616f42fbb5cdaaa2db7b6b45e455121da19756","first_computed_at":"2026-05-17T23:39:19.262842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:19.262842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WzcrMuPSQSdee8hb6nNyW8rcTfw7z55U7gkmVVTJKWiizLKZ2B75LUGODvyhrGPG5dlzFtE7vWJh3HPZoiQvBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:19.263731Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13875","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7cf9e4885c957d4c2516545a097d1a414b8470e9dc293ad626183c79024ec7b","sha256:ed136807ceb5e28b334e297753e4aa49cb1d33de084418e50e4a5291704965e8"],"state_sha256":"2ae21f27ea0cc6c27d6ada9a03606585776fc051c079e4c4fcdd37ee1fe4dc1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jbGNteDsLrw/Ugu+oI+aR3nYvGB2uJ5yfdUpkNgTTiNjMqoDpQyAWNPk/j7MK3MHRCAnA2CoSka+3/36vEwLBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T16:15:10.909455Z","bundle_sha256":"9a25a5b0bb311dc64877a7a64bcc566ba8b318feedb294db900d73d811eb5765"}}