{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:RI5PXCWI5L5L47HBWF7IHG6PST","short_pith_number":"pith:RI5PXCWI","schema_version":"1.0","canonical_sha256":"8a3afb8ac8eafabe7ce1b17e839bcf94c42718c3b3954502712f34cda251952a","source":{"kind":"arxiv","id":"2605.20113","version":1},"attestation_state":"computed","paper":{"title":"Null player neutrality in TU-games: Egalitarian and Shapley solutions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"econ.TH","authors_text":"J. C. Gon\\c{c}alves-Dosantos, J. S\\'anchez-Soriano, R. Mart\\'inez","submitted_at":"2026-05-19T17:00:23Z","abstract_excerpt":"We introduce and study the axiom of null player neutrality in the context of cooperative games with transferable utility (TU-games). This axiom weakens the classical coalitional strategic equivalence: rather than requiring that augmenting a game by a null-player game leaves that player's payoff unchanged, it only requires that any change in payoff be independent of the specific augmenting game, provided both the null-player condition and the grand-coalition value are preserved. We show that efficiency, linearity, symmetry, and null player neutrality together characterize the family of all real"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.20113","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"econ.TH","submitted_at":"2026-05-19T17:00:23Z","cross_cats_sorted":[],"title_canon_sha256":"38a9cdefb1ef59ecab936d58041016116d2541f0219a2ad2d94f6a5eeb7b443d","abstract_canon_sha256":"8319a12d8d1b5ced458f7af0e154d6334f039b5fafba1553547cb04e6e8fc33c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T02:06:02.573295Z","signature_b64":"Pf/hj4aiJpXC+HAvMiCqR2F5QkevjAN8TzxNKk9QfqcM+yZ9OLOWJjIvCYacXPQQa8XAyLBO+zAnCFZ3g+FVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a3afb8ac8eafabe7ce1b17e839bcf94c42718c3b3954502712f34cda251952a","last_reissued_at":"2026-05-20T02:06:02.572660Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T02:06:02.572660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Null player neutrality in TU-games: Egalitarian and Shapley solutions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"econ.TH","authors_text":"J. C. Gon\\c{c}alves-Dosantos, J. S\\'anchez-Soriano, R. Mart\\'inez","submitted_at":"2026-05-19T17:00:23Z","abstract_excerpt":"We introduce and study the axiom of null player neutrality in the context of cooperative games with transferable utility (TU-games). This axiom weakens the classical coalitional strategic equivalence: rather than requiring that augmenting a game by a null-player game leaves that player's payoff unchanged, it only requires that any change in payoff be independent of the specific augmenting game, provided both the null-player condition and the grand-coalition value are preserved. We show that efficiency, linearity, symmetry, and null player neutrality together characterize the family of all real"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20113","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/2605.20113/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.20113","created_at":"2026-05-20T02:06:02.572754+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.20113v1","created_at":"2026-05-20T02:06:02.572754+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20113","created_at":"2026-05-20T02:06:02.572754+00:00"},{"alias_kind":"pith_short_12","alias_value":"RI5PXCWI5L5L","created_at":"2026-05-20T02:06:02.572754+00:00"},{"alias_kind":"pith_short_16","alias_value":"RI5PXCWI5L5L47HB","created_at":"2026-05-20T02:06:02.572754+00:00"},{"alias_kind":"pith_short_8","alias_value":"RI5PXCWI","created_at":"2026-05-20T02:06:02.572754+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RI5PXCWI5L5L47HBWF7IHG6PST","json":"https://pith.science/pith/RI5PXCWI5L5L47HBWF7IHG6PST.json","graph_json":"https://pith.science/api/pith-number/RI5PXCWI5L5L47HBWF7IHG6PST/graph.json","events_json":"https://pith.science/api/pith-number/RI5PXCWI5L5L47HBWF7IHG6PST/events.json","paper":"https://pith.science/paper/RI5PXCWI"},"agent_actions":{"view_html":"https://pith.science/pith/RI5PXCWI5L5L47HBWF7IHG6PST","download_json":"https://pith.science/pith/RI5PXCWI5L5L47HBWF7IHG6PST.json","view_paper":"https://pith.science/paper/RI5PXCWI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.20113&json=true","fetch_graph":"https://pith.science/api/pith-number/RI5PXCWI5L5L47HBWF7IHG6PST/graph.json","fetch_events":"https://pith.science/api/pith-number/RI5PXCWI5L5L47HBWF7IHG6PST/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RI5PXCWI5L5L47HBWF7IHG6PST/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RI5PXCWI5L5L47HBWF7IHG6PST/action/storage_attestation","attest_author":"https://pith.science/pith/RI5PXCWI5L5L47HBWF7IHG6PST/action/author_attestation","sign_citation":"https://pith.science/pith/RI5PXCWI5L5L47HBWF7IHG6PST/action/citation_signature","submit_replication":"https://pith.science/pith/RI5PXCWI5L5L47HBWF7IHG6PST/action/replication_record"}},"created_at":"2026-05-20T02:06:02.572754+00:00","updated_at":"2026-05-20T02:06:02.572754+00:00"}