{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3EJAPOYHFEW74BXN7DDJWNSZQE","short_pith_number":"pith:3EJAPOYH","canonical_record":{"source":{"id":"1705.10116","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2017-05-29T11:03:56Z","cross_cats_sorted":[],"title_canon_sha256":"d5ad917cacb300f5eb0806d2faf5b871e88a49bc23b0496878e0fbd8e84ecedb","abstract_canon_sha256":"2e8e952c0d23a319b67f766b8ebfc632393071a01afd3322e425ef8c2d367f5b"},"schema_version":"1.0"},"canonical_sha256":"d91207bb07292dfe06edf8c69b36598134beccf3317e194d6fb7cfceda627314","source":{"kind":"arxiv","id":"1705.10116","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10116","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10116v1","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10116","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"pith_short_12","alias_value":"3EJAPOYHFEW7","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3EJAPOYHFEW74BXN","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3EJAPOYH","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3EJAPOYHFEW74BXN7DDJWNSZQE","target":"record","payload":{"canonical_record":{"source":{"id":"1705.10116","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2017-05-29T11:03:56Z","cross_cats_sorted":[],"title_canon_sha256":"d5ad917cacb300f5eb0806d2faf5b871e88a49bc23b0496878e0fbd8e84ecedb","abstract_canon_sha256":"2e8e952c0d23a319b67f766b8ebfc632393071a01afd3322e425ef8c2d367f5b"},"schema_version":"1.0"},"canonical_sha256":"d91207bb07292dfe06edf8c69b36598134beccf3317e194d6fb7cfceda627314","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:31.929565Z","signature_b64":"W2Lrx1pZ0PeHDPVEyhWBD1K5QsFe/HVh8dbIcttOKCQ65sbR0xGzSdi4YdfbmWmGekfcLThPVBqoKH26UAnkDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d91207bb07292dfe06edf8c69b36598134beccf3317e194d6fb7cfceda627314","last_reissued_at":"2026-05-18T00:43:31.929106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:31.929106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.10116","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":"2026-05-18T00:43:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QLw5+O6svPjLsWZJmEBCCfQWQ6xzDsHfWLy2nIJ8jZHxXuiynjEeQVq5A+wmD950cjjhwL/wUMXPtUMoezL1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:12:22.700303Z"},"content_sha256":"3db54ed32f5027814aed7e78710e149d3deb083e56f9b357f8f0dc82275d00ee","schema_version":"1.0","event_id":"sha256:3db54ed32f5027814aed7e78710e149d3deb083e56f9b357f8f0dc82275d00ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3EJAPOYHFEW74BXN7DDJWNSZQE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional Hedonic Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Dominik Peters, Felix Brandt, Florian Brandl, Haris Aziz, Martin Olsen, Paul Harrenstein","submitted_at":"2017-05-29T11:03:56Z","abstract_excerpt":"The work we present in this paper initiated the formal study of fractional hedonic games, coalition formation games in which the utility of a player is the average value he ascribes to the members of his coalition. Among other settings, this covers situations in which players only distinguish between friends and non-friends and desire to be in a coalition in which the fraction of friends is maximal. Fractional hedonic games thus not only constitute a natural class of succinctly representable coalition formation games, but also provide an interesting framework for network clustering. We propose"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10116","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":""},"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":"2026-05-18T00:43:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"apoxnkVtbwm/MPvDIy0P1pBc5dv+/AKMEMB83Yl4dq9JpL4ELXMt57B/CICfSMbMn6qIersU15RfEG36S7QfDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:12:22.700838Z"},"content_sha256":"ee1aa4594cc92587f66a495433441c74446d27c7d3aec66e09225ec0e681f3b7","schema_version":"1.0","event_id":"sha256:ee1aa4594cc92587f66a495433441c74446d27c7d3aec66e09225ec0e681f3b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3EJAPOYHFEW74BXN7DDJWNSZQE/bundle.json","state_url":"https://pith.science/pith/3EJAPOYHFEW74BXN7DDJWNSZQE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3EJAPOYHFEW74BXN7DDJWNSZQE/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":"2026-05-27T21:12:22Z","links":{"resolver":"https://pith.science/pith/3EJAPOYHFEW74BXN7DDJWNSZQE","bundle":"https://pith.science/pith/3EJAPOYHFEW74BXN7DDJWNSZQE/bundle.json","state":"https://pith.science/pith/3EJAPOYHFEW74BXN7DDJWNSZQE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3EJAPOYHFEW74BXN7DDJWNSZQE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3EJAPOYHFEW74BXN7DDJWNSZQE","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":"2e8e952c0d23a319b67f766b8ebfc632393071a01afd3322e425ef8c2d367f5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2017-05-29T11:03:56Z","title_canon_sha256":"d5ad917cacb300f5eb0806d2faf5b871e88a49bc23b0496878e0fbd8e84ecedb"},"schema_version":"1.0","source":{"id":"1705.10116","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10116","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10116v1","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10116","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"pith_short_12","alias_value":"3EJAPOYHFEW7","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3EJAPOYHFEW74BXN","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3EJAPOYH","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:ee1aa4594cc92587f66a495433441c74446d27c7d3aec66e09225ec0e681f3b7","target":"graph","created_at":"2026-05-18T00:43:31Z","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":"The work we present in this paper initiated the formal study of fractional hedonic games, coalition formation games in which the utility of a player is the average value he ascribes to the members of his coalition. Among other settings, this covers situations in which players only distinguish between friends and non-friends and desire to be in a coalition in which the fraction of friends is maximal. Fractional hedonic games thus not only constitute a natural class of succinctly representable coalition formation games, but also provide an interesting framework for network clustering. We propose","authors_text":"Dominik Peters, Felix Brandt, Florian Brandl, Haris Aziz, Martin Olsen, Paul Harrenstein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2017-05-29T11:03:56Z","title":"Fractional Hedonic Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10116","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":"sha256:3db54ed32f5027814aed7e78710e149d3deb083e56f9b357f8f0dc82275d00ee","target":"record","created_at":"2026-05-18T00:43:31Z","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":"2e8e952c0d23a319b67f766b8ebfc632393071a01afd3322e425ef8c2d367f5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2017-05-29T11:03:56Z","title_canon_sha256":"d5ad917cacb300f5eb0806d2faf5b871e88a49bc23b0496878e0fbd8e84ecedb"},"schema_version":"1.0","source":{"id":"1705.10116","kind":"arxiv","version":1}},"canonical_sha256":"d91207bb07292dfe06edf8c69b36598134beccf3317e194d6fb7cfceda627314","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d91207bb07292dfe06edf8c69b36598134beccf3317e194d6fb7cfceda627314","first_computed_at":"2026-05-18T00:43:31.929106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:31.929106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W2Lrx1pZ0PeHDPVEyhWBD1K5QsFe/HVh8dbIcttOKCQ65sbR0xGzSdi4YdfbmWmGekfcLThPVBqoKH26UAnkDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:31.929565Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.10116","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3db54ed32f5027814aed7e78710e149d3deb083e56f9b357f8f0dc82275d00ee","sha256:ee1aa4594cc92587f66a495433441c74446d27c7d3aec66e09225ec0e681f3b7"],"state_sha256":"8daa1f5cf65463da4bf9e761572ac15222f444efe0846181631a6325ccea6269"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MGNgBI5wfmWb0ZeUinJjWogRmPaPZFdp2N4RpwJN9+RbTtFXNyBWNMr2VT96Z8LjGQMBaA+zxyIbQMkRjVkyDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T21:12:22.703061Z","bundle_sha256":"4c02a183fd70716db356d317713f90fcc612bf505ff54fddbb3c2d195f27f046"}}