{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3U2JQLZR7VBFXHN3C42ISVH2CP","short_pith_number":"pith:3U2JQLZR","canonical_record":{"source":{"id":"1508.06420","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-08-26T09:25:17Z","cross_cats_sorted":["cs.CC","cs.DS"],"title_canon_sha256":"b949ef14fc485e290dd4cfef32310031c885da38bb0f9b1e2163b15a5e78a041","abstract_canon_sha256":"347e1215cec90b78f56f132e75029f8bf183d97ed2e1bce2aad533dc9a71d767"},"schema_version":"1.0"},"canonical_sha256":"dd34982f31fd425b9dbb17348954fa13fd339729e506f99922860f4a66a4a6ea","source":{"kind":"arxiv","id":"1508.06420","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06420","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06420v2","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06420","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"pith_short_12","alias_value":"3U2JQLZR7VBF","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3U2JQLZR7VBFXHN3","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3U2JQLZR","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3U2JQLZR7VBFXHN3C42ISVH2CP","target":"record","payload":{"canonical_record":{"source":{"id":"1508.06420","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-08-26T09:25:17Z","cross_cats_sorted":["cs.CC","cs.DS"],"title_canon_sha256":"b949ef14fc485e290dd4cfef32310031c885da38bb0f9b1e2163b15a5e78a041","abstract_canon_sha256":"347e1215cec90b78f56f132e75029f8bf183d97ed2e1bce2aad533dc9a71d767"},"schema_version":"1.0"},"canonical_sha256":"dd34982f31fd425b9dbb17348954fa13fd339729e506f99922860f4a66a4a6ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:41.010066Z","signature_b64":"88ameIYlz3Rhk4pzK/avpcmokR+Z4d5psHZEMNCd6RsyK/Pl9sOzFQfioGlhZHFSESesOhJPUCY4VeJFgvKlBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd34982f31fd425b9dbb17348954fa13fd339729e506f99922860f4a66a4a6ea","last_reissued_at":"2026-05-18T01:06:41.009590Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:41.009590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.06420","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":"2026-05-18T01:06:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n5cc0x0LCmLyEQ/zASfbjjRI46ew/ucaklbF3Gmn6K0xCZRgCwumy0GDq3HNfnUpNXfhblXeF5g6kHP5fmNiAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T08:30:05.373705Z"},"content_sha256":"3336e2f0da6f1554256c384745b7981894ac79acffc1349970d29cf5d8e4fd7e","schema_version":"1.0","event_id":"sha256:3336e2f0da6f1554256c384745b7981894ac79acffc1349970d29cf5d8e4fd7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3U2JQLZR7VBFXHN3C42ISVH2CP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Stable Fixtures Problem with Payments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"cs.GT","authors_text":"Dani\\\"el Paulusma, P\\'eter Bir\\'o, P\\'eter Wojuteczky, Walter Kern","submitted_at":"2015-08-26T09:25:17Z","abstract_excerpt":"We generalize two well-known game-theoretic models by introducing multiple partners matching games, defined by a graph $G=(N,E)$, with an integer vertex capacity function $b$ and an edge weighting $w$. The set $N$ consists of a number of players that are to form a set $M\\subseteq E$ of 2-player coalitions $ij$ with value $w(ij)$, such that each player $i$ is in at most $b(i)$ coalitions. A payoff vector is a mapping $p: N \\times N \\rightarrow {\\mathbb R}$ with $p(i,j)+p(j,i)=w(ij)$ if $ij\\in M$ and $p(i,j)=p(j,i)=0$ if $ij\\notin M$. The pair $(M,p)$ is called a solution. A pair of players $i,j"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06420","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":"2026-05-18T01:06:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YwPtJTovKg9YDedQzw+hqUzwQnC3CTJspJgVITuDgrjupYNIO4qrE9btu9VP+ekL0UbQlWm1RIe4Dn7jnLGGCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T08:30:05.374410Z"},"content_sha256":"bf5c9682b43b7b6e421f8ef7f40979fd656af4f3e1957098798bb6334d36f597","schema_version":"1.0","event_id":"sha256:bf5c9682b43b7b6e421f8ef7f40979fd656af4f3e1957098798bb6334d36f597"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3U2JQLZR7VBFXHN3C42ISVH2CP/bundle.json","state_url":"https://pith.science/pith/3U2JQLZR7VBFXHN3C42ISVH2CP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3U2JQLZR7VBFXHN3C42ISVH2CP/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":"2026-05-25T08:30:05Z","links":{"resolver":"https://pith.science/pith/3U2JQLZR7VBFXHN3C42ISVH2CP","bundle":"https://pith.science/pith/3U2JQLZR7VBFXHN3C42ISVH2CP/bundle.json","state":"https://pith.science/pith/3U2JQLZR7VBFXHN3C42ISVH2CP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3U2JQLZR7VBFXHN3C42ISVH2CP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3U2JQLZR7VBFXHN3C42ISVH2CP","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":"347e1215cec90b78f56f132e75029f8bf183d97ed2e1bce2aad533dc9a71d767","cross_cats_sorted":["cs.CC","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-08-26T09:25:17Z","title_canon_sha256":"b949ef14fc485e290dd4cfef32310031c885da38bb0f9b1e2163b15a5e78a041"},"schema_version":"1.0","source":{"id":"1508.06420","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06420","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06420v2","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06420","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"pith_short_12","alias_value":"3U2JQLZR7VBF","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3U2JQLZR7VBFXHN3","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3U2JQLZR","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:bf5c9682b43b7b6e421f8ef7f40979fd656af4f3e1957098798bb6334d36f597","target":"graph","created_at":"2026-05-18T01:06:41Z","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 generalize two well-known game-theoretic models by introducing multiple partners matching games, defined by a graph $G=(N,E)$, with an integer vertex capacity function $b$ and an edge weighting $w$. The set $N$ consists of a number of players that are to form a set $M\\subseteq E$ of 2-player coalitions $ij$ with value $w(ij)$, such that each player $i$ is in at most $b(i)$ coalitions. A payoff vector is a mapping $p: N \\times N \\rightarrow {\\mathbb R}$ with $p(i,j)+p(j,i)=w(ij)$ if $ij\\in M$ and $p(i,j)=p(j,i)=0$ if $ij\\notin M$. The pair $(M,p)$ is called a solution. A pair of players $i,j","authors_text":"Dani\\\"el Paulusma, P\\'eter Bir\\'o, P\\'eter Wojuteczky, Walter Kern","cross_cats":["cs.CC","cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-08-26T09:25:17Z","title":"The Stable Fixtures Problem with Payments"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06420","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":"sha256:3336e2f0da6f1554256c384745b7981894ac79acffc1349970d29cf5d8e4fd7e","target":"record","created_at":"2026-05-18T01:06:41Z","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":"347e1215cec90b78f56f132e75029f8bf183d97ed2e1bce2aad533dc9a71d767","cross_cats_sorted":["cs.CC","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-08-26T09:25:17Z","title_canon_sha256":"b949ef14fc485e290dd4cfef32310031c885da38bb0f9b1e2163b15a5e78a041"},"schema_version":"1.0","source":{"id":"1508.06420","kind":"arxiv","version":2}},"canonical_sha256":"dd34982f31fd425b9dbb17348954fa13fd339729e506f99922860f4a66a4a6ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd34982f31fd425b9dbb17348954fa13fd339729e506f99922860f4a66a4a6ea","first_computed_at":"2026-05-18T01:06:41.009590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:41.009590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"88ameIYlz3Rhk4pzK/avpcmokR+Z4d5psHZEMNCd6RsyK/Pl9sOzFQfioGlhZHFSESesOhJPUCY4VeJFgvKlBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:41.010066Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06420","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3336e2f0da6f1554256c384745b7981894ac79acffc1349970d29cf5d8e4fd7e","sha256:bf5c9682b43b7b6e421f8ef7f40979fd656af4f3e1957098798bb6334d36f597"],"state_sha256":"7876e12a6248e20ce3b21cbddfd5cb4205aa5f140edec4f3bda9b12d6653413d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u79NdIcGib38enM4nL/+cXVDE+E7sU/boxzkygJ+ZQtoCsotO4ia+FNEekJgnUk10fUJtu+aQnSu011v2UacAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T08:30:05.378247Z","bundle_sha256":"43dd7f47cca33315c5447a97df9a7f92085b906ddd35a0b222db41ca5412d7a6"}}