{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BFPGGGVJR5FJKQ3QN2AL3G74UA","short_pith_number":"pith:BFPGGGVJ","canonical_record":{"source":{"id":"1703.03513","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-10T01:54:01Z","cross_cats_sorted":[],"title_canon_sha256":"307511a7bf9d54b470445c0ac2321a91ddd0220beca2f3f1e2b725909328c58a","abstract_canon_sha256":"712d66842c40ec18bc18bfeac8e954bab73af26a51ccd70b9fc902113f4525db"},"schema_version":"1.0"},"canonical_sha256":"095e631aa98f4a9543706e80bd9bfca030e61daae52903a5d0bdad28aab2d501","source":{"kind":"arxiv","id":"1703.03513","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.03513","created_at":"2026-05-18T00:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"1703.03513v1","created_at":"2026-05-18T00:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03513","created_at":"2026-05-18T00:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"BFPGGGVJR5FJ","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BFPGGGVJR5FJKQ3Q","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BFPGGGVJ","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BFPGGGVJR5FJKQ3QN2AL3G74UA","target":"record","payload":{"canonical_record":{"source":{"id":"1703.03513","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-10T01:54:01Z","cross_cats_sorted":[],"title_canon_sha256":"307511a7bf9d54b470445c0ac2321a91ddd0220beca2f3f1e2b725909328c58a","abstract_canon_sha256":"712d66842c40ec18bc18bfeac8e954bab73af26a51ccd70b9fc902113f4525db"},"schema_version":"1.0"},"canonical_sha256":"095e631aa98f4a9543706e80bd9bfca030e61daae52903a5d0bdad28aab2d501","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:58.925557Z","signature_b64":"jRzzb3EDp/Gon0MUB1oTKS8oTKnIp6B6NpAGgb+l3RUWEMi7FyItFvZUpBmwXrzhETrp/KR99ClqwEkL/EDWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"095e631aa98f4a9543706e80bd9bfca030e61daae52903a5d0bdad28aab2d501","last_reissued_at":"2026-05-18T00:48:58.925006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:58.925006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.03513","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":"2026-05-18T00:48:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oHWRO+Rs7yRtjybB7ZDO/JLQ/Q3vvjGFwgeonaVvuDKopbNCa+CDhd4+HXepHqemo2cU5Dfx1vo/17GSLsfmBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:41:15.826910Z"},"content_sha256":"b6502800053ef8c841129162749ef76029c5e4577dc615b76a24937f47af8f5c","schema_version":"1.0","event_id":"sha256:b6502800053ef8c841129162749ef76029c5e4577dc615b76a24937f47af8f5c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BFPGGGVJR5FJKQ3QN2AL3G74UA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perfect fractional matchings in k-out hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jeff Kahn, Pat Devlin","submitted_at":"2017-03-10T01:54:01Z","abstract_excerpt":"Extending the notion of (random) $k$-out graphs, we consider when the $k$-out hypergraph is likely to have a perfect fractional matching. In particular, we show that for each $r$ there is a $k=k(r)$ such that the $k$-out $r$-uniform hypergraph on $n$ vertices has a perfect fractional matching with high probability (i.e., with probability tending to $1$ as $n\\to \\infty$) and prove an analogous result for $r$-uniform $r$-partite hypergraphs. This is based on a new notion of hypergraph expansion and the observation that sufficiently expansive hypergraphs admit perfect fractional matchings. As a f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03513","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":"2026-05-18T00:48:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rSQ37sk8KevochYNLeVzNvrE9UMcaNjlzmtmFrT75/C6tqmR2BvDMHwWk3FT42kcRFcFd88Avkj8Ndix3L/CAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T11:41:15.827255Z"},"content_sha256":"78f929e1a80bfd94faa94a6b3d3ff9d8b7fc28da482b7aff100c536644415f38","schema_version":"1.0","event_id":"sha256:78f929e1a80bfd94faa94a6b3d3ff9d8b7fc28da482b7aff100c536644415f38"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BFPGGGVJR5FJKQ3QN2AL3G74UA/bundle.json","state_url":"https://pith.science/pith/BFPGGGVJR5FJKQ3QN2AL3G74UA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BFPGGGVJR5FJKQ3QN2AL3G74UA/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":"2026-06-02T11:41:15Z","links":{"resolver":"https://pith.science/pith/BFPGGGVJR5FJKQ3QN2AL3G74UA","bundle":"https://pith.science/pith/BFPGGGVJR5FJKQ3QN2AL3G74UA/bundle.json","state":"https://pith.science/pith/BFPGGGVJR5FJKQ3QN2AL3G74UA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BFPGGGVJR5FJKQ3QN2AL3G74UA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BFPGGGVJR5FJKQ3QN2AL3G74UA","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":"712d66842c40ec18bc18bfeac8e954bab73af26a51ccd70b9fc902113f4525db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-10T01:54:01Z","title_canon_sha256":"307511a7bf9d54b470445c0ac2321a91ddd0220beca2f3f1e2b725909328c58a"},"schema_version":"1.0","source":{"id":"1703.03513","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.03513","created_at":"2026-05-18T00:48:58Z"},{"alias_kind":"arxiv_version","alias_value":"1703.03513v1","created_at":"2026-05-18T00:48:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03513","created_at":"2026-05-18T00:48:58Z"},{"alias_kind":"pith_short_12","alias_value":"BFPGGGVJR5FJ","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BFPGGGVJR5FJKQ3Q","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BFPGGGVJ","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:78f929e1a80bfd94faa94a6b3d3ff9d8b7fc28da482b7aff100c536644415f38","target":"graph","created_at":"2026-05-18T00:48:58Z","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":"Extending the notion of (random) $k$-out graphs, we consider when the $k$-out hypergraph is likely to have a perfect fractional matching. In particular, we show that for each $r$ there is a $k=k(r)$ such that the $k$-out $r$-uniform hypergraph on $n$ vertices has a perfect fractional matching with high probability (i.e., with probability tending to $1$ as $n\\to \\infty$) and prove an analogous result for $r$-uniform $r$-partite hypergraphs. This is based on a new notion of hypergraph expansion and the observation that sufficiently expansive hypergraphs admit perfect fractional matchings. As a f","authors_text":"Jeff Kahn, Pat Devlin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-10T01:54:01Z","title":"Perfect fractional matchings in k-out hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03513","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:b6502800053ef8c841129162749ef76029c5e4577dc615b76a24937f47af8f5c","target":"record","created_at":"2026-05-18T00:48:58Z","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":"712d66842c40ec18bc18bfeac8e954bab73af26a51ccd70b9fc902113f4525db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-10T01:54:01Z","title_canon_sha256":"307511a7bf9d54b470445c0ac2321a91ddd0220beca2f3f1e2b725909328c58a"},"schema_version":"1.0","source":{"id":"1703.03513","kind":"arxiv","version":1}},"canonical_sha256":"095e631aa98f4a9543706e80bd9bfca030e61daae52903a5d0bdad28aab2d501","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"095e631aa98f4a9543706e80bd9bfca030e61daae52903a5d0bdad28aab2d501","first_computed_at":"2026-05-18T00:48:58.925006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:58.925006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jRzzb3EDp/Gon0MUB1oTKS8oTKnIp6B6NpAGgb+l3RUWEMi7FyItFvZUpBmwXrzhETrp/KR99ClqwEkL/EDWAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:58.925557Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.03513","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6502800053ef8c841129162749ef76029c5e4577dc615b76a24937f47af8f5c","sha256:78f929e1a80bfd94faa94a6b3d3ff9d8b7fc28da482b7aff100c536644415f38"],"state_sha256":"5827d192eb16fd58331c0402d368b7f1420c9e08428aa206f7e2f16ba6a644dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zyUUVXfCCFgifbOrVAWuzQUOu5hlHY5IwweWPFwMR0iP0xzeHqkxtW5zTs6PL9X9hZt7R7btQmlhSWybbuf4CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T11:41:15.830118Z","bundle_sha256":"7a81284ada7b08d4cbc75910855ae6802479819a7343a1b8f0988ae85472a7ee"}}