{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:HDFNGVXUPVCTP75SCDQMHVQ4M7","short_pith_number":"pith:HDFNGVXU","canonical_record":{"source":{"id":"1902.00682","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-02T10:14:35Z","cross_cats_sorted":[],"title_canon_sha256":"285f5762d74fb10b3cd8f857ece1283d115338d79b6baa5c39ef75063d33af44","abstract_canon_sha256":"96794e955e80b690613b92003a349c9e965bd8ede9165b322c80c0e80098e48c"},"schema_version":"1.0"},"canonical_sha256":"38cad356f47d4537ffb210e0c3d61c67fdf779f98de77f2699b9eac9baf32fcb","source":{"kind":"arxiv","id":"1902.00682","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00682","created_at":"2026-05-17T23:54:52Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00682v1","created_at":"2026-05-17T23:54:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00682","created_at":"2026-05-17T23:54:52Z"},{"alias_kind":"pith_short_12","alias_value":"HDFNGVXUPVCT","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"HDFNGVXUPVCTP75S","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"HDFNGVXU","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:HDFNGVXUPVCTP75SCDQMHVQ4M7","target":"record","payload":{"canonical_record":{"source":{"id":"1902.00682","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-02T10:14:35Z","cross_cats_sorted":[],"title_canon_sha256":"285f5762d74fb10b3cd8f857ece1283d115338d79b6baa5c39ef75063d33af44","abstract_canon_sha256":"96794e955e80b690613b92003a349c9e965bd8ede9165b322c80c0e80098e48c"},"schema_version":"1.0"},"canonical_sha256":"38cad356f47d4537ffb210e0c3d61c67fdf779f98de77f2699b9eac9baf32fcb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:52.447447Z","signature_b64":"H08qHM5sf3uTrjTbpp5UBsSzlBhNlzu3mlb4/ip3BmtykN9hhxtID/P5qLY3FbDxWEIicPitZVGD76SWm+yQDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38cad356f47d4537ffb210e0c3d61c67fdf779f98de77f2699b9eac9baf32fcb","last_reissued_at":"2026-05-17T23:54:52.446927Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:52.446927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.00682","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":"2026-05-17T23:54:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+lUmM+oXdv2muD8RdqrfvAQ6FTIIjY+n16bAQv3EmpTfSzfnlPiFFCLSOe7X1OXNSZgmJDtGDbYygWOEAFB9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:35:00.658402Z"},"content_sha256":"2f685a3674f0e65be01afb2d243f248aef1267a79bf5b4f8fdfc0d96bbc6180d","schema_version":"1.0","event_id":"sha256:2f685a3674f0e65be01afb2d243f248aef1267a79bf5b4f8fdfc0d96bbc6180d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:HDFNGVXUPVCTP75SCDQMHVQ4M7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vector clique decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Raphael Yuster","submitted_at":"2019-02-02T10:14:35Z","abstract_excerpt":"Let $F_k$ be the set of graphs on $k$ vertices. For a graph $G$, a $k$-decomposition is a set of induced subgraphs of $G$, each isomorphic to an element of $F_k$, such that each pair of vertices of $G$ is in exactly one element of the set. A fundamental result of Wilson is that for all $n=|V(G)|$ sufficiently large, $G$ has a $k$-decomposition if and only if $G$ is $k$-divisible.\n  Let ${\\bf v} \\in {\\mathbb R}^{|F_k|}$ be indexed by $F_k$. For a $k$-decomposition $L$ of $G$, let $\\nu_{\\bf v}(L) = \\sum_{F \\in F_k} {\\bf v}_F d_{L,F}$ where $d_{L,F}$ is the fraction of elements of $L$ isomorphic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00682","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":"2026-05-17T23:54:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bREfkkPDNEEyMpO9plUWcQP0NY6d7txXfOKcUMPIcQ+jjMCrlUsRu7WtJc4U1LSW88tI/henCCD2+rTxPsEsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:35:00.659031Z"},"content_sha256":"6738d6407153a7d7a384d4689504962e2ce4df3a1bfef010a30acad00a9f7824","schema_version":"1.0","event_id":"sha256:6738d6407153a7d7a384d4689504962e2ce4df3a1bfef010a30acad00a9f7824"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HDFNGVXUPVCTP75SCDQMHVQ4M7/bundle.json","state_url":"https://pith.science/pith/HDFNGVXUPVCTP75SCDQMHVQ4M7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HDFNGVXUPVCTP75SCDQMHVQ4M7/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":"2026-05-31T06:35:00Z","links":{"resolver":"https://pith.science/pith/HDFNGVXUPVCTP75SCDQMHVQ4M7","bundle":"https://pith.science/pith/HDFNGVXUPVCTP75SCDQMHVQ4M7/bundle.json","state":"https://pith.science/pith/HDFNGVXUPVCTP75SCDQMHVQ4M7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HDFNGVXUPVCTP75SCDQMHVQ4M7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:HDFNGVXUPVCTP75SCDQMHVQ4M7","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":"96794e955e80b690613b92003a349c9e965bd8ede9165b322c80c0e80098e48c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-02T10:14:35Z","title_canon_sha256":"285f5762d74fb10b3cd8f857ece1283d115338d79b6baa5c39ef75063d33af44"},"schema_version":"1.0","source":{"id":"1902.00682","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00682","created_at":"2026-05-17T23:54:52Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00682v1","created_at":"2026-05-17T23:54:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00682","created_at":"2026-05-17T23:54:52Z"},{"alias_kind":"pith_short_12","alias_value":"HDFNGVXUPVCT","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"HDFNGVXUPVCTP75S","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"HDFNGVXU","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:6738d6407153a7d7a384d4689504962e2ce4df3a1bfef010a30acad00a9f7824","target":"graph","created_at":"2026-05-17T23:54:52Z","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":"Let $F_k$ be the set of graphs on $k$ vertices. For a graph $G$, a $k$-decomposition is a set of induced subgraphs of $G$, each isomorphic to an element of $F_k$, such that each pair of vertices of $G$ is in exactly one element of the set. A fundamental result of Wilson is that for all $n=|V(G)|$ sufficiently large, $G$ has a $k$-decomposition if and only if $G$ is $k$-divisible.\n  Let ${\\bf v} \\in {\\mathbb R}^{|F_k|}$ be indexed by $F_k$. For a $k$-decomposition $L$ of $G$, let $\\nu_{\\bf v}(L) = \\sum_{F \\in F_k} {\\bf v}_F d_{L,F}$ where $d_{L,F}$ is the fraction of elements of $L$ isomorphic ","authors_text":"Raphael Yuster","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-02T10:14:35Z","title":"Vector clique decompositions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00682","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":"sha256:2f685a3674f0e65be01afb2d243f248aef1267a79bf5b4f8fdfc0d96bbc6180d","target":"record","created_at":"2026-05-17T23:54:52Z","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":"96794e955e80b690613b92003a349c9e965bd8ede9165b322c80c0e80098e48c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-02T10:14:35Z","title_canon_sha256":"285f5762d74fb10b3cd8f857ece1283d115338d79b6baa5c39ef75063d33af44"},"schema_version":"1.0","source":{"id":"1902.00682","kind":"arxiv","version":1}},"canonical_sha256":"38cad356f47d4537ffb210e0c3d61c67fdf779f98de77f2699b9eac9baf32fcb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38cad356f47d4537ffb210e0c3d61c67fdf779f98de77f2699b9eac9baf32fcb","first_computed_at":"2026-05-17T23:54:52.446927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:52.446927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H08qHM5sf3uTrjTbpp5UBsSzlBhNlzu3mlb4/ip3BmtykN9hhxtID/P5qLY3FbDxWEIicPitZVGD76SWm+yQDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:52.447447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.00682","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f685a3674f0e65be01afb2d243f248aef1267a79bf5b4f8fdfc0d96bbc6180d","sha256:6738d6407153a7d7a384d4689504962e2ce4df3a1bfef010a30acad00a9f7824"],"state_sha256":"d2869f729b270cef51f2c250c174114df1884cd4673cbdd16ef1bb43ad363d1c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MQ4XuxNNZEfhhwKGMwv4U9J894nA0duZsmxSwkAPSxmF2OiDg4au28XLmO6T5zeZtwlChE7kf/9WAwmbOUjVAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:35:00.662267Z","bundle_sha256":"512693a5af174d443c5409b54f164e4741d6b0256f08c1dc7fa13129aa39f086"}}