{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CXMH6ADA6DI54ZJSOFQQIDBXBQ","short_pith_number":"pith:CXMH6ADA","canonical_record":{"source":{"id":"1705.09638","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-26T16:21:48Z","cross_cats_sorted":[],"title_canon_sha256":"05be90701ce24420de02417596d9161825f4880c716497624ac97470f47c6acb","abstract_canon_sha256":"bf6eb3006cd99e04f655c0d1c892467edcc35392f415edfc28b6f16940ec6afe"},"schema_version":"1.0"},"canonical_sha256":"15d87f0060f0d1de65327161040c370c24a0f2f181f6bf8a9df76d6ff38a5909","source":{"kind":"arxiv","id":"1705.09638","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09638","created_at":"2026-05-18T00:09:00Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09638v2","created_at":"2026-05-18T00:09:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09638","created_at":"2026-05-18T00:09:00Z"},{"alias_kind":"pith_short_12","alias_value":"CXMH6ADA6DI5","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CXMH6ADA6DI54ZJS","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CXMH6ADA","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CXMH6ADA6DI54ZJSOFQQIDBXBQ","target":"record","payload":{"canonical_record":{"source":{"id":"1705.09638","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-26T16:21:48Z","cross_cats_sorted":[],"title_canon_sha256":"05be90701ce24420de02417596d9161825f4880c716497624ac97470f47c6acb","abstract_canon_sha256":"bf6eb3006cd99e04f655c0d1c892467edcc35392f415edfc28b6f16940ec6afe"},"schema_version":"1.0"},"canonical_sha256":"15d87f0060f0d1de65327161040c370c24a0f2f181f6bf8a9df76d6ff38a5909","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:00.615629Z","signature_b64":"vmENNaTF6zyfQALZ3XF7AdyARzEL553TGziOo9fZ5NrS27ZcO8k9K7F1Hr1ardXMZmu3jBSEGxxFDANgtPCTDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15d87f0060f0d1de65327161040c370c24a0f2f181f6bf8a9df76d6ff38a5909","last_reissued_at":"2026-05-18T00:09:00.614908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:00.614908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.09638","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":"2026-05-18T00:09:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P4sWI1P7bcdcX4ds7xkT5cnklyKbPfJqXETtGJetbevUvIieyrXSZz3ZEpKPGVxc7zYCRqvggszl7ZWJO03dAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:16:21.664770Z"},"content_sha256":"0070b078a3643516cfca0f39407c1a99119bb788849c4616886f86f84686b865","schema_version":"1.0","event_id":"sha256:0070b078a3643516cfca0f39407c1a99119bb788849c4616886f86f84686b865"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CXMH6ADA6DI54ZJSOFQQIDBXBQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multidesigns for a graph pair of order 6","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dan Roberts, Yizhe Gao","submitted_at":"2017-05-26T16:21:48Z","abstract_excerpt":"Given two graphs $G$ and $H$, a $(G,H)$-multidecomposition of $K_{n}$ is a partition of the edges of $K_{n}$ into copies of $G$ and $H$ such that at least one copy of each is used. We give necessary and sufficient conditions for the existence of $(C_{6},\\overline{C}_{6})$-multidecomposition of $K_{n}$ where $C_{6}$ denotes a cycle of length 6 and $\\overline{C}_{6}$ denotes the complement of $C_{6}$.\n  A $(G,H)$-multipacking of $K_{n}$ is a partition of a subset of the edges of $K_{n}$ into copies of $G$ and $H$ such that at least one copy of each is used. The set consisting of the edges of $K_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09638","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":"2026-05-18T00:09:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hTHfM7bzXw9gM4h9ns7ZBx/jQZjTaIULLYwd6wpZ5RLB04jK/YHV59IcKbIR+f9PP06pwtMg76EgEomy6BmLBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:16:21.665134Z"},"content_sha256":"fb5d65020c923c3adfaac31160a38c4db90d93814c98d468a71303d359c39c19","schema_version":"1.0","event_id":"sha256:fb5d65020c923c3adfaac31160a38c4db90d93814c98d468a71303d359c39c19"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CXMH6ADA6DI54ZJSOFQQIDBXBQ/bundle.json","state_url":"https://pith.science/pith/CXMH6ADA6DI54ZJSOFQQIDBXBQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CXMH6ADA6DI54ZJSOFQQIDBXBQ/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":"2026-05-26T08:16:21Z","links":{"resolver":"https://pith.science/pith/CXMH6ADA6DI54ZJSOFQQIDBXBQ","bundle":"https://pith.science/pith/CXMH6ADA6DI54ZJSOFQQIDBXBQ/bundle.json","state":"https://pith.science/pith/CXMH6ADA6DI54ZJSOFQQIDBXBQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CXMH6ADA6DI54ZJSOFQQIDBXBQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CXMH6ADA6DI54ZJSOFQQIDBXBQ","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":"bf6eb3006cd99e04f655c0d1c892467edcc35392f415edfc28b6f16940ec6afe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-26T16:21:48Z","title_canon_sha256":"05be90701ce24420de02417596d9161825f4880c716497624ac97470f47c6acb"},"schema_version":"1.0","source":{"id":"1705.09638","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09638","created_at":"2026-05-18T00:09:00Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09638v2","created_at":"2026-05-18T00:09:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09638","created_at":"2026-05-18T00:09:00Z"},{"alias_kind":"pith_short_12","alias_value":"CXMH6ADA6DI5","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CXMH6ADA6DI54ZJS","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CXMH6ADA","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:fb5d65020c923c3adfaac31160a38c4db90d93814c98d468a71303d359c39c19","target":"graph","created_at":"2026-05-18T00:09:00Z","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":"Given two graphs $G$ and $H$, a $(G,H)$-multidecomposition of $K_{n}$ is a partition of the edges of $K_{n}$ into copies of $G$ and $H$ such that at least one copy of each is used. We give necessary and sufficient conditions for the existence of $(C_{6},\\overline{C}_{6})$-multidecomposition of $K_{n}$ where $C_{6}$ denotes a cycle of length 6 and $\\overline{C}_{6}$ denotes the complement of $C_{6}$.\n  A $(G,H)$-multipacking of $K_{n}$ is a partition of a subset of the edges of $K_{n}$ into copies of $G$ and $H$ such that at least one copy of each is used. The set consisting of the edges of $K_","authors_text":"Dan Roberts, Yizhe Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-26T16:21:48Z","title":"Multidesigns for a graph pair of order 6"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09638","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":"sha256:0070b078a3643516cfca0f39407c1a99119bb788849c4616886f86f84686b865","target":"record","created_at":"2026-05-18T00:09:00Z","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":"bf6eb3006cd99e04f655c0d1c892467edcc35392f415edfc28b6f16940ec6afe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-26T16:21:48Z","title_canon_sha256":"05be90701ce24420de02417596d9161825f4880c716497624ac97470f47c6acb"},"schema_version":"1.0","source":{"id":"1705.09638","kind":"arxiv","version":2}},"canonical_sha256":"15d87f0060f0d1de65327161040c370c24a0f2f181f6bf8a9df76d6ff38a5909","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15d87f0060f0d1de65327161040c370c24a0f2f181f6bf8a9df76d6ff38a5909","first_computed_at":"2026-05-18T00:09:00.614908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:00.614908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vmENNaTF6zyfQALZ3XF7AdyARzEL553TGziOo9fZ5NrS27ZcO8k9K7F1Hr1ardXMZmu3jBSEGxxFDANgtPCTDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:00.615629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.09638","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0070b078a3643516cfca0f39407c1a99119bb788849c4616886f86f84686b865","sha256:fb5d65020c923c3adfaac31160a38c4db90d93814c98d468a71303d359c39c19"],"state_sha256":"8804cfb3ca307526cc52609e63ef9c3e0cc6b24d2a366d48aaa1e4eea8591c12"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2uApQ4/Sz+529JF7RJsr2Brm7wk46HtDN9lQbaExLChvpchVwaKfS0HOL+G6AvDji/nHxIzxreLEf4TOYOQPCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T08:16:21.667699Z","bundle_sha256":"6233cec01a52fd8403f4df40596d29213d299d610ff630a05e7d319dad0a58de"}}