{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BSUJ56B5QO6IEIVSLFJTCPUOGA","short_pith_number":"pith:BSUJ56B5","canonical_record":{"source":{"id":"1301.2931","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-14T12:00:55Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"4b8aa06917a790a850602229fdd576bf40f6c14c2741600c8bf00c0fd031fb41","abstract_canon_sha256":"291bac86bfb978c0e3b738d4c8e9becb2de1b1a0bae00a777f1dc97020ff201c"},"schema_version":"1.0"},"canonical_sha256":"0ca89ef83d83bc8222b25953313e8e303988232cb5f0a31b390ea582f7668a7e","source":{"kind":"arxiv","id":"1301.2931","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2931","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2931v1","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2931","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"pith_short_12","alias_value":"BSUJ56B5QO6I","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BSUJ56B5QO6IEIVS","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BSUJ56B5","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BSUJ56B5QO6IEIVSLFJTCPUOGA","target":"record","payload":{"canonical_record":{"source":{"id":"1301.2931","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-14T12:00:55Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"4b8aa06917a790a850602229fdd576bf40f6c14c2741600c8bf00c0fd031fb41","abstract_canon_sha256":"291bac86bfb978c0e3b738d4c8e9becb2de1b1a0bae00a777f1dc97020ff201c"},"schema_version":"1.0"},"canonical_sha256":"0ca89ef83d83bc8222b25953313e8e303988232cb5f0a31b390ea582f7668a7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:27.762899Z","signature_b64":"xW7UrKSj/kee1uqu2R2NeFETWuvTd58LSnuMgrcjPh13Yb3TGRQqkxa2taIpM+JbNmikbUCjRPe7UARu6qOaCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ca89ef83d83bc8222b25953313e8e303988232cb5f0a31b390ea582f7668a7e","last_reissued_at":"2026-05-18T03:36:27.762454Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:27.762454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.2931","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":"2026-05-18T03:36:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O1XxvEnMAkL0a/OE43GkJYNu+bLrxof1QMB1P9n8QLQgIMd3ka2VL+VPcCucbYGGLquzkPN35hYQvAuC9qjABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T02:57:54.024466Z"},"content_sha256":"330e8fad9bb43a71cb279fcaddf59e5d7b8ae7b3e4e6acfc78017f33464e28f1","schema_version":"1.0","event_id":"sha256:330e8fad9bb43a71cb279fcaddf59e5d7b8ae7b3e4e6acfc78017f33464e28f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BSUJ56B5QO6IEIVSLFJTCPUOGA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Prescribed matchings extend to Hamiltonian cycles in hypercubes with faulty edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CO","authors_text":"Fan Wang, Heping Zhang","submitted_at":"2013-01-14T12:00:55Z","abstract_excerpt":"Ruskey and Savage asked the following question: Does every matching of $Q_{n}$ for $n\\geq2$ extend to a Hamiltonian cycle of $Q_{n}$? J. Fink showed that the question is true for every perfect matching, and solved the Kreweras' conjecture. In this paper we consider the question in hypercubes with faulty edges. We show that every matching $M$ of at most $2n-1$ edges can be extended to a Hamiltonian cycle of $Q_{n}$ for $n\\geq2$. Moreover, we can prove that when $n\\geq4$ and $M$ is nonempty this result still holds even if $Q_{n}$ has at most $n-1-\\lceil\\frac{|M|}{2}\\rceil$ faulty edges with one "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2931","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":"2026-05-18T03:36:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oivy+UcxYtLtLemIHPFpOfd7ACYRNMcIqQ6Tl2ajkPoHqmfmPoezHk3PjvxevIGjq5Sbs9k7fua/kldbskH6CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T02:57:54.024807Z"},"content_sha256":"03bfa179043035da29ea3ff016e3e8a46a14fab15e43fae044d0c931d732437a","schema_version":"1.0","event_id":"sha256:03bfa179043035da29ea3ff016e3e8a46a14fab15e43fae044d0c931d732437a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BSUJ56B5QO6IEIVSLFJTCPUOGA/bundle.json","state_url":"https://pith.science/pith/BSUJ56B5QO6IEIVSLFJTCPUOGA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BSUJ56B5QO6IEIVSLFJTCPUOGA/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":"2026-06-20T02:57:54Z","links":{"resolver":"https://pith.science/pith/BSUJ56B5QO6IEIVSLFJTCPUOGA","bundle":"https://pith.science/pith/BSUJ56B5QO6IEIVSLFJTCPUOGA/bundle.json","state":"https://pith.science/pith/BSUJ56B5QO6IEIVSLFJTCPUOGA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BSUJ56B5QO6IEIVSLFJTCPUOGA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BSUJ56B5QO6IEIVSLFJTCPUOGA","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":"291bac86bfb978c0e3b738d4c8e9becb2de1b1a0bae00a777f1dc97020ff201c","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-14T12:00:55Z","title_canon_sha256":"4b8aa06917a790a850602229fdd576bf40f6c14c2741600c8bf00c0fd031fb41"},"schema_version":"1.0","source":{"id":"1301.2931","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2931","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2931v1","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2931","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"pith_short_12","alias_value":"BSUJ56B5QO6I","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BSUJ56B5QO6IEIVS","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BSUJ56B5","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:03bfa179043035da29ea3ff016e3e8a46a14fab15e43fae044d0c931d732437a","target":"graph","created_at":"2026-05-18T03:36:27Z","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":"Ruskey and Savage asked the following question: Does every matching of $Q_{n}$ for $n\\geq2$ extend to a Hamiltonian cycle of $Q_{n}$? J. Fink showed that the question is true for every perfect matching, and solved the Kreweras' conjecture. In this paper we consider the question in hypercubes with faulty edges. We show that every matching $M$ of at most $2n-1$ edges can be extended to a Hamiltonian cycle of $Q_{n}$ for $n\\geq2$. Moreover, we can prove that when $n\\geq4$ and $M$ is nonempty this result still holds even if $Q_{n}$ has at most $n-1-\\lceil\\frac{|M|}{2}\\rceil$ faulty edges with one ","authors_text":"Fan Wang, Heping Zhang","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-14T12:00:55Z","title":"Prescribed matchings extend to Hamiltonian cycles in hypercubes with faulty edges"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2931","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":"sha256:330e8fad9bb43a71cb279fcaddf59e5d7b8ae7b3e4e6acfc78017f33464e28f1","target":"record","created_at":"2026-05-18T03:36:27Z","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":"291bac86bfb978c0e3b738d4c8e9becb2de1b1a0bae00a777f1dc97020ff201c","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-14T12:00:55Z","title_canon_sha256":"4b8aa06917a790a850602229fdd576bf40f6c14c2741600c8bf00c0fd031fb41"},"schema_version":"1.0","source":{"id":"1301.2931","kind":"arxiv","version":1}},"canonical_sha256":"0ca89ef83d83bc8222b25953313e8e303988232cb5f0a31b390ea582f7668a7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ca89ef83d83bc8222b25953313e8e303988232cb5f0a31b390ea582f7668a7e","first_computed_at":"2026-05-18T03:36:27.762454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:27.762454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xW7UrKSj/kee1uqu2R2NeFETWuvTd58LSnuMgrcjPh13Yb3TGRQqkxa2taIpM+JbNmikbUCjRPe7UARu6qOaCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:27.762899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2931","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:330e8fad9bb43a71cb279fcaddf59e5d7b8ae7b3e4e6acfc78017f33464e28f1","sha256:03bfa179043035da29ea3ff016e3e8a46a14fab15e43fae044d0c931d732437a"],"state_sha256":"32ecf5c7b8c9f71574f7e052483407d10e198500989602c9b57945329e396b6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1cizVNWKQMW7NB/mHp0L5zhuutnxCcqTjXUJbBFq7Ck4/97+kE5GolC5OytTSNr8+RSBQ5VvK2iEDmvMaARsAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T02:57:54.026754Z","bundle_sha256":"12e5ffe73fb72f7b38f74e99c7175c89108fe12508e2be825372d074d3c44532"}}