{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:L47IMO7CFZFN2VDYN4RXAMJOMP","short_pith_number":"pith:L47IMO7C","canonical_record":{"source":{"id":"1510.02689","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2015-10-09T14:42:53Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"40aacba1779b18c3da221474db9803306af9369291b3be1b64bcfe25f94483e6","abstract_canon_sha256":"b0c4ef8f3794af68f679d0661254439324414713c5a218877c5077dfab000309"},"schema_version":"1.0"},"canonical_sha256":"5f3e863be22e4add54786f2370312e63d467167367adf2e41b1f1484fec507c4","source":{"kind":"arxiv","id":"1510.02689","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.02689","created_at":"2026-05-18T01:30:41Z"},{"alias_kind":"arxiv_version","alias_value":"1510.02689v1","created_at":"2026-05-18T01:30:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02689","created_at":"2026-05-18T01:30:41Z"},{"alias_kind":"pith_short_12","alias_value":"L47IMO7CFZFN","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"L47IMO7CFZFN2VDY","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"L47IMO7C","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:L47IMO7CFZFN2VDYN4RXAMJOMP","target":"record","payload":{"canonical_record":{"source":{"id":"1510.02689","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2015-10-09T14:42:53Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"40aacba1779b18c3da221474db9803306af9369291b3be1b64bcfe25f94483e6","abstract_canon_sha256":"b0c4ef8f3794af68f679d0661254439324414713c5a218877c5077dfab000309"},"schema_version":"1.0"},"canonical_sha256":"5f3e863be22e4add54786f2370312e63d467167367adf2e41b1f1484fec507c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:41.712886Z","signature_b64":"MoqeNTxA7OMp/Xd+XLcb68T9f9aUOoyMSVq6FAvNXb9ZpiGjTeDQjmAlYG82A4kri8Yp3qtjj2ccl1zp2wn+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f3e863be22e4add54786f2370312e63d467167367adf2e41b1f1484fec507c4","last_reissued_at":"2026-05-18T01:30:41.712193Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:41.712193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.02689","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":"2026-05-18T01:30:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WQ2DToLHoFc3phu3tCa4ITHtCKiA/bcxqLc5eNfezWUvQhTAWfUfuHIkM1KopQa5Q5AZJtUqxaoptFRt2jWkDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T07:07:15.382372Z"},"content_sha256":"60bb7e0833c76dd28a7adc7982ed38f4b718f5b024ceb3a25aa7b788945c163d","schema_version":"1.0","event_id":"sha256:60bb7e0833c76dd28a7adc7982ed38f4b718f5b024ceb3a25aa7b788945c163d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:L47IMO7CFZFN2VDYN4RXAMJOMP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hamiltonian Properties of DCell Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DC","authors_text":"Alejandro Erickson, Jianxi Fan, Xiaohua Jia, Xi Wang","submitted_at":"2015-10-09T14:42:53Z","abstract_excerpt":"DCell has been proposed for data centers as a server centric interconnection network structure. DCell can support millions of servers with high network capacity by only using commodity switches. With one exception, we prove that a $k$ level DCell built with $n$ port switches is Hamiltonian-connected for $k \\geq 0$ and $n \\geq 2$. Our proof extends to all generalized DCell connection rules for $n\\ge 3$. Then, we propose an $O(t_k)$ algorithm for finding a Hamiltonian path in $DCell_{k}$, where $t_k$ is the number of servers in $DCell_{k}$. What's more, we prove that $DCell_{k}$ is $(n+k-4)$-fau"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02689","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":"2026-05-18T01:30:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IC+bDm3C7/fOw3cIrDwkcJUu4pFJamkR05d4p795N01/qgyhCv5xju9NQ5kRfzf66QaYdGjTteTWtyar+3VaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T07:07:15.382859Z"},"content_sha256":"ec6908f097c7be932039bdf97765697479f987af14591e47f476425333a6f603","schema_version":"1.0","event_id":"sha256:ec6908f097c7be932039bdf97765697479f987af14591e47f476425333a6f603"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L47IMO7CFZFN2VDYN4RXAMJOMP/bundle.json","state_url":"https://pith.science/pith/L47IMO7CFZFN2VDYN4RXAMJOMP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L47IMO7CFZFN2VDYN4RXAMJOMP/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":"2026-05-24T07:07:15Z","links":{"resolver":"https://pith.science/pith/L47IMO7CFZFN2VDYN4RXAMJOMP","bundle":"https://pith.science/pith/L47IMO7CFZFN2VDYN4RXAMJOMP/bundle.json","state":"https://pith.science/pith/L47IMO7CFZFN2VDYN4RXAMJOMP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L47IMO7CFZFN2VDYN4RXAMJOMP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:L47IMO7CFZFN2VDYN4RXAMJOMP","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":"b0c4ef8f3794af68f679d0661254439324414713c5a218877c5077dfab000309","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2015-10-09T14:42:53Z","title_canon_sha256":"40aacba1779b18c3da221474db9803306af9369291b3be1b64bcfe25f94483e6"},"schema_version":"1.0","source":{"id":"1510.02689","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.02689","created_at":"2026-05-18T01:30:41Z"},{"alias_kind":"arxiv_version","alias_value":"1510.02689v1","created_at":"2026-05-18T01:30:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02689","created_at":"2026-05-18T01:30:41Z"},{"alias_kind":"pith_short_12","alias_value":"L47IMO7CFZFN","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"L47IMO7CFZFN2VDY","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"L47IMO7C","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:ec6908f097c7be932039bdf97765697479f987af14591e47f476425333a6f603","target":"graph","created_at":"2026-05-18T01:30:41Z","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":"DCell has been proposed for data centers as a server centric interconnection network structure. DCell can support millions of servers with high network capacity by only using commodity switches. With one exception, we prove that a $k$ level DCell built with $n$ port switches is Hamiltonian-connected for $k \\geq 0$ and $n \\geq 2$. Our proof extends to all generalized DCell connection rules for $n\\ge 3$. Then, we propose an $O(t_k)$ algorithm for finding a Hamiltonian path in $DCell_{k}$, where $t_k$ is the number of servers in $DCell_{k}$. What's more, we prove that $DCell_{k}$ is $(n+k-4)$-fau","authors_text":"Alejandro Erickson, Jianxi Fan, Xiaohua Jia, Xi Wang","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2015-10-09T14:42:53Z","title":"Hamiltonian Properties of DCell Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02689","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":"sha256:60bb7e0833c76dd28a7adc7982ed38f4b718f5b024ceb3a25aa7b788945c163d","target":"record","created_at":"2026-05-18T01:30:41Z","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":"b0c4ef8f3794af68f679d0661254439324414713c5a218877c5077dfab000309","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2015-10-09T14:42:53Z","title_canon_sha256":"40aacba1779b18c3da221474db9803306af9369291b3be1b64bcfe25f94483e6"},"schema_version":"1.0","source":{"id":"1510.02689","kind":"arxiv","version":1}},"canonical_sha256":"5f3e863be22e4add54786f2370312e63d467167367adf2e41b1f1484fec507c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f3e863be22e4add54786f2370312e63d467167367adf2e41b1f1484fec507c4","first_computed_at":"2026-05-18T01:30:41.712193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:41.712193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MoqeNTxA7OMp/Xd+XLcb68T9f9aUOoyMSVq6FAvNXb9ZpiGjTeDQjmAlYG82A4kri8Yp3qtjj2ccl1zp2wn+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:41.712886Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.02689","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60bb7e0833c76dd28a7adc7982ed38f4b718f5b024ceb3a25aa7b788945c163d","sha256:ec6908f097c7be932039bdf97765697479f987af14591e47f476425333a6f603"],"state_sha256":"3f408e0c479ab616edeab858078b46827a47a1ae29bffa2f1cc61284675aaea4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bP/+6giKuzilr9H7Bq+5v+f4pGIkPQi685VCcsba8i5CU7vMkcRPnY5woLGrQP7a5qvbm4odwtexPlvwHGy7Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T07:07:15.386475Z","bundle_sha256":"8ecfb29e638fd23e12a0a26d46b865ff559a06004780a4fbdff5dcc6a1fe4d18"}}