{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WTX6UQ3TZ74O4DEZYMQWFWIL7R","short_pith_number":"pith:WTX6UQ3T","canonical_record":{"source":{"id":"1110.4697","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-21T03:45:48Z","cross_cats_sorted":["cs.NI"],"title_canon_sha256":"9fe8d0f86a7b0e04fc093d2d8b9f23b0265209d38c9904126f1f41dd7c4c878b","abstract_canon_sha256":"4b39b2b3ba83d58a23b6192d87fbddf6f7fe6981417fe4b22c0341129d2af74d"},"schema_version":"1.0"},"canonical_sha256":"b4efea4373cff8ee0c99c32162d90bfc6ab15e54cf03cd366d5a90eca36d2251","source":{"kind":"arxiv","id":"1110.4697","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4697","created_at":"2026-05-18T02:43:45Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4697v3","created_at":"2026-05-18T02:43:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4697","created_at":"2026-05-18T02:43:45Z"},{"alias_kind":"pith_short_12","alias_value":"WTX6UQ3TZ74O","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WTX6UQ3TZ74O4DEZ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WTX6UQ3T","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WTX6UQ3TZ74O4DEZYMQWFWIL7R","target":"record","payload":{"canonical_record":{"source":{"id":"1110.4697","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-21T03:45:48Z","cross_cats_sorted":["cs.NI"],"title_canon_sha256":"9fe8d0f86a7b0e04fc093d2d8b9f23b0265209d38c9904126f1f41dd7c4c878b","abstract_canon_sha256":"4b39b2b3ba83d58a23b6192d87fbddf6f7fe6981417fe4b22c0341129d2af74d"},"schema_version":"1.0"},"canonical_sha256":"b4efea4373cff8ee0c99c32162d90bfc6ab15e54cf03cd366d5a90eca36d2251","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:45.813177Z","signature_b64":"u5sPTkAHX5dzm3f8b/hxQlGiv8i6ICNVyKQ5IQObZUSe5abeE3yxf01qv4nflp0EnjIXrEMqM4/7qbKMOmmvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4efea4373cff8ee0c99c32162d90bfc6ab15e54cf03cd366d5a90eca36d2251","last_reissued_at":"2026-05-18T02:43:45.812786Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:45.812786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.4697","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:43:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dNkPxwwP2HnD+yODwMTSNe9gWKixyDGFONueWasJj9NDrR2hvfx7bFSVUMTvtKFomUssg7onpYGUlZvjPftDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:24:24.096292Z"},"content_sha256":"ae73813ac205e01d030f1f3dbe74fb37e93a48c10cfdba42b755d84c6fc6b548","schema_version":"1.0","event_id":"sha256:ae73813ac205e01d030f1f3dbe74fb37e93a48c10cfdba42b755d84c6fc6b548"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WTX6UQ3TZ74O4DEZYMQWFWIL7R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal queue-size scaling in switched networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NI"],"primary_cat":"math.PR","authors_text":"D. Shah, N. S. Walton, Y. Zhong","submitted_at":"2011-10-21T03:45:48Z","abstract_excerpt":"We consider a switched (queuing) network in which there are constraints on which queues may be served simultaneously; such networks have been used to effectively model input-queued switches and wireless networks. The scheduling policy for such a network specifies which queues to serve at any point in time, based on the current state or past history of the system. In the main result of this paper, we provide a new class of online scheduling policies that achieve optimal queue-size scaling for a class of switched networks including input-queued switches. In particular, it establishes the validit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4697","kind":"arxiv","version":3},"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":"2026-05-18T02:43:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mNXGgtBgLBeyhzigBXKkTwZ9YUomDnIcJpL8wPUaYZpcvzfqoSy0y2YvFcKs/ljfbBgNsU5lQBuWyJROhSvpDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:24:24.096655Z"},"content_sha256":"0b3ac960bffb046cacca77e67dfaa68d2fef1d729817a762e0ec738072ade43e","schema_version":"1.0","event_id":"sha256:0b3ac960bffb046cacca77e67dfaa68d2fef1d729817a762e0ec738072ade43e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WTX6UQ3TZ74O4DEZYMQWFWIL7R/bundle.json","state_url":"https://pith.science/pith/WTX6UQ3TZ74O4DEZYMQWFWIL7R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WTX6UQ3TZ74O4DEZYMQWFWIL7R/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":"2026-06-04T06:24:24Z","links":{"resolver":"https://pith.science/pith/WTX6UQ3TZ74O4DEZYMQWFWIL7R","bundle":"https://pith.science/pith/WTX6UQ3TZ74O4DEZYMQWFWIL7R/bundle.json","state":"https://pith.science/pith/WTX6UQ3TZ74O4DEZYMQWFWIL7R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WTX6UQ3TZ74O4DEZYMQWFWIL7R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WTX6UQ3TZ74O4DEZYMQWFWIL7R","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":"4b39b2b3ba83d58a23b6192d87fbddf6f7fe6981417fe4b22c0341129d2af74d","cross_cats_sorted":["cs.NI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-21T03:45:48Z","title_canon_sha256":"9fe8d0f86a7b0e04fc093d2d8b9f23b0265209d38c9904126f1f41dd7c4c878b"},"schema_version":"1.0","source":{"id":"1110.4697","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4697","created_at":"2026-05-18T02:43:45Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4697v3","created_at":"2026-05-18T02:43:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4697","created_at":"2026-05-18T02:43:45Z"},{"alias_kind":"pith_short_12","alias_value":"WTX6UQ3TZ74O","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WTX6UQ3TZ74O4DEZ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WTX6UQ3T","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:0b3ac960bffb046cacca77e67dfaa68d2fef1d729817a762e0ec738072ade43e","target":"graph","created_at":"2026-05-18T02:43:45Z","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":"We consider a switched (queuing) network in which there are constraints on which queues may be served simultaneously; such networks have been used to effectively model input-queued switches and wireless networks. The scheduling policy for such a network specifies which queues to serve at any point in time, based on the current state or past history of the system. In the main result of this paper, we provide a new class of online scheduling policies that achieve optimal queue-size scaling for a class of switched networks including input-queued switches. In particular, it establishes the validit","authors_text":"D. Shah, N. S. Walton, Y. Zhong","cross_cats":["cs.NI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-21T03:45:48Z","title":"Optimal queue-size scaling in switched networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4697","kind":"arxiv","version":3},"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:ae73813ac205e01d030f1f3dbe74fb37e93a48c10cfdba42b755d84c6fc6b548","target":"record","created_at":"2026-05-18T02:43:45Z","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":"4b39b2b3ba83d58a23b6192d87fbddf6f7fe6981417fe4b22c0341129d2af74d","cross_cats_sorted":["cs.NI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-21T03:45:48Z","title_canon_sha256":"9fe8d0f86a7b0e04fc093d2d8b9f23b0265209d38c9904126f1f41dd7c4c878b"},"schema_version":"1.0","source":{"id":"1110.4697","kind":"arxiv","version":3}},"canonical_sha256":"b4efea4373cff8ee0c99c32162d90bfc6ab15e54cf03cd366d5a90eca36d2251","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4efea4373cff8ee0c99c32162d90bfc6ab15e54cf03cd366d5a90eca36d2251","first_computed_at":"2026-05-18T02:43:45.812786Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:45.812786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u5sPTkAHX5dzm3f8b/hxQlGiv8i6ICNVyKQ5IQObZUSe5abeE3yxf01qv4nflp0EnjIXrEMqM4/7qbKMOmmvAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:45.813177Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4697","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae73813ac205e01d030f1f3dbe74fb37e93a48c10cfdba42b755d84c6fc6b548","sha256:0b3ac960bffb046cacca77e67dfaa68d2fef1d729817a762e0ec738072ade43e"],"state_sha256":"afca7c2d78771776f52c64aa54ae8b867cae73d7d84bd53288dd467360c88013"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P+PrYt7pKFAjjfNn/3Oj90nEd47/IkITtkDnJnTEcn2vGc9Y4XBog9V9rrPHpG15VAlntumn9r2Uv2unSt8ICg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:24:24.098557Z","bundle_sha256":"2fe31e126f9866fe4ebd06938f198c708b69052c639b7e1d198136fc7bcbeff1"}}