{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:U57S44DCGHDC3TVVWBANJHYQXH","short_pith_number":"pith:U57S44DC","canonical_record":{"source":{"id":"1306.5002","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-20T21:03:29Z","cross_cats_sorted":[],"title_canon_sha256":"cc99da675fe5b17fbb623ccb1722d4fe017f8decf24618f1055cff01f60210e2","abstract_canon_sha256":"103a837b8067d3b45142bfe282ac048023adb4d61121532e9afe8dd640cad826"},"schema_version":"1.0"},"canonical_sha256":"a77f2e706231c62dceb5b040d49f10b9def4de05b5bdff30cadf69e7afc9eb56","source":{"kind":"arxiv","id":"1306.5002","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5002","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5002v1","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5002","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"pith_short_12","alias_value":"U57S44DCGHDC","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U57S44DCGHDC3TVV","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U57S44DC","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:U57S44DCGHDC3TVVWBANJHYQXH","target":"record","payload":{"canonical_record":{"source":{"id":"1306.5002","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-20T21:03:29Z","cross_cats_sorted":[],"title_canon_sha256":"cc99da675fe5b17fbb623ccb1722d4fe017f8decf24618f1055cff01f60210e2","abstract_canon_sha256":"103a837b8067d3b45142bfe282ac048023adb4d61121532e9afe8dd640cad826"},"schema_version":"1.0"},"canonical_sha256":"a77f2e706231c62dceb5b040d49f10b9def4de05b5bdff30cadf69e7afc9eb56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:19.996749Z","signature_b64":"NBTMUuGnfysOyGKd6ctqOSUU45gA0J+WMw1a5hXqawi+SulsCHNGYzOMfMy/BGEHIM5dlXwSjDpZ/hL7eTPZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a77f2e706231c62dceb5b040d49f10b9def4de05b5bdff30cadf69e7afc9eb56","last_reissued_at":"2026-05-18T03:20:19.996129Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:19.996129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.5002","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":"2026-05-18T03:20:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fuULYJO/mmEZUgrsmXYU5azVO8xOAuBOhyR7mLgrMrK8EqvjreuT7K+pPdIHRSK1l5Q5QQ3SU+byzlGALhkdBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T17:52:58.471445Z"},"content_sha256":"d03b19f41ec549e4af9071f4d0fc93c73e9a2c133c52979ff6d933c78ac6062a","schema_version":"1.0","event_id":"sha256:d03b19f41ec549e4af9071f4d0fc93c73e9a2c133c52979ff6d933c78ac6062a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:U57S44DCGHDC3TVVWBANJHYQXH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A fixed-point approximation for a routing model in equilibrium","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Graham Brightwell, Malwina Luczak","submitted_at":"2013-06-20T21:03:29Z","abstract_excerpt":"We use a method of Luczak (arXiv:1212.3231) to investigate the equilibrium distribution of a dynamic routing model on a network. In this model, there are $n$ nodes, each pair joined by a link of capacity $C$. For each pair of nodes, calls arrive for this pair of endpoints as a Poisson process with rate $\\lambda$. A call for endpoints $\\{u,v\\}$ is routed directly onto the link between the two nodes if there is spare capacity; otherwise $d$ two-link paths between $u$ and $v$ are considered, and the call is routed along a path with lowest maximum load, if possible. The duration of each call is an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5002","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":"2026-05-18T03:20:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QSTN4onKJKJSKNrcx1iyn7kSBNlX4a/VmBxIxTyrqgDyEerj4CmzNCiHnA0WpEc87KC5n9+W2HLOcBf9ANtMAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T17:52:58.471781Z"},"content_sha256":"521fbd89d67801461d5365c61031e822b96e8eb5638f5c6ce01c38d15a3ffe85","schema_version":"1.0","event_id":"sha256:521fbd89d67801461d5365c61031e822b96e8eb5638f5c6ce01c38d15a3ffe85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U57S44DCGHDC3TVVWBANJHYQXH/bundle.json","state_url":"https://pith.science/pith/U57S44DCGHDC3TVVWBANJHYQXH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U57S44DCGHDC3TVVWBANJHYQXH/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":"2026-07-03T17:52:58Z","links":{"resolver":"https://pith.science/pith/U57S44DCGHDC3TVVWBANJHYQXH","bundle":"https://pith.science/pith/U57S44DCGHDC3TVVWBANJHYQXH/bundle.json","state":"https://pith.science/pith/U57S44DCGHDC3TVVWBANJHYQXH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U57S44DCGHDC3TVVWBANJHYQXH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:U57S44DCGHDC3TVVWBANJHYQXH","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":"103a837b8067d3b45142bfe282ac048023adb4d61121532e9afe8dd640cad826","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-20T21:03:29Z","title_canon_sha256":"cc99da675fe5b17fbb623ccb1722d4fe017f8decf24618f1055cff01f60210e2"},"schema_version":"1.0","source":{"id":"1306.5002","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5002","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5002v1","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5002","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"pith_short_12","alias_value":"U57S44DCGHDC","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U57S44DCGHDC3TVV","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U57S44DC","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:521fbd89d67801461d5365c61031e822b96e8eb5638f5c6ce01c38d15a3ffe85","target":"graph","created_at":"2026-05-18T03:20:19Z","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 use a method of Luczak (arXiv:1212.3231) to investigate the equilibrium distribution of a dynamic routing model on a network. In this model, there are $n$ nodes, each pair joined by a link of capacity $C$. For each pair of nodes, calls arrive for this pair of endpoints as a Poisson process with rate $\\lambda$. A call for endpoints $\\{u,v\\}$ is routed directly onto the link between the two nodes if there is spare capacity; otherwise $d$ two-link paths between $u$ and $v$ are considered, and the call is routed along a path with lowest maximum load, if possible. The duration of each call is an","authors_text":"Graham Brightwell, Malwina Luczak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-20T21:03:29Z","title":"A fixed-point approximation for a routing model in equilibrium"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5002","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:d03b19f41ec549e4af9071f4d0fc93c73e9a2c133c52979ff6d933c78ac6062a","target":"record","created_at":"2026-05-18T03:20:19Z","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":"103a837b8067d3b45142bfe282ac048023adb4d61121532e9afe8dd640cad826","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-20T21:03:29Z","title_canon_sha256":"cc99da675fe5b17fbb623ccb1722d4fe017f8decf24618f1055cff01f60210e2"},"schema_version":"1.0","source":{"id":"1306.5002","kind":"arxiv","version":1}},"canonical_sha256":"a77f2e706231c62dceb5b040d49f10b9def4de05b5bdff30cadf69e7afc9eb56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a77f2e706231c62dceb5b040d49f10b9def4de05b5bdff30cadf69e7afc9eb56","first_computed_at":"2026-05-18T03:20:19.996129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:19.996129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NBTMUuGnfysOyGKd6ctqOSUU45gA0J+WMw1a5hXqawi+SulsCHNGYzOMfMy/BGEHIM5dlXwSjDpZ/hL7eTPZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:19.996749Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5002","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d03b19f41ec549e4af9071f4d0fc93c73e9a2c133c52979ff6d933c78ac6062a","sha256:521fbd89d67801461d5365c61031e822b96e8eb5638f5c6ce01c38d15a3ffe85"],"state_sha256":"26d182ea754ec466872251fe7c306f86368a7e4c3761f47456b83e7cc20fd9eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jlQytIIJAcvTj4MxK1ZqcKSbqkDwl/ZJFdEDoayci251zRETcn6r46TmybcHoKtwOiQ7mqWJU+h2GJt7AvEIDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T17:52:58.473621Z","bundle_sha256":"801dd354dabe91b5a3340005fb8b320b606c6c6fd99c60aafb8a91091a37c352"}}