{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VA52YHFB3EDPS3VK64CYZS7TYF","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":"913cceb3ba5a7128af5f5f385cf1a0ddacd8a465aade85e7cd8ff9c03b5ebbf7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-07-09T17:25:37Z","title_canon_sha256":"28e5f064e6eab52021218802917724fa5a0809d5fa8ddd5b154a8cd1ac7bb774"},"schema_version":"1.0","source":{"id":"1607.02637","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.02637","created_at":"2026-05-18T01:11:16Z"},{"alias_kind":"arxiv_version","alias_value":"1607.02637v1","created_at":"2026-05-18T01:11:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02637","created_at":"2026-05-18T01:11:16Z"},{"alias_kind":"pith_short_12","alias_value":"VA52YHFB3EDP","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VA52YHFB3EDPS3VK","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VA52YHFB","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:008c44c866562a987eb14a742f01127a1492427a7dd43c4869e07ea1f494e0cb","target":"graph","created_at":"2026-05-18T01:11:16Z","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 define a \\emph{thermal network}, which is a network where the flow functionality of a node depends upon its temperature. This model is inspired by several types of real-life networks, and generalizes some conventional network models wherein nodes have fixed capacities and the problem is to maximize the flow through the network. In a thermal network, the temperature of a node increases as traffic moves through it, and nodes may also cool spontaneously over time, or by employing cooling packets. We analyze the problems of maximizing the flow from a source to a sink for both these cases, for a","authors_text":"Samiksha Sarwari, Shrisha Rao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-07-09T17:25:37Z","title":"Network Flows Under Thermal Restrictions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02637","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":"sha256:09f8c33308d5ab8c4f47aeecbe6fa4f0e3f51c6a507b7aacfc55fc2afc6b922f","target":"record","created_at":"2026-05-18T01:11:16Z","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":"913cceb3ba5a7128af5f5f385cf1a0ddacd8a465aade85e7cd8ff9c03b5ebbf7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-07-09T17:25:37Z","title_canon_sha256":"28e5f064e6eab52021218802917724fa5a0809d5fa8ddd5b154a8cd1ac7bb774"},"schema_version":"1.0","source":{"id":"1607.02637","kind":"arxiv","version":1}},"canonical_sha256":"a83bac1ca1d906f96eaaf7058ccbf3c1728f9ae7a425a25edb9e8afc1fd70aab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a83bac1ca1d906f96eaaf7058ccbf3c1728f9ae7a425a25edb9e8afc1fd70aab","first_computed_at":"2026-05-18T01:11:16.572441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:16.572441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jky48Xr3kb1u/+yKkTcSCyu1zAAw5FWxjHfm8JUWkuCEsdbpmqZyGh4N7o3l8hv2YriyMwpqvEfqJwltJ8IrBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:16.572898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.02637","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09f8c33308d5ab8c4f47aeecbe6fa4f0e3f51c6a507b7aacfc55fc2afc6b922f","sha256:008c44c866562a987eb14a742f01127a1492427a7dd43c4869e07ea1f494e0cb"],"state_sha256":"4a22e8cf7067451d9fe6a2529cbd3d803824f4e72f277c4f8bd092a678c8d3a5"}