An explicit construction disproves the undirected multiple-unicast conjecture

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Stable ID

cs-undirected-multiple-unicast-counterexample-2026

Revision

cs-undirected-multiple-unicast-counterexample-2026.v1

Field

Theoretical computer science · Network coding, information theory and theoretical computer science

Evidence

Tier 1 · Peer reviewed: No

Record state

Provisional · Explicit verifier-backed preprint counterexample

Last checked

2026-10-19

AI role

The authors report that GPT-6 found a nondeterministic design. They converted it into a causal construction, applied orientation and local search, and supplied an exact symbolic verifier and simulator.

Record details

Problem or result

Undirected multiple-unicast network-coding conjecture

Authors

Mark Braverman and Zhongtian He

Institutions

Princeton University

Result date

Preprint submitted October 7, 2026

Why it matters

The paper supplies a finite explicit witness against a long-standing network-coding conjecture rather than only an existential separation.

Limits

The executable checker is author-supplied rather than an independent replication, the amplified family depends on the cited theorem, and the large construction has not been peer reviewed or independently replayed in the sources checked.

Sources

1. Primary: Braverman and He multiple-unicast counterexample
2. Verification artifact: Counterexample symbolic verifier and simulator

Correction and revision history

1. 2026-10-19 — Added after primary-source, scope, status, AI-role and limitation review.

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