Agenda Structural Challenge Canonical mathematics structural-challenge, mathematics Does there exist a strongly polynomial-time algorithm for deciding or solving linear programming problems, independent of numerical bit-size in the relevant sense?
Mathematics Structural Challenge Ledger

Strongly Polynomial Optimization Challenge

S9 smale derived smale derived External: externally open τ response: further investigation

Does there exist a strongly polynomial-time algorithm for deciding or solving linear programming problems, independent of numerical bit-size in the relevant sense?

See the paired Strongly Polynomial Optimization Challenge — Challenge Response on the Results lane for the program's current response status, registry evidence, verification route, and external-review boundary.

Current status: further investigation.

Challenge statement

Does there exist a strongly polynomial-time algorithm for deciding or solving linear programming problems, independent of numerical bit-size in the relevant sense?

Why this challenge is in the ledger

Tests the relationship between geometry, computation, feasibility, and optimization. Clean route-to-knowledge challenge.

τ-facing burden

Show whether τ-address geometry, interface width, or admissible transition structure gives a new invariant relevant to strong polynomiality.

First reviewer questions

  1. Does τ produce an algorithm, a lower-bound obstruction, or a complexity invariant?
  2. Is the τ invariant independent of numeric magnitude in the strong-polynomial sense?
  3. How does it relate to existing interior-point, simplex, and real-computation frameworks?

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