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?
Current τ response
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
- Does τ produce an algorithm, a lower-bound obstruction, or a complexity invariant?
- Is the τ invariant independent of numeric magnitude in the strong-polynomial sense?
- How does it relate to existing interior-point, simplex, and real-computation frameworks?
Source anchors
Source anchors are background references, not endorsements of Panta Rhei claims.