Blankline published a verifiable record of agentic search: external memory led the model to a new packing structure for 26 circles
Blankline opened its agentic search archive: 91 attempts, coordinates, and three stages behind one result
On August 31, the Blankline Research team published a technical report and a repository on the following problem: place 26 circles inside a unit square without overlap while maximizing the sum of their radii. The repository contains the final coordinates, verification programs, and records from the full series of attempts.
The language model wrote programs that searched for the center coordinates and radii of the 26 circles. A separate script checked whether any circle extended beyond the square or overlapped another circle. An invalid configuration received a score of zero.
External memory is a separate store of short records from previous attempts. After each attempt, it received a record describing what had increased the sum of the radii and what had caused a failure. Before the next run, the model received these records together with the task. In 46 of the 91 attempts, the AVOID field lists earlier errors, and the accompanying script matches four such summaries against the archive. On attempt No. 77, the best result increased from 2.627796 to 2.635871.
Two scripts verify different properties of the final coordinates. verify.mjs recalculates the sum of the radii as 2.635917599028 and accepts the configuration with a tolerance of one billionth. contact-graph.mjs constructs the contact graph: its vertices represent circles, and its edges connect pairs of circles that touch. The graph's degree sequence, which gives the number of contacts for each circle, differs between the Blankline solution and the three published coordinate sets from AlphaEvolve, Packomania, and Hyra. This proves that the contact graphs remain distinct even after the circles are renumbered.
The final sum of the radii resulted from three phases. The best result from the memory-based loop was 2.635907462261. The authors then applied their own script for linear optimization of the radii and rearrangement of the structure, obtaining 2.635912195016. In the final phase, a separate program searched over random initial conditions and parent configurations without calling the model, increasing the value to 2.635917599028.
The What AI Found registry distinguishes AI results by verification status and the machine's contribution. The Blankline archive reveals the same distinctions within a single run: the coordinates can be recalculated, the attempt log can be read in sequence, and the contributions of the model-based loop, the script authors, and the final search can be examined separately.