# STAGED > Build the whole board from scratch with no pre-set frame, in stages, letting the border emerge last from whatever pieces are left. - Canonical page (with interactive figures/demos): https://eternity2.dev/research/lab/experiments/raphael-anjou/pipelines/staged/ - Updated: 2026-07-21 - Topics: construction - Reproduce: `just research-record-boards` - Source: Beam search (this project's concept page): the staged construction primitive — https://github.com/raphael-anjou/eternity2/blob/main/web/content/research/build/construct/beam-search.mdx --- Almost every solver starts by locking down the border, because the border is the most constrained part and pinning it shrinks the search. STAGED is an experiment in refusing that crutch. It builds the board in stages from the top down with all 256 pieces free, and never commits to a border until the very end, when the border simply falls out of what remains. The question it answers: can you reach a strong board without ever anchoring to a frame? ## How it works The build runs in four stages. The first two fill the top half of the board with a fast plain search, banking the partial boards that survive. At the handoff, a cheap admissible estimate throws out any partial that clearly can't be finished well, so later stages only work on promising starts. The third stage grows the next band of rows from those survivors. The fourth is an exact finisher on the bottom rows that minimizes mismatches, and it chooses the bottom border last, against whatever pieces are still unused. So the frame is not designed up front; it emerges as a consequence of everything above it. > **[Figure]** Interactive: the stage-by-stage build — interactive: StageBuildDiagram. Rendered on the canonical page (link above); not shown in this markdown export. ## The result STAGED reaches 436 of 480 from scratch, with an emergent border and all five official clues respected, built end to end with no frame to lean on. That's well below the records, and that gap is the finding: it measures how much the usual frame-first anchor is worth, and it showed the frame-free machinery works at full scale. Along the way it pinned down the anatomy of the very best boards: they are a perfect block of most of the board plus a thin band of mismatches concentrated in a few top rows. That shape is what later builders aim to reproduce on purpose. ## Method Four stages, each handing survivors to the next through an admissible filter. 1. **Top-half beams (stages 1–2).** Fill the top half with a fast plain search, banking the partial boards that survive. All 256 pieces are free, no frame is pinned. 2. **Admissible handoff.** At each stage boundary, a cheap *admissible* estimate (an optimistic upper bound on the best possible finish) discards any partial that provably can't be completed well. Because the estimate never under-counts the achievable score, discarding is safe, it only removes partials that cannot win. 3. **Band grow (stage 3).** Extend the surviving partials down the next band of rows. 4. **Exact finisher (stage 4).** Solve the bottom rows exactly, minimizing mismatches, and *choose the border last* from whatever pieces remain. The frame is not designed up front; it falls out of everything above it. The result is 436 from scratch with an emergent border, all five clues respected, well below the records, and that gap is the measurement: it prices what the usual frame-first anchor is worth. The by-product mattered more than the score: STAGED pinned the anatomy of the best boards, a large perfect block plus a thin band of mismatches in a few top rows, the target shape later builders aim at deliberately. ## Reproduce Stochastic (the top-half beams use randomized tie-breaking), so a re-run won't reproduce the exact board; the committed 436 board is the artifact of record and is checkable in the viewer. The engine is the shared beam producer, run in stages so the border emerges last rather than being fixed first. It needs no corpus or seed board, so a runnable backing directory for the full staged pipeline is planned alongside the other from-scratch builders. ## Open questions Can a generator that deliberately spends its mismatches in the top rows, to keep the rest perfect, reach the 450s frame-free? How much of the 436-to-record gap is the missing frame anchor versus the harder endgame? And does a learned finish-quality estimate pick better survivors than the cheap admissible one? ## Related - [CLOISTER](https://eternity2.dev/research/lab/experiments/raphael-anjou/pipelines/cloister) — Fix a perfect border, then search the interior with the border's edges treated as hard constraints from the very first cell. - [BANDSAW](https://eternity2.dev/research/lab/experiments/raphael-anjou/meet-in-the-middle/bandsaw) — Solve a band of rows exactly by meeting in the middle, to find the true best ending and to measure how far ahead an endgame can be decided. - [Beam search](https://eternity2.dev/research/build/construct/beam-search) — Keep the K most promising partial boards alive at once and grow them cell by cell. Beam search is the workhorse behind this project's from-scratch builders, and a clean illustration of why breadth alone stalls in the deep interior.