Constructive spectrum

The problem

A one-move-ahead search asks which column scores most right now. But a chain that clears a dozen discs is assembled several moves before it fires: the high-numbered discs have to be stored in columns whose heights will still be right when the chain is triggered. A covered row rises after every five placed discs and changes every column's height at once, so a shape that is worth nothing on the move it is built can be worth a great deal two rises later, or can be worth nothing then either. Whether steering toward a described board shape across a whole rise cycle is worth more than taking the best-scoring column now had not been measured.

Proposed solution

Carry an explicit picture of a healthy board and steer toward it. The picture has four parts: columns at a variety of heights rather than a flat wall, so discs of many different numbers have somewhere useful to land; gray discs that can still be reached and opened rather than buried; discs sitting on top of each column that leave the discs beneath them playable; and stored high-numbered discs whose trigger conditions coincide.

A trigger key is the pair (which disc arrives, which column it goes in). Two stored discs that share a key are worth much more than two that do not, because the player only ever gets one disc at a time. The family page shows the underlying shape on a real board: a stack that is inert until the rise makes its run the right length.

The target is deliberately asymmetric. Carrying less load than the reference motif is safe and carrying more incurs rapidly increasing debt, and reservoir size and trigger coverage stop paying once they match the motif, so the planner earns nothing for filling the board.

Everything the planner reads is public: the visible board, the visible next disc and the position in the five-drop cycle. The oracle curriculum appears in this source only to measure what the target motif looks like, and the ledger and the source header both record that no oracle action, future disc, reveal randomness, seed, score, level, move index or history enters the deployed policy.

How it works

1. Run a conventional three-ply search on the public position and keep a shortlist: its best column, plus the runner-up if it is within 2,500 utility units. If only one column qualifies, that column is played and no planning happens.
2. For each shortlisted column, simulate forward to the end of the current five-drop cycle plus one further build cycle, with a bounded beam and seven sampled chance outcomes at each step. The horizon adapts between 3 and 7 moves depending on where in the cycle the position sits.
3. Score the end of each simulated line by the target picture, in score-like units so that the two rise bonuses inside the horizon still count, rather than by the points collected along the way.
4. Play the shortlisted column with the best average. The output at every position is one column.

What happened

Against the one-move-ahead fair search on 32 paired games, the planner averaged 266,695.500 points against 157,198.063 and won 25 of the 32 on score and survival together (completed, ledger-recorded, ledger section "Explicit reservoir and constructive-cycle policies"). It also survived longer and cleared and revealed more per move. That is the strongest retained result in this family.

It did not displace the four-move search. Three follow-ups were run and all three were rejected. Letting the planner override the four-move search on its top two near-equal columns switched moves often enough to lose its fitting quartet outright. Stretching the continuation from seven moves to twelve improved the means and missed the frozen robustness gate, and going on to seventeen made things much worse before twenty-seven partly recovered. Admitting the twelve-move answer only when it dominated the seven-move answer on a shared scenario panel improved the means again and produced fewer joint wins than its gate required. Neither of the last two opened a screen, so none of this reached a confirmation cohort.

What we learned

Planning across a complete rise cycle carries information a one-move policy does not have, and 32 paired games was enough to see it. The same signal pushed into a stronger search as an override damaged it, through the failure mode this family keeps producing: frequent switching on unstable comparisons between near-equal columns.

Longer continuations did not become more accurate by being longer. Seven moves to twelve helped, twelve to seventeen hurt badly, and twenty-seven only partly recovered, so a sampled continuation policy has a length past which its own noise costs more than the extra look-ahead buys. The four-game fitting comparison behind the depth-4 override is a quartet, wide enough to see a deficit that large and nowhere near wide enough to certify its size.

The direction the strategy landscape records from here is to make multi-cycle comparison between sibling columns affordable and stable: cheaper verified continuations, common random futures shared across siblings, admissible early elimination. Whether any of that makes the constructive signal safe inside a four-move search is the open question.

Agent contextRecords and provenanceopen ↓close ↑

Records: experiment index "Constructive and reservoir policies", rows for constructive-spectrum.cpp (completed), the constructive D4 shield, the constructive horizon scale and the H12 risk gate (all rejected); ledger section "Explicit reservoir and constructive-cycle policies (rejected)", which records the completed base planner and the three rejected variants together. audit-03 rows 4421–4441 checked these figures as internally consistent.

Frozen configuration, from the source: analysis seeds 0x3d690000–0x3d69003f (64 games), Stage A seeds 0x3d69c000–0x3d69c01f (32 games), 1,000-move cap, 7 chance samples, horizon 3–7, tactical depth 3, shortlist of 2, near-tie margin 2,500, centre-first column order 3,2,4,1,5,0,6, policy seed CSP1, 30-minute wall limit and 256 MiB RSS limit. The horizon-scale and risk-gate variants reuse that exact configuration and change only the one thing named. The depth-4 shield uses the reference full-width fair-D4 root with five chance strata and returns exact depth-4 whenever the shortlist is a singleton.

Historical source hashes are recorded in the ledger; the reproducibility guide warns that the tree was reorganised after those hashes were frozen, so they intentionally no longer match current bytes.

Agent contextFull results tableopen ↓close ↑

Run	Games	Candidate	Comparator
Stage A	32	266,695.500 / 79.500, 25 joint wins	fair D1 157,198.063 / 49.875
Depth-4 shield, fitting	4	283,286 / 83.750, 37.0% switches, 1 pair won	exact D4 372,870.500 / 106.250
Horizon ablation	32	H12 299,730.563 / 88.344, 16 joint wins	H7 258,223.938 / 77.219; H17 202,634 / 61.969; H27 261,633 / 77.938
H12 Pareto risk gate	32	302,114.906 / 89.281, 286/918 switched, 17 joint wins	H7 254,541.344 / 76.344; 20 wins required

Scores are mean points per game and mean moves per game. The H12 Pareto risk gate is coefficient-free: it accepted the 12-move answer over the 7-move one only when it dominated on mean return, lower-quartile return, terminal count and flow across a shared 21-scenario panel.

Agent contextValidity, gates and limitationsopen ↓close ↑

The four-game depth-4 fitting comparison is a quartet, not a cohort: four paired games is enough to see a deficit that large and nowhere near enough to certify its size. The 32-game Stage A comparisons are screens.

The horizon ablation's frozen robustness gate failed at H12 despite the better mean, on 16 joint wins. The H12 Pareto risk gate switched 286 of 918 disagreements and produced 17 joint wins where 20 were required. Neither of those two experiments opened a screen. Nothing here was measured on the protected or final cohorts, which remain unopened.

Agent contextScoring modeopen ↓close ↑

All four runs are corrected 17,000-point Hardcore results, and audit-03 checked them for internal consistency. No historical 7,000-point figure appears on this page, so nothing here is compared across scoring modes.