Constructive spectrum

Rather than asking "which column scores most now?", this planner asks "what should the board look like when the next row rises, and which column heads there?" — and on 32 paired games that question was worth 266,696 points against the one-move-ahead reference's 157,198.

The intuition

The planner carries an explicit picture of a healthy board and steers toward it. Four things make up that picture:

• a spectrum of heights — columns at a variety of heights rather than a flat wall, so that discs of many different numbers have somewhere useful to land;
• accessible edge covers — gray discs that can still be reached and opened, rather than buried;
• safe caps — the discs sitting on top of each column should not be ones that block everything beneath them;
• overlapping trigger keys — stored high-numbered discs whose trigger conditions coincide, so that one arriving disc can set off several of them.

A "trigger key" is just the pair (which disc arrives, which column it goes in). Two stored discs whose keys are the same are worth much more than two whose keys differ, because the player only ever gets one disc at a time. The family page shows the underlying mechanism 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; carrying more incurs rapidly increasing debt. Reservoir size and trigger coverage stop paying once they match the motif, so the planner is not rewarded for simply filling the board.

How it works

1. A conventional three-ply search runs first and produces 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 is.
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 matter, not by the points collected along the way.
4. Play the shortlisted column with the best average.

Everything read is public. The oracle curriculum appears in this source only to measure what the target motif looks like; the ledger and the source header both state that no oracle action, future disc, reveal randomness, seed, score, level, move index or history enters the deployed policy.

What happened

Against the one-move-ahead fair search, on 32 complete games, the planner averaged 266,695.5 points and 79.5 moves versus 157,198.1 and 49.9 — and won 25 of the 32 paired games, with higher clear and reveal flow. That is the strongest result in this family and a genuine demonstration that planning across a complete rise cycle contains information a one-move policy does not have.

It did not survive contact with the four-move search. Three follow-ups were run and all three were rejected:

• As a tie-break on top of depth 4, allowed to touch only the top two near-equal columns, it averaged 283,286 against exact depth-4's 372,870.5 on the same four fitting games. It changed 37.0% of moves and won one of the four pairs.
• Making the continuation longer helped, then stopped helping. Twelve moves of continuation beat seven (299,730.6 / 88.3 against 258,223.9 / 77.2 on 32 fitting games), but won only 16 joint games and failed the frozen robustness gate. Seventeen moves collapsed to 202,634 / 62.0; twenty-seven recovered only to 261,633 / 77.9.
• Admitting the longer horizon only when it was safe — a coefficient-free gate that 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 — improved the means again (302,114.9 / 89.3 against 254,541.3 / 76.3) but switched only 286 of 918 disagreements and produced 17 joint wins where the gate required 20.

Neither of the last two opened a screen, so none of this ever reached a confirmation cohort.

The technical record

Status: completed (base planner) — ledger-recorded, with three rejected variants recorded in the same section of the experiment history §"Explicit reservoir and constructive-cycle policies (rejected)". All are corrected 17,000-point results, checked as internally consistent by audit 03 rows 4421–4441.

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

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.

The four-game 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. Nothing here was measured on the protected or final cohorts, which remain unopened.

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

Sources: constructive-spectrum.cpp, constructive-spectrum-depth4.cpp, constructive-horizon-scale.cpp, constructive-h12-risk-gate.cpp.

What this taught us, and what is still open

• Complete-cycle planning beats a one-move policy decisively. That is the family's central positive finding, and the ledger records it as the reason the idea stays alive.
• The same signal, injected into a stronger search as an override, damaged it. Frequent switching on unstable comparisons between near-equal columns is the named failure mode, and it recurs across the repository.
• Longer is not better: 7 → 12 helped, 12 → 17 hurt badly, 17 → 27 partly recovered. A sampled continuation policy does not become a reliable evaluator by being run for longer.
• The open direction recorded in the strategy landscape is to make multi-cycle comparison between sibling columns affordable and stable — cheaper verified continuations, shared random futures across siblings, early elimination — rather than to plan further.