---
title: Constructive spectrum
family: constructive-reservoir
summary: Plans a five-drop cycle toward a target board with spread-out heights, reachable covered discs, and shared triggers. It clearly beat the one-move-ahead reference.
status: completed
evidence: ledger-recorded
reads: public
---

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.

<EvidenceLabel status="completed" evidence="ledger-recorded" reads="public" />

## 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](/approaches/constructive-reservoir) 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.

<TechnicalDetails title="The technical record">

**Status: completed (base planner); ledger-recorded**, with three rejected
variants recorded in the same section of the
[experiment history](/docs/research/history) §"Explicit reservoir and
constructive-cycle policies (rejected)". All are corrected 17,000-point
results, checked as internally consistent by
[audit 03](/docs/exploratory/audit-03-claim-arithmetic) 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](/docs/reproducibility)'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`.

</TechnicalDetails>

## 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](/docs/strategies) 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.