Trajectory throughput

Line up an ordinary player and a player that is allowed to cheat on the same games, chop both games into five-move windows, and compare the windows: what is the cheat doing that the honest player is not?

The intuition

The natural question — "why do our policies die?" — is hard to answer by staring at final scores, because the answer arrives dozens of moves after the mistake. The trick used here is to compare windows rather than games.

A window is one complete five-drop cycle, ending exactly at a rise. Because both players get the same seed and are compared window against window at the same point in the game, differences in what happened inside a window are differences in play, not differences in luck or in how long each survived.

For each window the program records what the board looked like and what flowed through it: how many gray discs were cracked, how many were revealed, how many numbered discs cleared, how many chain waves and how deep the deepest was, how many boards were cleared outright, how many moves were "quiet" (building without scoring), how many produced more than one wave, and how much stored trigger potential was spent. Alongside those it records board-shape measures — height, occupancy, cover load, direct and latent chain potential, and clog patterns such as adjacent 1s and triple 2s — and, for the searching arms, the search depth and work per move.

The comparison then asks which of those quantities most separates the privileged arm from the honest ones. Whatever that is, is a candidate description of "a game that sustains itself".

How it works

1. Play the same seeds with each arm: the perfect-information planner (a depth-4 beam of width 128 over known hidden values), the hand-written combined evaluator inside a bounded search, and optionally a trained DQN checkpoint.
2. Cut every game at completed five-move boundaries and emit one record per window per arm.
3. Match windows across arms by seed and by window position, so every comparison is like-for-like.
4. Rank the measured quantities by how strongly they separate the arms. The report's own note is careful about this: the separation figure is the mean difference divided by the standard deviation of per-seed mean differences, "a ranking aid, not a causal estimate", precisely so that repeated windows from one game do not masquerade as independent games.
5. Use training and calibration seeds only; validation and final seeds are never opened.

What happened

This is the analysis that produced the flow targets the rest of the repository quotes: roughly 2.4 numbered clears and 1.4 reveals per move as the region associated with games that keep going. The research status carries them with an explicit warning attached — "treat these as diagnostic targets from limited runs, not proven universal thresholds" — and this page repeats the warning, because the run that produced them survives only as a task record.

Two later, independently recorded results speak to the same numbers and are worth reading next to them:

• Finding 01 derives 2.400 and 1.400 rather than measuring them: every five-move cycle puts five placed discs plus a seven-disc covered row onto a 49-cell board, so 12/5 and 7/5 are the break-even rates. It measures the depth-4 reference at 1.973 clears and 1.090 reveals per move over 64 paired games — a structural deficit of 18% and 22%.
• Finding 06 measures a clairvoyant planner at 2.3663 clears and 1.3832 reveals per move on 64 fresh tapes. It also carries two published correction notices, including one stating that no legal policy tested reached flow balance; the best legal arm reached 2.2309 clears per move, 93.0% of the requirement.

So the target region this diagnostic pointed at has held up as a description of what the ceiling looks like. What no retained record shows is a legal policy reaching it.

The technical record

Status: completed — task-record only. The experiment index records: "this analysis motivated the approximate 2.4-clear and 1.4-reveal sustainability targets." There is no ledger entry, protocol, artifact hash or retained per-window data; audit 04 §B.2 lists it as task-record only and notes that it is the only file in the repository that counts board clears.

Defaults, from the source: training seeds from 0x2d700000, calibration seeds from 0x5d700000, validation seeds from 0x7d700000 reserved and untouched, 4 games each, a 100-move cap, window = 5 moves, oracle depth 4 with beam width 128, baseline search depth 4 with a 20,000-unit work cap. The privileged arm is planOracleMove from approaches/oracle-curriculum/perfect-information-oracle. The report begins with its own warning string about the oracle's status.

Both of the corroborating findings above are exploratory documents at the development/pilot tier, not ledger results, and finding 06 explicitly warns that its eight original master tapes favour long games. The clairvoyant figures there are stated to be unaffected by that bias; the fair depth-4 comparator on those tapes is not.

Source: main.ts.

What this taught us, and what is still open

• Comparing matched five-move windows, rather than whole games, is a way to see a policy's mistakes near where they happen.
• A privileged planner shows what a sustained game looks like. It does not show how to get there, and none of the legal policies measured since have.
• The 2.4 / 1.4 pair has survived contact with two later analyses, one of which derives it from the board's arithmetic — but the run on this page is a task record and cannot be re-derived from anything retained here.