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CB-WP-0025 T05: the search works, and it falsified this pass's own

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affordability projection

games/ground/src/search.rs, five tests. It finds real winning lines and
replays them through validate/fold to group_success.

Two bugs in my own work, found and fixed here.

THE TRAVERSAL WAS WRONG. It branched on "the first seat with any legal
command" and stopped there, so a later seat never acted if an earlier one
was already selected but still had a legal move. Restructured around what
the rules oblige: a seat without a selection MUST select (GR-R02) and
nothing else can happen first; after Reveal the optional actions branch
freely and the aggregate rejects Resolve until the obligatory ones are
done -- so the search needs no phase logic of its own.

AND MY REWIND WAS OFF BY ONE ROUND, replaying the round it was meant to
search. That is why the first run reported 3 nodes and looked like a
working search.

Measured with the real search, rewinding real games to the start of their
last K rounds:

  2p K=1  exhausted, 8,103 nodes, ~29 ms
  2p K=2  budget cut at 2,000,000 nodes, ~5 s
  3p K=2  win found, 41 nodes, ~157 us

The spec's own falsifier said "§3 fails if K=2 proves unaffordable at four
seats". IT FAILED AT TWO. The projection assumed a joint product per
round; the search explores sequential per-seat decisions, so orderings
multiply the tree far beyond width^seats. That is the second projection
this pass published in place of a measurement -- C1's timer was the first.

THE ASYMMETRY IS THE OPERATIVE FINDING. Finding a win is cheap: DFS
stumbles onto one in tens of nodes. Proving none exists needs exhaustion.
So the witness feature is affordable now at any K a player would ask
about, and the winnable fraction (ADR-0013 D4) is NOT, because its
negative half must exhaust every deal it counts. K=1 is the honest default
for exhaustive answers today; making K=2 exhaustible needs transposition
or move-ordering, neither of which this pass built. specs §3 and §3.1
corrected accordingly, and the K=2 default withdrawn.

The negative control that makes "winnable" falsifiable: 2p seed 7 over its
last round returns NoneFound with exhausted=true in ~8k nodes -- a real
negative, not a budget cut wearing a verdict's clothes. And the visible/
hidden marking is tested both ways, since a marking that can only say YES
is decoration.

make all: exit 0. loop-lint clean.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
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tegwick 2026-08-05 19:10:25 +02:00
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49
specs/RetrospectiveAnalysis.md
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@ -74,7 +74,19 @@ and this sentence is what the player reads.
## 3. The bound
**Exhaustive over the last `K` rounds**, table treated as one co-operative
agent choosing joint selections. `K = 2` by default.
agent choosing joint selections.
**`K = 1` for an exhaustive answer; `K` may be larger when a witness is
all that is wanted.** ADR-0013 said `K = 2` by default; §3.1's measurement
overrides it, and the difference is which question is being asked:
| answer | needs | affordable `K` today |
|---|---|---|
| *"here is a winning line"* | one success | 2+ — DFS finds one in tens of nodes |
| *"there is no winning line"* | exhaustion | **1** — `K=2` exceeded 2×10⁶ nodes at two seats |
A `K` that cannot be exhausted may still emit a witness; it may **not**
report `NoneFound { exhausted: true }`, and the type keeps those apart.
Bounded in **rounds**, not nodes: *"winnable from round 4"* means something
to a player; *"winnable within 100,000 nodes"* does not. A node budget is a
@ -106,10 +118,37 @@ widths:
| 3 | ~1.6×10⁵ | **~0.8 s** |
| 4 | ~5.7×10⁵ | **~2.9 s** |
**So `K = 2` is affordable at two, three and four seats, and is not at
five or six** — joint branching there exceeds 10⁶ per round. Five and six
seats require a smaller `K`, and the tool must reduce it and **say that it
did** rather than silently searching less.
> ### The projection above was wrong, and the real search falsified it
>
> **Measured 2026-08-05 with the search built in T05**, rewinding real
> games to the start of their last `K` rounds:
>
> | case | result |
> |---|---|
> | 2p, `K=1` | **exhausted** in 8,103 nodes, ~29 ms — a real negative |
> | 2p, `K=2` | **budget cut** at 2,000,000 nodes, ~5 s — not exhausted |
> | 3p, `K=2` | win found in 41 nodes, ~157 µs |
>
> §6's falsifier said *"§3 fails if K=2 proves unaffordable in practice at
> four seats"*. **It failed at two.**
>
> The projection assumed a joint product per round. The search explores
> **sequential per-seat decisions**, and the post-Reveal phase branches
> over every seat's options at every level, so orderings multiply the tree
> far beyond `width^seats`.
>
> **And the asymmetry is the operative fact:** *finding* a win is cheap —
> depth-first stumbles onto one in tens of nodes — while *proving none
> exists* is expensive, because it must exhaust the space. So:
>
> - **the witness feature (§2) is affordable now**, at any `K` a player
> would ask about;
> - **the winnable fraction (§4.2) is not**, because its "not winnable"
> half requires exhaustion on every deal it counts.
>
> `K = 1` is the honest default for exhaustive answers today. Making
> `K = 2` exhaustible needs transposition or move-ordering, neither of
> which this pass built.
**The published 112–161 µs/node figure is withdrawn** (CB-RES-0008 §1.2,
challenge C1) and must not be quoted from anywhere.