test(layered-path): pin k-prefix stability for solve_k_best

[PhysShell]

Test-only. One test file, no production code. S7 Slice C's acceptance
(7d0c0cb) is not reopened — this pins a contract that was specified and left
unasserted after closure.

The property

A caller that shows three alternatives and then asks for five must not watch the
first three renumber themselves:

for a fixed problem and min_distance:
  solve_k_best(k = i).paths == prefix(solve_k_best(k = N).paths, i)   for every i ≤ N

The accepted engine already satisfies it — neither the enumeration order nor the
greedy diversity filter reads k — so this is a characterization test, not
a red→green fix. Nothing was broken on purpose to manufacture a red phase.

It was specified, though: the still-draft deterministic-search proposal (#176)
asks for it in as many words — "requesting more results never changes the
prefix already returned". "True by construction" is exactly the kind of claim
that quietly stops holding one refactor later without anything failing.

What is compared

Per rank, not merely per path list:

• the ordinal vector;
• total_cost.to_bits();
• the full Debug rendering, which carries every step and edge with its axes,
  rationale entries, weights and provenance.

f64 renders in shortest round-trip form, so a cost differing in a single bit
renders differently — "the same path" cannot quietly become "the same indices,
differently computed".

Swept over all 120 width vectors for 1–4 layers over widths 1–3, every
min_distance, and every k below the widest request, with an anti-vacuity
floor on the number of ranks actually compared.

exhausted is deliberately excluded from the compared prefix: it describes the
search, not the paths, and a request for fewer alternatives can legitimately
stop before the space runs out.

Verification

• cargo test --workspace — 1454 passed, 0 failed (1453 before, +1)
• cargo clippy --workspace --all-targets -- -D warnings — clean
• cargo fmt --all --check — clean

🤖 Generated with Claude Code

https://claude.ai/code/session_01TvcPGrQsgY4HqzmdDcRqvu

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Generated by Claude Code

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