test(cliffs): invert the elevation by level set - #18 is ONE TERM of vulcanus_elev

[wormeyman]

The collapsed rule from #81 is also an instrument. A cell carries a cliff exactly when its corner elevations straddle cliff_elevation_0, so sweeping that threshold measures the elevation field the generator reads - the one thing an expression sample cannot do, since calculate_tile_properties answers for its own channel and whether the two agree was the open question.

19 levels, cliff_elevation_0 20..200 step 10, region [0,0], rule collapsed:

cliff_elevation_0	game	ours	ours/game
20	658	979	1.49
40	603	816	1.35
70	335	463	1.38
110	142	200	1.41
120	122	126	1.03
150	117	117	1.00
200	97	97	1.00

A clean edge at 120. At or above it every level is 1.00-1.04 and the same cells (both/game > 0.9, not merely the same count); below it every level is 1.20-1.49. Worst high 1.04 vs best low 1.20 - a threshold, not a drift, which is why the spec asserts the gap rather than two bounds separately.

Why 120 is not arbitrary

vulcanus_elev =
  vulcanus_elevation_offset
    + lerp(lerp(120 * vulcanus_basalt_lakes_multisample,
                20 + vulcanus_mountains_func * vulcanus_mountains_elevation_multiplier,
                vulcanus_mountains_biome),
           vulcanus_ashlands_func,
           vulcanus_ashlands_biome)

vulcanus_basalt_lakes is a min(1, ...), so the basalt-lakes branch saturates at exactly 120. Everything above 120 comes from the mountains and ashlands branches - which contain no multisample - and the port reproduces those exactly. Everything below is governed by vulcanus_basalt_lakes_multisample: the only multisample in the chain, and the only term with no Nauvis counterpart.

So the residual is that one term, and the port is exact everywhere else in the field. That is a far smaller target than "the Vulcanus elevation".

The mechanism to suspect

multisample's own docs: it evaluates "in a separate noise program with a larger grid" whose "sub-grids are copied to the main program". The cliff generator walks the 4-tile corner lattice; calculate_tile_properties does not - and that is the channel vulcanus-multisample-NOTES.md measured multisample(e,dx,dy) == e(x+dx,y+dy) through, and the channel every elevation fixture was captured through. A min() of four samples is an erosion operator, so a coarser effective grid smooths the field exactly the way a 40% over-placement implies.

What this does NOT say

Neither the multisample port nor the corner-fields fixture is refuted - both are correct in their channel. What has never been tested is whether the primitive behaves the same when the calling program's grid is 4 tiles rather than 1. The tile renderer, which consumes vulcanus_elevation through that same 1-tile channel, is not implicated by any of this.

Does not fix #18. pnpm run verify: 309 files clean, 1302 passed / 3 skipped, preview 12 passed.

🤖 Generated with Claude Code

https://claude.ai/code/session_01GRx1CU29RKLsRuUAErEDRB