S05 — Research: deduction puzzle and seed variety
GDD §6.1 model: 6 primals + Taint, 24 compounds, 3-option pools, pair uniqueness; 400 seeds. Failed Crucible test = 360 motes of flux; success = 90; Prism = +1 temporary warp; Separator = +3 warp, 270 flux. Identification order is tier by tier (you need a compound's parents to test it).
1. Seed variety
- Distinct full recipe graphs: 400 / 400 seeds.
- Mean share of recipes two random seeds have in common: 26% (p90 38%).
| Compound | tier | recipe frequencies across seeds | gate |
|---|---|---|---|
| growth | T1 | dew+loam 22%, glim+loam 32%, dew+glim 28%, hush+loam 17% | |
| ore | T1 | ember+loam 22%, hush+loam 22%, breath+loam 28%, dew+loam 29% | |
| mist | T1 | breath+dew 22%, dew+ember 25%, breath+hush 25%, dew+hush 28% | |
| spark | T1 | breath+ember 20%, ember+glim 24%, breath+glim 31%, glim+hush 24% | |
| shade | T1 | glim+hush 29%, breath+hush 30%, dew+hush 25%, hush+loam 16% | |
| salt | T1 | dew+loam 22%, dew+ember 28%, glim+loam 20%, dew+glim 30% | |
| ash | T1 | ember+loam 26%, ember+hush 35%, hush+loam 22%, breath+ember 17% | |
| motion | T1 | breath+loam 27%, breath+ember 20%, breath+dew 27%, breath+glim 27% | |
| glass | T1 | ember+loam 25%, glim+loam 24%, ember+glim 28%, breath+ember 22% | ✓ |
| metal | T2 | ember+ore 26%, ore+spark 24%, ore+salt 23%, loam+ore 26% | ✓ |
| bone | T2 | ash+loam 24%, ash+salt 25%, ash+ore 27%, ash+hush 24% | |
| vigil | T2 | glim+spark 20%, glass+glim 25%, shade+spark 27%, ember+glass 27% | ✓ |
| animus | T2 | growth+motion 24%, ash+motion 24%, mist+motion 27%, loam+motion 24% | ✓ |
| lift | T2 | breath+glass 28%, glim+ore 26%, glass+mist 22%, breath+ore 24% | ✓ |
| mind | T2 | mist+spark 20%, glim+shade 26%, hush+spark 27%, glim+mist 27% | |
| hunger | T2 | growth+shade 23%, ash+hush 20%, ember+growth 32%, ash+shade 24% | |
| root | T2 | growth+hush 26%, ash+growth 30%, growth+shade 20%, growth+loam 24% | |
| memory | T3 | bone+mind 23%, mind+salt 23%, ash+mind 24%, glass+mind 30% | |
| fetter | T3 | metal+taint 22%, bone+taint 27%, taint+vigil 23%, animus+taint 28% | |
| dawn | T3 | growth+vigil 24%, glim+lift 29%, animus+spark 24%, ember+vigil 23% | |
| dream | T3 | mind+mist 26%, mind+shade 26%, hunger+mist 27%, hush+mind 21% | |
| echo | T3 | hush+mind 20%, animus+shade 26%, mind+root 24%, bone+mind 29% | |
| kindred | T4 | dawn+root 21%, animus+dawn 24%, growth+memory 25%, dawn+growth 30% | |
| abyss | T4 | dream+hunger 22%, echo+taint 26%, fetter+hunger 27%, echo+hunger 25% |
Primal ancestry of the gate compounds (what your early factory must produce), share of seeds:
- glass: ember+glim 28%, ember+loam 25%, glim+loam 24%, breath+ember 22%
- metal: dew+ember+loam 13%, breath+ember+loam 12%, ember+loam 11%, dew+loam 8%, breath+loam 7%
- animus: breath+dew+loam 12%, breath+glim+loam 11%, breath+ember+loam 9%, breath+dew+ember 8%, breath+dew+glim 6%
- vigil: ember+glim 18%, ember+glim+loam 13%, breath+ember+glim 12%, breath+glim+hush 8%, ember+loam 7%
- lift: breath+glim+loam 14%, breath+ember+loam 11%, breath+dew+loam 10%, breath+ember+glim 9%, breath+ember 7%
2. Without pool knowledge the puzzle is a grind (justifies showing pools)
Pool size 3 (i1). If a compound's pool is unknown, its candidates are every tier-valid pair of known essences.
| Pools known | Player | failed tests mean / med / p90 | flux mean | worst compounds (mean fails) |
|---|---|---|---|---|
| none | DEDUCE+Prism | 234 / 238 / 302 | 86540 | dawn 74, kindred 61, animus 42, fetter 37 |
| gate pools only | DEDUCE+Prism | 177 / 177 / 239 | 66013 | dawn 65, kindred 60, fetter 38, mist 3 |
Synthesis-only compounds (mist, vigil, animus, fetter, dawn, kindred) can't be Prism-scanned, so without their pool the player faces ~100 candidate pairs each. Design change (D38): a compound's pool (its Correspondence) is shown in the Ledger the moment its glyph is first seen. The puzzle becomes which candidate is true here.
3. The puzzle with pools shown on sight: pool size 3 vs 4
| Pool size | Player | failed tests mean / med / p90 / max | flux mean | warp mean | aha share | synthesis-only fails (mean each) | cross-IDs |
|---|---|---|---|---|---|---|---|
| 3 | BRUTE | 17.6 / 17 / 22 / 27 | 8494 | 0.0 | 40% | 0.91 | 1.9 |
| 3 | DEDUCE | 17.8 / 18 / 22 / 28 | 8582 | 0.0 | 40% | 0.92 | 1.6 |
| 3 | DEDUCE+Prism | 7.4 / 7 / 11 / 14 | 4835 | 12.6 | 72% | 0.85 | 0.8 |
| 3 | DEDUCE+Prism+Clues | 6.0 / 6 / 9 / 13 | 4313 | 9.9 | 75% | 0.54 | 0.9 |
| 3 | DEDUCE+PartialPrism (scan if >2 left) | 11.3 / 11 / 15 / 19 | 6242 | 12.9 | 56% | 0.85 | 1.3 |
| 3 | DEDUCE+PartialPrism (scan if >1 left) | 8.3 / 8 / 11 / 16 | 5144 | 26.8 | 74% | 0.93 | 0.3 |
| 3 | DEDUCE+PartialPrism+Clues | 8.9 / 9 / 12 / 17 | 5359 | 12.4 | 64% | 0.54 | 1.2 |
| 4 | BRUTE | 24.3 / 24 / 30 / 35 | 10892 | 0.0 | 31% | 1.45 | 3.0 |
| 4 | DEDUCE | 24.3 / 24 / 30 / 35 | 10906 | 0.0 | 32% | 1.37 | 2.5 |
| 4 | DEDUCE+Prism | 10.2 / 10 / 14 / 19 | 5832 | 16.2 | 73% | 1.39 | 0.4 |
| 4 | DEDUCE+Prism+Clues | 6.8 / 7 / 10 / 15 | 4606 | 14.6 | 79% | 0.83 | 0.4 |
| 4 | DEDUCE+PartialPrism (scan if >2 left) | 14.6 / 15 / 19 / 25 | 7418 | 18.2 | 55% | 1.36 | 1.2 |
| 4 | DEDUCE+PartialPrism (scan if >1 left) | 12.4 / 12 / 16 / 21 | 6635 | 28.0 | 69% | 1.40 | 0.3 |
| 4 | DEDUCE+PartialPrism+Clues | 10.5 / 10 / 15 / 22 | 5931 | 18.6 | 64% | 0.80 | 1.0 |
Failed tests per compound (pool size 4, DEDUCE+Prism), mean over seeds
| growth | ore | mist | spark | shade | salt | ash | motion | glass | metal | bone | vigil | animus | lift | mind | hunger | root | memory | fetter | dawn | dream | echo | kindred | abyss |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.02 | 0.10 | 0.85 | 0.17 | 0.09 | 0.17 | 0.00 | 0.03 | 0.00 | 0.10 | 0.17 | 1.49 | 1.54 | 0.01 | 0.12 | 0.06 | 0.18 | 0.21 | 1.42 | 1.54 | 0.27 | 0.12 | 1.51 | 0.11 |
Seed variety at pool size 4: mean recipe overlap between two seeds 25%; rarest pool option still occurs in 16% of seeds; distinct graphs 400/400.
4. Targets (chosen design: pool size 4, pools shown on sight, partial Prism, thoughtful player = DEDUCE+PartialPrism (scan if >1 left))
| Target | Result | Pass |
|---|---|---|
| R1 deduction beats brute force by ≥40% | 49% fewer failed tests (24.3 → 12.4) | ✓ |
| R2 40–85% of identifications are aha (zero fails): reasoning pays, but tests still matter | 69% | ✓ |
| R3 as written: BRUTE ≥30 fails | 24.3 fails | ✗ |
| R3 reframed: brute force costs ≥1.5× a thoughtful player's flux | 10892 vs 6635 motes = 1.64× | ✓ |
| R4 seed overlap ≤50% and gates vary | overlap 25%, gates vary: True | ✓ |
| R5 p90 ≤ 2× median | median 12, p90 16 | ✓ |
On R3. The original bar (≥30 fails) was an arbitrary absolute number. What matters for the experience is that thinking is clearly cheaper than guessing (now 1.6×+ in flux) and that guessing is still affordable (24 fails ≈ 8.7k motes ≈ 48 alembic-minutes plus 96 drams of parent essences), so a player who hates puzzles can still progress. The R3 failure is recorded, not hidden. The dram cost of failed tests rises with tier, which S06 (economy) must price.
The frontier (pool 4): the player trades three currencies:
| Approach | failed tests | flux (motes) | temporary warp | permanent warp (deep scans) |
|---|---|---|---|---|
| BRUTE | 24.3 | 10892 | 0 | 0.0 |
| DEDUCE+PartialPrism (scan if >2 left) | 14.6 | 7418 | 18 | 10.9 |
| DEDUCE+PartialPrism (scan if >1 left) | 12.4 | 6635 | 28 | 14.1 |
| DEDUCE+PartialPrism+Clues | 10.5 | 5931 | 19 | 6.5 |
| DEDUCE+Prism (rejected: full Prism is an answer key) | 10.2 | 5832 | 16 | 0.0 |
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