Slide candidate taxonomies against the founder's bar — expected collisions
under 0.01 at target supply — priced in components, transactions and
bytes, beside PEPi's measured census. The ruling is the founder's; this page
only makes its arithmetic visible. Inputs are prefilled from
PROMPT_CATALOG_v7 §2 (30 × 6 ≈ 729M × colour axis ≈ 30B) and
every reference number is from the tree.
self-check: recomputing the spec's own worked example…
Candidate taxonomy
layer (catalog §2 shape)
variants
gate %
avg rects
Gated layers get one free "absent" outcome —
a gate is one integer, never duplicated slots (catalog §2 rule).
Byte pricing anchors at the codec's hardcoded 96 grid and scales
≈ ½ at 48 (≈ ¼ the cells, recovered partly by run-merging) — shown, not assumed.
The arithmetic
PEPi, measured — the bar to match
layer
files per level (L1…L6)
L6 draw
bodies
6, 14, 1, 1, 1, 1
1
cloths gated 60%
0, 0, 74, 80, 92, 117
117 + absent
eyes
0, 12, 12, 12, 12, 12
12
mouths
0, 11, 11, 11, 11, 11
11
accessories gated 37%
0, 13, 20, 30, 44, 80
80 + absent
hats gated 37%
0, 28, 51, 57, 73, 75
75 + absent
ears
0, 0, 0, 0, 0, 0
declared, shipped empty — the upload-order cautionary tale
body colour
runtime draw, 42-entry array
42
measured anchor
value
L6 combination space (uniform)
≈ 4.03 billion — 167²/2N ≈ 3.5 × 10⁻⁶
target: < 0.01 expected collisions
N > 1.25 B at 5,000 · 50 M at 1,000 · 20 B at 20,000
catalog §2 prefill
30 × 6 = 729 M × colour ≈ 30 B → ~180 components
rect / transaction ceiling
675 (2²⁴ gas cap, binary-searched; 676 over-caps)
on-chain bytes
Rect 4 B · RectColored 7 B · SSTORE2 blob 24,576 B
smallest reference piece
782 rects — nothing whole fits one transaction
Two numbers, both true: the uniform bound
(k²/2N, the spec §4 figure) and the weighted figure (Σp² per axis — absence
gates concentrate mass: two cloths "collide" most often by both being absent).
For PEPi at 167 the uniform figure is 3.5×10⁻⁶ but the weighted figure is
≈ — — still comfortably rare, and the gap is the
lesson: size BNRi on the weighted number.
What C-1 rules, all in one place
What C-1 rules — all in one place
1 · The taxonomy itself — layers and variants per layer (the sliders above). 2 · The colour axis — HD weights vs uniform array; it changes the math materially. 3 · The level count, which is currently contradictory in the tree:
CONSENT-1 D-8 promises 8 levels; the reference implementation ships
levelsCount = 6 with thresholds 11/22/33/44/56
(SPEC-ERC20I-MECHANICS-1 §2). C-1 should rule the count so the encoder,
the gate thresholds and the consent text agree — the levels flag is part of this
ruling, not separate from it. 4 · Implicitly, C-3 — grid 48 vs 96 halves every byte figure; one toggle, shown above.
Numbers from the tree: SPEC-ERC20I-MECHANICS-1 §2/§3/§4/§7,
SPEC-INSCRIPTION-COMPAT-1 §3.3, PROMPT_CATALOG_v7 §2.
Model: independent axes, birthday approximation. The avg-rects-per-component
column is an editable assumption (components are far smaller than whole
sprites; the smallest whole piece measures 782 rects). AGPL-3.0-only with the
repo. Corrections are part of the exhibit.