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name: finder-color-walk description: Deterministic triadic fanout over file-sets with macOS Finder label coloring, GF(3) conservation, and Strong Parallelism Invariance (SPI). trit: 0

finder-color-walk

Deterministic triadic fanout over a file-set, with macOS Finder label coloring, supporting GF(3) conservation and Strong Parallelism Invariance (SPI).

Contract

Inputs

• Root path(s) to enumerate files (user-supplied).
• Optional filters (extensions, max depth, ignore globs).
• Policy:
  • raw (default): color_at(file) only; SPI holds; GF(3) not guaranteed.
  • gf3_balanced: colors are assigned in position-aligned triplets across the 3 routed fibers; GF(3) holds.

Outputs

• A (file → color) assignment and a (file → fiber) routing.
• Optional application of macOS Finder label colors.

Guarantees

SPI (Strong Parallelism Invariance)

For a fixed file-set, policy, and seed:

• routing is deterministic and order-independent
• color assignment is deterministic and order-independent

Formally: any permutation of the same input file-set yields the same final mapping.

GF(3) conservation (policy = gf3_balanced)

Let the three fibers be sorted lists F0,F1,F2 of equal length N. For each index i define trits t0(i), t1(i), t2(i) ∈ {0,1,2} as assigned to F0[i],F1[i],F2[i]. Then for all i:

• t0(i) + t1(i) + t2(i) ≡ 0 (mod 3)

Implementation: choose t0,t1 deterministically; set t2 := (-t0-t1) mod 3.

Files

• schema.jl — Catlab ACSet schema: FileColorWalk.
• triadic_router.bb — GF(3)-balanced routing into 3 fibers.
• finder_color_walk.bb — single-stream walk (policy raw).
• parallel_walk.bb — 3-stream walk + gf3_balanced coloring.
• spi_test.py — verifies SPI + GF(3) (where requested).
• INTERLEAVED.md — 4-corpus synthesis notes.

Quick start

Route files into 3 fibers

bb triadic_router.bb --root . --out fibers.json

Apply GF(3)-balanced colors (dry-run by default)

bb parallel_walk.bb --fibers fibers.json --policy gf3_balanced --dry-run

Verify invariants

python spi_test.py --fibers fibers.json --policy gf3_balanced

macOS Finder label mapping

Trits → label colors (customize inside scripts):

• 0: None
• 1: Green
• 2: Blue

Related Skills (Backlinks)

Skill	Trit	Integration
google-workspace	0	Drive file coloring via drive_color_walk.py
gay-mcp	+1	SplitMix64 algorithm, trit-to-hue mapping
triad-interleave	+1	Schedule file walks in balanced triplets
bisimulation-game	-1	Verify file state equivalence
spi-parallel-verify	-1	Strong Parallelism Invariance verification

Comparison with Related Skills

vs gay-mcp

• gay-mcp: Pure color generation, OkLCH space, hex output
• finder-color-walk: File-focused, routing + coloring, Finder integration
• Shared: SplitMix64 RNG, GF(3) trits, SPI guarantee

vs triad-interleave

• triad-interleave: Stream scheduling, temporal ordering
• finder-color-walk: Spatial routing into fibers
• Shared: 3-way balanced triplets, GF(3) conservation

vs bisimulation-game

• bisimulation-game: State equivalence verification
• finder-color-walk: Deterministic state generation
• Integration: Use bisim to verify color assignments match across systems

Integration Bridge

# drive_color_walk.py bridges:
#   google-workspace MCP (file listing) 
#   → finder-color-walk (GF(3) routing)
#   → gay-mcp (color generation)
#   → Finder/Drive labels

from google_workspace import list_drive_items
from finder_color_walk import route_to_fibers, gf3_color
from gay import SplitMixTernary

files = list_drive_items(folder_id="root")
fibers = route_to_fibers(files, seed=0x42D)
colored = gf3_color(fibers, seed=0x42D)
# Apply to both Drive (via MCP) and Finder (via xattr)