khipu-computational-toolkit

Phase 5: Color Analysis

Generated: 2026-03-08
Database: K-CAT SQLite database (built from KFG source data)
Script: scripts/run_phase5_color.py
Inputs: data/kfg/khipu_database.db · data/processed/phase3_clusters.csv
Status: ✅ Complete

Research Questions

What is the color vocabulary of the KFG corpus? How concentrated is it?
Does having a white cord in the first position of a cord group associate with higher summation complexity?
Is color diversity associated with structural complexity cluster (Simple vs. Complex)?
Do cord value distributions differ by color code?
Which colors co-occur across the corpus?

Data

62,746 cord records in the KFG database; 76,258 cord-color entries (compound cords contribute multiple rows)
cord_colors table: normalized — compound color strings such as W:MB are split into individual components (W at sequence_ord=0, MB at sequence_ord=1)
cords.color retains the original compound string for reference
20.3% of cords have compound colors (two or more components)

Results

1. Color Vocabulary

visualizations/phase5/color_vocab.png
Data: data/processed/phase5_color_vocab.csv

color_code	n_entries	% entries	n_khipus	% khipus
W (white)	20,936	27.5%	551	77.7%
AB (mottled buff)	11,170	14.6%	397	56.0%
MB (mottled brown)	9,291	12.2%	416	58.7%
YB (yellowish brown)	4,729	6.2%	208	29.3%
KB (khaki brown)	3,921	5.1%	309	43.6%
B (brown)	3,251	4.3%	136	19.2%
GG (grayish green)	1,559	2.0%	174	24.5%
LB (light brown)	1,401	1.8%	70	9.9%
NB (natural brown)	1,349	1.8%	45	6.3%
DB (dark brown)	1,120	1.5%	74	10.4%

Total distinct normalized color codes: 2,830.

The top 10 codes account for approximately 77% of all cord-color entries. White is the most common single code and appears in 77.7% of khipus. The 2,830 distinct codes include many rare compound combinations unique to individual khipus.

2. White Cord First-Position Test

visualizations/phase5/white_cord_analysis.png

Operationalization: A khipu is coded has_white_first_cord = True if any pendant cord (hierarchy_level = 0) in any of its cord groups has position_in_group = 1 and a color beginning with W.

Group	n khipus	Mean pattern types	Complex rate
No white first cord	287	2.22	14.3%
Has white first cord	422	2.92	18.2%

Test	Result	Significant?
Pattern types: Mann-Whitney U (greater)	p < 0.0001	✅
Cluster (Simple/Complex): chi-square	χ² = 1.66, p = 0.198	❌

Khipus with white first-position cords have significantly more pattern types on average (+0.70, p < 0.0001), but the difference in Complex classification rate is not statistically significant.

Caveat: The KFG position_in_group column encodes position within a cord group, not ordinal position across the whole khipu. Results may differ under alternative operationalizations.

3. Color Diversity by Cluster

visualizations/phase5/color_diversity_by_cluster.png
Data: data/processed/phase5_color_diversity.csv

Cluster	n	Mean unique colors	Median
Simple	591	7.3	5
Complex	118	23.6	17

Mann-Whitney U (Complex > Simple): p = 6.83 × 10⁻²⁵

Complex khipus use on average 3.2× as many distinct color codes as Simple khipus. Notable outliers: KH0082 (236 unique colors) and KH0083 (151 unique colors), both from the Leymebamba cache, substantially influence the Complex mean.

4. Color-Value Association

visualizations/phase5/color_value_correlation.png

Test: Kruskal-Wallis H-test across 12 most common color codes, restricted to cords with non-zero numeric values.

Statistic	Value
H	987.18
p	1.10 × 10⁻²⁰⁴

Median non-zero cord value by color code (top 12):

Color	Median value
NB (natural brown)	42
DB (dark brown)	15
W (white)	13
AB (mottled buff)	10
YB (yellowish brown)	10
B (brown)	10
HB (hot brown)	7.5
GG (grayish green)	6
MB (mottled brown)	6
LB (light brown)	6
KB (khaki brown)	6
RB (reddish brown)	6

The association is highly significant, but multiple confounds are present: cord position (NB and DB appear disproportionately on specific hierarchy levels), corpus composition (NB appears in only 45 khipus), and khipu-level effects (khipus recording large values may use certain colors). Causal direction is not established.

5. Color Co-occurrence

visualizations/phase5/color_cooccurrence.png

The co-occurrence matrix counts khipus containing both color X and color Y. Selected pairings:

Pair	Co-occurring khipus
W + MB	336
W + AB	325
AB + MB	322
W + GG	158
AB + GG	150
MB + GG	148

W co-occurs with nearly every other major color, as expected given its 77.7% corpus presence. AB and MB appear together nearly as often as either appears alone (322 joint vs 397/416 individual). LB and NB show more isolated co-occurrence patterns with fewer pairings to the dominant AB/MB group.

Limitations

NB sample size. Only 45 khipus carry NB cords; the high median value (42) is based on a small sample.
White-first operationalization. position_in_group = 1 may not map exactly onto the Clindaniel/Ascher concept.
Color-diversity outliers. KH0082 (236 unique colors) and KH0083 (151) heavily influence the Complex mean. Both are from the Leymebamba cache and are also outliers in cord count and summation coverage.

How to Re-run

python scripts/run_phase5_color.py

Requires Phase 3 to have run first (reads data/processed/phase3_clusters.csv).

Output	Description
`data/processed/phase5_color_vocab.csv`	Color frequency table
`data/processed/phase5_color_diversity.csv`	Per-khipu color diversity metrics
`data/processed/phase5_stat_results.csv`	Statistical test results
`visualizations/phase5/`	All PNG figures

White-cord hypothesis after Clindaniel (2019); color codes follow KFG extended Ascher notation. See Citations and Acknowledgments in the project README for primary sources.

Corpus sweep run against K-CAT SQLite database. Re-run with scripts/run_phase5_color.py to refresh.

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