Generated: 2026-03-08
Database: K-CAT SQLite database (built from KFG source data)
Script: scripts/run_phase10_summation.py
Inputs: data/kfg/khipu_database.db · Phase 7/8/9 assignments
Status: ✅ Complete
What fraction of parent-child cord groups satisfy the additive summation constraint (parent ≈ sum of children)? How are zero-value cords distributed across khipu types? What observable features predict summation compliance?
Data scope: 709 khipus, 62,746 cords, 10,381 parent-child groups.
For every parent cord with at least one subsidiary child, the summation ratio r = sum(children) / parent_value is computed. Groups are classified:
| Class | Ratio range | Count | Share |
|---|---|---|---|
sub |
r < 0.50 | 2,565 | 24.7% |
trivial_parent_zero |
parent = 0 | 2,126 | 20.5% |
children_all_zero |
all children = 0 | 1,967 | 18.9% |
supra |
r > 1.50 | 1,469 | 14.2% |
partial_sub |
0.50 ≤ r < 0.95 | 1,119 | 10.8% |
compliant |
0.95 ≤ r ≤ 1.05 | 680 | 6.6% |
partial_supra |
1.05 < r ≤ 1.50 | 455 | 4.4% |
The ratio distribution is tested for clustering near simple fractions (1/10, 1/5, 1/3, 1/2, 2/3, 1/1, 2/1, 10/1).
Per-khipu: fraction of pendant cords with value = 0, fraction of subsidiary cords with value = 0, cross-tabulated with behavioral cluster and tree depth.
Logistic regression (L2, class-weight balanced) with 5-fold CV predicting whether a khipu has ≥ 10% summation-compliant groups. Features: tree depth, branching entropy, % round-5 values, % zero cords, balance score, behavioral cluster (OHE), structural type (OHE).
The additive model (parent = sum(children)) applies to 6.6% of parent-child groups.
The three most common classes:
sub (24.7%): Children sum to less than half the parent value. Median summation ratio across the corpus is 0.35 — parent values are typically about three times the sum of their recorded subsidiaries.trivial_parent_zero (20.5%) and children_all_zero (18.9%): Together 39.4% of all groups — hierarchy is present but values are zero on one side of the relationship.supra (14.2%): Children sum exceeds the parent value.| Ratio landmark | Occurrences | Share |
|---|---|---|
| 1/1 (compliant) | 680 | 8.2% |
| 1/10 | 382 | 4.6% |
| 1/2 | 310 | 3.8% |
| 1/3 | 282 | 3.4% |
| 1/5 | 271 | 3.3% |
| 2/3 | 183 | 2.2% |
| 2/1 | 268 | 3.2% |
| 10/1 | 52 | 0.6% |
The 1/1 landmark is the strongest concentration. No single non-unity landmark dominates. The spread across fractional ratios (1/10 through 2/3) indicates a mixture of ratio patterns in the corpus.
| Cluster | Median % zeros | Summation compliance | Median ratio |
|---|---|---|---|
| B1 | 100.0% | 0.0% | — |
| B2 | 31.6% | 6.9% | 0.50 |
| B3 | 15.1% | 0.0% | 0.29 |
| B4 | 20.7% | 4.2% | 0.36 |
| B5 | 14.3% | 0.0% | 0.28 |
| B6 | 17.6% | 0.0% | 0.22 |
B1 = 100% zeros, confirming Phase 8’s finding that B1 khipus carry no numeric content. B2 has the highest compliance rate (6.9%) and median ratio (0.50). B3, B5, B6 show 0% median compliance with median ratios in the 0.22–0.29 range.
| Measure | T1 (n = 653) | T2 (n = 56) | p-value |
|---|---|---|---|
| Median % compliant groups | 0.0% | 4.1% | < 0.001 *** |
| Median % zero-value cords | 17.6% | 26.9% | < 0.001 *** |
T2 khipus have both more summation-compliant groups and more zero-value cords.
Logistic regression predicting “high-compliance khipu” (≥ 10% of groups compliant):
5-fold CV ROC-AUC = 0.736 ± 0.053
Top predictors by absolute coefficient magnitude:
| Rank | Feature | coefficient | Direction | ||
|---|---|---|---|---|---|
| 1 | depth |
1.18 | deeper → more compliant | ||
| 2 | beh_B2 |
0.42 | B2 → more compliant | ||
| 3 | pct_zero |
0.38 | more zeros → higher compliance | ||
| 4 | beh_B1 |
0.35 | B1 → more compliant (trivially — zero-zero groups excluded from testing) | ||
| 5 | beh_B4 |
0.32 | B4 → more compliant |
Depth is the strongest predictor: deeper khipus are more likely to contain compliant parent-child groups.
cord_name / parent_cord transcription. Errors would inflate the supra and sub classes.| File | Description |
|---|---|
data/processed/phase10_summation_groups.csv |
Per-parent-group: children sum, parent value, ratio, compliance class |
data/processed/phase10_zero_analysis.csv |
Per-khipu: zero rates, compliance rates, behavioral label |
visualizations/phase10/ratio_distribution.png |
Log-scale ratio histogram + compliance class breakdown |
visualizations/phase10/compliance_by_cluster.png |
Compliance rate and zero rate by behavioral cluster |
visualizations/phase10/zero_cord_patterns.png |
Zero distribution patterns across khipus |
visualizations/phase10/compliance_predictors.png |
Feature importances and round-5 vs compliance scatter |
Corpus sweep run against K-CAT SQLite database. Re-run with scripts/run_phase10_summation.py to refresh.