NUMERATA: A Multi-Axis Framework for Evaluating Numeral Systems

In the paper's words

NUMERATA v2.0 extends the 8-axis framework with Distinction-Based Primality (WP0.3/9th axis) and meta-analysis validation (MCS=0.875, 5/5 predictions confirmed). Sunburst notation makes primality visually immediate.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. The scoring rubric is validated through inter-rater reliability (ICC > 0.80 target) and factor analysis ($\geq 3$ independent factors predicted).

   from 3.3 Scoring Rubric

How it is done

1. Then we tested whether our nine yardsticks give different rankings than the speed-only approach.

   from Simplified Abstract

2. Most people never ask whether the numeral system they use could be better designed.

   from 1.1 The Evaluation Problem

3. This reframes the Fundamental Theorem of Arithmetic: Every composite score decomposes uniquely into a canonical polyrhythm of prime meters.

   from 2.4.3 Primality Redefined

4. Dimension Container View (Set Theory) Distinction View (DCN) Number Nested set of sets Sequence of indications Multiplication Cartesian product of container sizes Counterpoint/canon of rhythms Primality Indivisible box (no proper divisors) Metrically irreducible rhythm Factorization Partition of container contents Decomposition of polyrhythm Fundamental Theorem Unique container decomposition Unique prime rhythm decomposition Neither view is "correct" — they make different properties cognitively accessible.

   from 2.4.4 The Container View vs. The Distinction View

What would falsify it

1. The distinction/containment axis is not just descriptive — it predicts which cognitive operations a system makes natural versus effortful.

   from 2.2 Distinction vs. Containment (WP0.2)

2. Phase 0-1 Prediction Meta-Analysis Finding Confirmed?

   from 6.5 Five of Five Predictions Confirmed

Where the claim stops

1. A prime number is a score that cannot be so arranged.

   from 2.4.3 Primality Redefined

2. However, only 4 of 9 axes have sufficient comparative data in the existing literature.

   from 7.1 The Framework Is Validated But Data-Limited

Where to read

1. Abstract205 words · 1 min
2. Simplified Abstract132 words · 1 min
3. 1. Introduction371 words · 2 min
4. 2. Foundations836 words · 4 min
5. 3. Structural Typology (WP1.3.2)299 words · 1 min
6. 4. Edge Cases and Hidden Assumptions (WP1.1.3+WP1.3)239 words · 1 min
7. 5. Case Study: The Sunburst Notation512 words · 2 min
8. 6. Meta-Analysis Validation — Phase 2b461 words · 2 min
9. 7. Discussion257 words · 1 min
10. 8. Conclusion130 words · 1 min
11. Appendix A: Deliverables78 words · 1 min
12. Appendix B: QNFO Silent Radix Prior Art27 words · 1 min