Canonical-Order Gradient in Quranic Verse Length

Abstract

QMR-010 examines how Quranic verse length changes across the canonical order of the fixed DATA-001 corpus.

The analysis treats the 6,236 verse records as an ordered sequence and measures verse length independently in:

• Arabic letters;
• whitespace-delimited words.

The principal verse-level result is a negative association between canonical position and verse length.

For Arabic letters:

For words:

The result is robust to several controls:

• equal-position decile summaries;
• letters versus words;
• RAW versus BODY;
• unweighted analysis of the 114 surahs;
• mean versus median surah-level verse length;
• leave-one-surah-out analysis;
• permutation of the 114 surahs as intact blocks.

Under the intact-surah block null, 0 of 100,000 permutations produced an absolute Spearman correlation at least as large as the observed value in either RAW or BODY.

The corrected Monte Carlo value is:

0.000009999900

This result is conditional on the explicit permutation null and must not be interpreted as the probability that the observed Quranic ordering arose by chance.

QMR-010 is classified as Previously Known at the level of the general length-ordering phenomenon. It does not claim discovery of the general tendency. Its contribution is the reproducible quantification and robustness analysis performed on the fixed DATA-001 corpus.

Research Question

Given the canonical ordering of DATA-001:

1. Is verse length associated with absolute verse position?
2. Does the result persist when verse length is measured in letters and in words?
3. Does it remain visible when each surah contributes only one mean or median value?
4. Is the result driven by any single surah?
5. How unusual is the observed verse-level association under a null model that preserves every surah and its internal verse order but randomizes the order of the 114 surahs?

Historical Recovery Context

QMR-010 emerged from the recovery of the 2025 record:

KS-Ω-2025-033 — “Architecture Divine & Point d’Or”

The historical record reported:

• initial value: 87.8
• final value: 19.0
• total gradient: approximately 78.4%

with the formula:

G = (L_initial - L_final) / L_initial × 100

The historical source does not define the boundaries of the initial and final segments sufficiently to reproduce the exact values 87.8 and 19.0.

Accordingly, QMR-010 does not present those historical endpoint values as reproduced.

Instead, the historical record is treated as a research lead that motivated a new, explicitly defined reconstruction on DATA-001.

Corpus

The analysis uses:

DATA-001 — Tanzil Quran Text, Simple Clean, Version 1.1

Canonical corpus SHA-256:

228df2a717671aeb9d2ff573002bd28d6b3f973f4bc7153554e3a81663d67610

Corpus invariants:

BODY removes the exact four-token opening Basmala prefix from verse 1 of 112 eligible surahs.

Surah 1 and Surah 9 are left unchanged.

No verse identifiers are removed.

Length Definitions

Arabic letters

Arabic-letter counts use characters satisfying both:

• Unicode Letter;
• Unicode Script=Arabic.

Spaces and non-letter characters do not contribute.

Words

Words are counted as whitespace-delimited tokens.

The two measurements are analyzed independently so that the result does not depend on one particular definition of textual length.

Verse-Level Result

Absolute verse position is numbered from:

1 to 6,236

For each verse, its canonical position is correlated with its length.

Arabic letters

RAW:

• Pearson r = -0.455295998008
• Spearman ρ = -0.559999212337

BODY:

• Pearson r = -0.460244834027
• Spearman ρ = -0.566540686969

Words

RAW:

• Pearson r = -0.451614855457
• Spearman ρ = -0.550214547969

BODY:

• Pearson r = -0.455943734066
• Spearman ρ = -0.555365714038

All four Spearman coefficients are negative and similar in magnitude.

The consistency between letters and words indicates that the observed trend is not specific to the Arabic-letter counting convention.

Equal-Position Decile Gradient

The 6,236 ordered verses are divided into ten contiguous position bins using deterministic boundaries based on:

floor(i × n / 10)

The comparison is therefore between fixed portions of the canonical verse sequence rather than selected surahs.

Arabic letters

Words

For both letters and words, the ten-decile profile contains:

• 7 decreases;
• 2 increases.

The result is therefore a strong global decline but not a perfectly monotonic decline.

Local reversals remain present.

Relation to the Historical 78.4% Value

The recovered 2025 record reported a total gradient of approximately:

78.4%

The modern RAW decile reconstruction gives:

• letters: 78.219550%
• words: 78.272515%

These values are numerically close to the historical 78.4%.

This proximity does not establish that the historical record used ten equal verse-position segments.

Because the old segment definition was not recovered, the historical 78.4% result and the modern decile result must remain distinct.

QMR-010 therefore reports the modern rule independently rather than retroactively assigning it to the 2025 record.

Unweighted Surah-Level Analysis

Verse-level analysis naturally gives more weight to surahs containing more verses.

As a control, QMR-010 also reduces each of the 114 surahs to a single mean or median verse-length value.

Each surah therefore contributes exactly one observation.

Arabic letters

Words

The negative relation therefore remains after eliminating the unequal weighting created by different surah verse counts.

Leave-One-Surah-Out Robustness

For the Arabic-letter surah-level analysis, QMR-010 removes each surah in turn and recomputes Spearman correlation across the remaining 113 surahs.

This produces 114 runs for each combination of:

• RAW mean;
• RAW median;
• BODY mean;
• BODY median.

Across all 456 leave-one-surah-out recalculations, every Spearman correlation remains negative.

RAW mean

Baseline:

ρ = -0.686131682494

Weakest after removing Surah 5:

ρ = -0.679105144857

Strongest after removing Surah 1:

ρ = -0.708714628209

RAW median

Baseline:

ρ = -0.684655057952

Weakest after removing Surah 112:

ρ = -0.677126792556

Strongest after removing Surah 1:

ρ = -0.704528379460

BODY mean

Baseline:

ρ = -0.729192866069

Weakest after removing Surah 112:

ρ = -0.722013943906

Strongest after removing Surah 1:

ρ = -0.748704065276

BODY median

Baseline:

ρ = -0.703802584571

Weakest after removing Surah 112:

ρ = -0.696047062372

Strongest after removing Surah 1:

ρ = -0.721989094028

The observed surah-level relation is therefore not dependent on any single surah.

Intact-Surah Block Permutation Null

A stronger control preserves the internal structure of each surah.

The null procedure is:

1. keep each of the 114 surahs intact;
2. preserve the internal verse order within every surah;
3. randomly permute only the order of the 114 surah blocks;
4. flatten the permuted blocks into a 6,236-verse sequence;
5. recalculate Spearman correlation between absolute position and Arabic-letter verse length;
6. compare the absolute permuted correlation with the absolute observed correlation.

The random seed is:

20260917

The final analysis uses:

100,000 permutations

RAW

Observed:

ρ = -0.559999212337

Extreme permutations:

0 of 100,000

Corrected Monte Carlo value:

(0 + 1) / (100000 + 1) = 0.000009999900

BODY

Observed:

ρ = -0.566540686969

Extreme permutations:

0 of 100,000

Corrected Monte Carlo value:

0.000009999900

Thus, no permutation among the 100,000 tested produced an absolute Spearman correlation at least as large as the canonical-order value.

This does not mean that the probability is zero.

The reported value is resolution-limited by the number of Monte Carlo permutations and is conditional on this particular null model.

Statistical Interpretation

The permutation result answers a narrow question:

How extreme is the observed verse-position association relative to random reorderings of intact surahs?

It does not answer:

What is the probability that the canonical Quranic order occurred by chance?

Those are different statements.

The Monte Carlo result is conditional on:

• DATA-001;
• the chosen verse-length metric;
• canonical verse order within each surah;
• intact-surah permutation;
• absolute Spearman correlation as the statistic.

The p-value is not the probability that the null hypothesis is true, and it is not a probability of intentionality.

Prior Art and Novelty

The general observation that the canonical Quranic ordering is associated with textual length is not new.

Descriptions of Quranic structure and earlier quantitative studies have long noted that, outside the opening surah and local exceptions, canonical ordering is broadly related to decreasing surah or verse length.

QMR-010 therefore does not claim discovery of the general tendency.

The classification is:

Previously Known

The contribution of QMR-010 is narrower:

• corpus fixation on DATA-001;
• explicit RAW/BODY definitions;
• verse-level Pearson and Spearman quantification;
• independent letter and word measurements;
• equal-position decile analysis;
• unweighted mean and median analysis across 114 surahs;
• leave-one-surah-out robustness;
• a 100,000-run intact-surah block permutation null;
• a frozen reproducible JSON artifact.

In the sources examined during this recovery, we did not identify this exact combination of protocol and robustness controls.

That statement is not an absolute claim that no earlier implementation exists.

Interpretation Limits

QMR-010 establishes a reproducible statistical property of the fixed canonical sequence under explicitly defined measurements.

It does not establish intentional design.

It does not establish that the canonical order was chosen in order to optimize verse-length decline.

It does not establish a causal mechanism.

It does not establish theological intent.

It does not constitute evidence of supernatural design.

The statistical result should therefore be interpreted as a property of the observed text ordering under the stated protocol, not as a metaphysical conclusion.

Reproducibility

Analysis implementation:

analysis/qmr-010.mjs

Primary analysis tests:

tests/qmr-010-analysis.node.mjs

Frozen report tests:

tests/qmr-010-report.integration.node.mjs

Artifact-writing tests:

tests/qmr-010-artifact.integration.node.mjs

Publication contract:

tests/qmr-010-publication.test.ts

Frozen artifact:

artifacts/qmr-010/qmr-010-data001-report.json

Artifact SHA-256:

839F79275B376554715E899E0F6D8B7CE7646E72A9D52BF222724E06BAE8D47E

Canonical DATA-001 SHA-256:

228df2a717671aeb9d2ff573002bd28d6b3f973f4bc7153554e3a81663d67610

The final frozen permutation protocol uses:

• 100,000 permutations;
• random seed 20260917;
• intact surah blocks;
• preserved internal verse order;
• two-sided comparison using absolute Spearman correlation;
• corrected Monte Carlo calculation (extreme + 1) / (B + 1).

Classification

Status: Observation

Evidence: E1 — Structured Pattern

Classification: Confirmatory

Novelty: Previously Known

Discovery: No

Publication state: Published

QMR-010 records a reproducible canonical-order verse-length gradient and its robustness under multiple measurement and structural controls, while separating that modern result from the unrecovered details of the 2025 historical gradient calculation.