Muqattaat Surah-Prefix Enrichment Under Global Permutation

Abstract

QMR-006 asks whether the disconnected-letter combinations, or muqattaat, assigned to their historical surahs are collectively more enriched in those surahs than would be expected if the same 29 prefixes were randomly reassigned among the same 29 muqattaat surahs.

For each surah-prefix assignment, the analysis computes an enrichment ratio:

R = proportion of the prefix letters in the surah / proportion of the same letters in the Quran

The 29 ratios are combined using their geometric mean.

The observed assignments are then compared with random permutations that preserve:

• the same 29 surahs;
• the same 29 prefix combinations;
• the same corpus;
• the same enrichment statistic.

Under BODY, the observed geometric mean is:

1.0605509294657305

Among 2,000,000 seeded permutations, 665 produce a score equal to or greater than the observed result.

Using the add-one Monte Carlo estimator:

p = 0.00033299983350008324

RAW produces a closely comparable result.

However, sensitivity analysis shows that a substantial part of the global signal is concentrated in a small number of strong associations, particularly Qaf, Sad, and Nun.

For that reason, QMR-006 remains:

Under Review

It is not classified as robust or as a discovery.

Research Question

Are the muqattaat letters placed at the beginning of their historical surahs collectively more frequent in those surahs than expected under random reassignment of the same prefix combinations?

The test does not ask whether every one of the 29 surahs is individually enriched.

It asks whether the actual 29-way matching between surahs and prefixes produces an unusually high global enrichment score.

Dataset & Counting Rules

• Dataset: DATA-001
• Methodology: METHOD-001
• Muqattaat surahs: 29
• Prefix combinations: 29
• Views: RAW and BODY
• Primary statistic: geometric mean of the 29 enrichment ratios
• Permutation count: 2,000,000
• Seed: 20260916
• Tail: permutation score greater than or equal to observed score
• Monte Carlo estimator: (exceedances + 1) / (permutations + 1)

The corpus SHA-256 used for the final reproducibility report is:

228df2a717671aeb9d2ff573002bd28d6b3f973f4bc7153554e3a81663d67610

No transliteration, stemming, spelling expansion, or silent character normalization is introduced by QMR-006.

Enrichment Statistic

For each historical assignment, let:

• S be the selected surah;
• L be the set of letters contained in its muqattaat prefix;
• f(S,L) be the proportion of characters in the surah belonging to L;
• f(Q,L) be the proportion of characters in the complete Quranic view belonging to L.

The per-surah enrichment ratio is:

R = f(S,L) / f(Q,L)

Interpretation:

• R > 1 means those letters are proportionally more frequent in the surah than in the Quran-wide baseline;
• R < 1 means they are proportionally less frequent;
• R = 1 means equal proportional frequency.

The global QMR-006 statistic is the geometric mean of all 29 ratios.

Null Model

The null model preserves the full set of 29 surahs and the full set of 29 historical prefix combinations.

Only the pairing is broken.

For each permutation:

1. the 29 prefixes are shuffled;
2. each shuffled prefix is assigned to one of the same 29 surah positions;
3. the 29 enrichment values are read from the fixed 29 × 29 enrichment matrix;
4. their geometric mean is computed;
5. the permutation is counted as an exceedance when its score is greater than or equal to the observed historical assignment score.

This null model therefore asks a narrow question:

Is the historical matching between these 29 surahs and these 29 prefix combinations unusually enriched relative to alternative matchings of the same objects?

It does not model every possible numerical hypothesis involving muqattaat.

Primary BODY Result

Under BODY:

• study size: 29
• observed geometric mean: 1.0605509294657305
• permutations: 2,000,000
• exceedances: 665
• Monte Carlo p-value: 0.00033299983350008324
• seed: 20260916

The result corresponds to a geometric-mean enrichment of approximately 6.06% above the Quran-wide letter-frequency baselines used by the statistic.

This does not mean that every muqattaat surah is enriched.

The individual distribution contains:

• 18 associations with R > 1;
• 11 associations with R < 1;
• 0 associations with R = 1.

RAW Result

Under RAW:

• study size: 29
• observed geometric mean: 1.0591373421750678
• permutations: 2,000,000
• exceedances: 696
• Monte Carlo p-value: 0.0003484998257500871
• seed: 20260916

RAW and BODY therefore produce closely comparable global results.

The small difference between the two views indicates that the full statistic is not strongly dependent on the BODY removal of the standard opening Basmala prefixes.

This RAW/BODY agreement does not establish general robustness under every possible corpus representation.

Strongest BODY Contributions

The five largest BODY enrichment ratios are:

Qaf, Sad, and Nun are therefore especially strong contributors to the global geometric mean.

The complete ranking of all 29 assignments is preserved in the reproducibility artifact.

Sensitivity Analysis

The strongest individual associations were removed sequentially to test how dependent the global result is on them.

Excluding Surah 50 / Qaf

After removing both:

• the Surah 50 row;
• the corresponding Qaf prefix column;

the reduced study contains 28 assignments.

Results:

• observed score: 1.0411531326619925
• exceedances: 12,363 / 2,000,000
• p-value: 0.006181996909001545

The signal is materially weaker than in the complete 29-way study.

Excluding Surahs 50 and 38 / Qaf and Sad

Study size:

27

Results:

• observed score: 1.026910959971505
• exceedances: 67,647 / 2,000,000
• p-value: 0.03382398308800846

The result is weakened further.

Excluding Surahs 38, 50, and 68 / Sad, Qaf, and Nun

Study size:

26

Results:

• observed score: 1.0197291823833257
• exceedances: 123,594 / 2,000,000
• p-value: 0.06179746910126545

Under this sensitivity analysis, the result no longer falls below the conventional 0.05 threshold.

Interpretation of the Sensitivity Result

The sensitivity analysis prevents a stronger claim than the evidence supports.

The complete 29-way historical matching produces an unusually high statistic under the registered permutation model.

But the effect is not evenly distributed across the 29 assignments.

In particular:

• Qaf contributes very strongly;
• Sad contributes very strongly;
• Nun contributes strongly;
• several additional assignments contribute moderate positive enrichment;
• 11 of the 29 historical assignments have enrichment below 1.

The appropriate interpretation is therefore a global association with concentrated contributions, not a universal enrichment rule applying strongly to every muqattaat surah.

Prior Art

The general idea of examining muqattaat through letter-frequency analysis predates Coran Codex.

In 2013, Halim Sayoud published Investigation on the Mystery of the Qur’an’s Disjointed Letters in QURANICA - International Journal of Quranic Research. The study applied seven text-analysis approaches to the disconnected letters, including character-frequency analysis.

Source:

Halim Sayoud, 2013 — Investigation on the Mystery of the Qur’an’s Disjointed Letters

More recent computational resources also examine the same broad frequency question.

QuranLab publishes a muqattaat dataset in which individual disconnected opening letters are compared with their frequency in their own surah and in the Quran as a whole through a frequency_ratio.

Source:

QuranLab — quran-ijaz dataset

StartQuran independently tests the claim that opening letters are unusually frequent in their associated surahs. Its procedure compares each letter’s share inside a surah with its Quran-wide share, ranks the letters by enrichment, and includes a control using surahs without disconnected-letter openings.

Source:

StartQuran — The Mystery Letters

These sources establish that the general frequency-enrichment question is not novel.

QMR-006 therefore does not claim novelty for:

• counting muqattaat letters inside their associated surahs;
• comparing those frequencies with Quran-wide frequencies;
• observing strong individual cases such as Qaf;
• asking whether disconnected opening letters are unusually frequent.

The QMR-006 protocol is narrower and structurally different.

It fixes:

• the same 29 historical muqattaat surahs;
• the same 29 historical prefix combinations;
• each complete prefix combination as one assignment unit;
• a combined-letter enrichment ratio for each surah-prefix assignment;
• the geometric mean of all 29 enrichment ratios as the global statistic;
• a 29 by 29 enrichment matrix;
• global reassignment of the 29 complete prefixes among the same 29 surahs;
• a seeded Monte Carlo comparison of the historical diagonal against those alternative assignments.

The Sayoud study, QuranLab dataset, and StartQuran analysis establish related frequency-based work, but the targeted review performed for QMR-006 did not locate documentation of this exact combination of:

29 complete prefix assignments + combined-letter enrichment + geometric-mean aggregation + global prefix reassignment by permutation.

That search result must be interpreted cautiously.

A targeted literature and web review cannot establish worldwide originality, and absence from the sources inspected is not evidence that no earlier researcher used the same procedure.

Failure to locate an earlier identical formulation is not proof of novelty.

For that reason, the novelty status remains:

Investigating

Multiple Testing

QMR-006 is exploratory.

The final permutation protocol is frozen and reproducible, but it emerged within a broader program of Quranic numerical investigation.

The p-value therefore describes rarity under this specific null model.

It must not be interpreted as correction for:

• every possible muqattaat statistic;
• every possible corpus representation;
• every possible letter grouping;
• every possible exclusion;
• every numerical hypothesis explored in Quranic research.

No exhaustive correction over the full research-choice space has been established.

Interpretation Standard

Fact

Under DATA-001:

• the BODY geometric mean for the actual 29 assignments is 1.0605509294657305;
• 18 assignments have enrichment above 1;
• 11 assignments have enrichment below 1;
• Qaf in Surah 50 has the largest BODY enrichment ratio;
• Sad in Surah 38 is second;
• Nun in Surah 68 is third.

Statistical interpretation

Under the frozen 29-prefix permutation model:

BODY p = 0.00033299983350008324

and:

RAW p = 0.0003484998257500871

The complete historical pairing is therefore unusual relative to random reassignments under this particular null model.

Sensitivity interpretation

After removing Qaf, Sad, and Nun:

p = 0.06179746910126545

The statistical strength of the full result therefore depends substantially on these strong contributors.

Claim

QMR-006 provides statistical evidence that the complete historical surah-prefix matching produces greater global enrichment than most random reassignments under the specified null model.

Not claimed

QMR-006 does not establish:

• that all 29 surahs individually show enrichment;
• robustness to every defensible analytical choice;
• independent replication;
• exhaustive multiple-testing correction;
• established historical novelty;
• supernatural origin;
• divine intent;
• theological significance.

No supernatural or divine conclusion follows from this result.

Why the Status Is Under Review

QMR-006 remains under review for several reasons.

First, the global result is strongly influenced by Qaf, Sad, and Nun.

Second, removing those three strongest associations changes the BODY permutation result from:

0.00033299983350008324

to:

0.06179746910126545

Third, the permutation model is one defensible null model, not the only possible null model.

Fourth, the general premise of unusual muqattaat letter frequencies is already present in prior work.

Fifth, the analysis is exploratory and does not represent exhaustive correction across the wider researcher-choice space.

These limitations support statistical evidence at E2 while withholding E3 or E4.

Limitations

The result is conditional on:

• DATA-001;
• the RAW/BODY definitions;
• the fixed set of 29 muqattaat surahs;
• the fixed historical prefix assignments;
• the combined-letter enrichment statistic;
• geometric-mean aggregation;
• the global prefix-permutation null model.

Alternative defensible choices may produce different results.

The sensitivity analysis also shows that the statistical result is not uniformly distributed across all 29 assignments.

The prior-art review cannot prove absence of an earlier identical formulation.

Verdict

Status: Under Review

Evidence level: E2

Classification: Exploratory

Novelty: Investigating

Discovery: No

The complete 29-way assignment produces a low Monte Carlo p-value under the frozen global permutation protocol.

RAW and BODY produce closely comparable results.

However, removal of the strongest Qaf, Sad, and Nun associations materially weakens the signal, reaching approximately p = 0.0618.

QMR-006 therefore remains under review rather than being classified as robust.

Reproducibility

Primary analysis:

analysis/qmr-006.mjs

Final DATA-001 report:

artifacts/qmr-006/qmr-006-data001-report.json

Corpus SHA-256:

228df2a717671aeb9d2ff573002bd28d6b3f973f4bc7153554e3a81663d67610

Final report parameters:

• 2,000,000 permutations
• seed 20260916
• RAW
• BODY
• BODY sensitivity excluding [50]
• BODY sensitivity excluding [50, 38]
• BODY sensitivity excluding [38, 50, 68]

The final reproducibility artifact also preserves the complete BODY ranking of all 29 historical assignments.