Testing Within-Surah Positional Enrichment of the Muqattaat Letters

Result

Scientific verdict: compatible-with-assignment-null.

The observed global positional statistic is slightly positive, but the pre-specified primary criterion was not satisfied.

The site’s rejected status applies to the specified claim of positive enrichment under its frozen decision rule. It does not mean that the null hypothesis has been proved or that all possible positional effects have been excluded.

Abstract

The muqattaat are disconnected letter sequences appearing at the openings of 29 Quranic surahs. LAB-002 tested the pre-specified hypothesis that the letters represented by each historical prefix occur unusually early within the corresponding carrier surah.

Each surah’s own muqattaat opening was removed before scoring. The remaining Arabic letters were assigned continuous positions normalized by surah length. A surah-level statistic measured displacement toward earlier positions, and the primary statistic was the unweighted mean over all 29 carrier surahs.

The observed BODY statistic was positive, T = 0.0019156552081341831. Under the frozen null that randomly reassigns historical prefixes among the same 29 fixed stripped surah texts, 2,000,000 permutations yielded p = 0.0536044731977634. The pre-specified primary threshold of 0.05 was not crossed.

An independent within-surah verse-order permutation control yielded p = 0.24426751146497708. The RAW sensitivity retained a positive direction but also failed the assignment-null threshold. Removing the predefined Qaf/Sad/Nun subgroup reversed the observed global direction.

The study is classified as compatible with the assignment null. No inference of intentionality or supernatural causation is made.

Research question and pre-specified decision rule

Do the letters represented by each historical muqattaat prefix occur earlier within its associated surah than expected under random reassignment of the historical prefixes among the 29 carrier surahs?

The directional alternative was specified before real-corpus scoring.

The primary criterion required BOTH:

1. Observed global T greater than zero.
2. One-sided assignment-null p-value less than or equal to 0.05.

Failure of either condition means that the primary criterion is not satisfied. A secondary sensitivity or control cannot replace this rule.

The design was frozen in Git before the real-corpus scoring. Here, “pre-specified” refers to that documented freeze and does not claim registration in an external public preregistration service.

Corpus and preprocessing

The analysis uses DATA-001: Tanzil Quran Text, Simple Clean, version 1.1.

The canonical source contains 114 surahs and 6,236 verses.

BODY removes the ordinary initial Basmala from the first verse of 112 eligible surahs, preserving S1:1 and S9:1 and all 6,236 verse identifiers.

BODY is the primary analysis. RAW is a pre-specified sensitivity.

For either view, each of the 29 carrier surahs has its own historical muqattaat opening removed before positional scoring. Surah 42 has the combined historical prefix represented across 42:1 and 42:2; both opening parts are removed.

In RAW, the ordinary initial Basmala remains where present, while the muqattaat opening itself is still removed before scoring.

The primary analysis applies no orthographic normalization.

Target letters and statistic

The targets for a carrier surah are the distinct Arabic letters in its historical muqattaat prefix. Repetition of a letter within that prefix does not give the letter additional prefix weight.

After opening removal, non-Arabic letters and separators do not contribute to positional indexing. Let N be the length of the resulting Arabic-letter sequence.

For a target occurrence at one-based letter index j:

x(j) = (j - 0.5) / N

The surah-level statistic is:

E = 0.5 - mean(target-occurrence positions)

Positive E indicates an earlier average target-letter position; negative E indicates a later one.

If a stripped surah has no target-letter occurrences, E is defined as zero and that surah remains in the population.

The global primary statistic is the unweighted mean:

T = (E_1 + E_2 + ... + E_29) / 29

This definition gives each carrier surah equal weight, rather than giving longer surahs more weight through their letter counts.

Primary null: historical-prefix reassignment

The 29 already-stripped surah texts remain fixed.

The 29 historical prefix labels are reassigned among those same texts. For every assignment, the global statistic T is recomputed.

Frozen parameters:

The randomization tests the historical association between the prefix sets and their carrier texts. It does not shuffle the letters or verses within the primary-null texts.

Primary BODY result

The observed statistic is:

T = +0.0019156552081341831

The 29 surah-level values have the following signs:

The positive global T therefore reflects effect magnitudes; it does not result from a majority of surahs having positive E.

The assignment-null simulation produced:

• extreme count: 107,208 out of 2,000,000 permutations;
• add-one p-value: 0.0536044731977634.

Since the p-value exceeds the pre-specified threshold of 0.05, the primary criterion is not satisfied.

Classification: compatible-with-assignment-null.

The result must not be reclassified as significant through rounding, secondary analyses, or a post-result change of threshold.

CONTROL-B: within-surah verse-order permutation

CONTROL-B preserves each historical prefix assignment, the content of each carrier surah, the number and content of its verse blocks, and the letter order within each block.

It independently shuffles the verse blocks inside each surah after the opening has been removed.

Frozen parameters and result:

The observed BODY T is not unusual under this structural control.

CONTROL-B asks a different question from NULL-A: it tests sensitivity to verse order while retaining the historical prefix assignments. It cannot rescue the failed primary assignment-null criterion.

RAW sensitivity

The RAW analysis retains the ordinary initial Basmala where present and removes each carrier surah’s own muqattaat opening before scoring.

RAW agrees with BODY on the positive descriptive direction and the failure to cross the assignment-null threshold.

RAW has a larger observed T but also a larger p-value. The observed statistic and its position in a changing null distribution are different quantities.

RAW remains a sensitivity, not a replacement primary analysis.

Leave-one-surah-out sensitivity

Removing each of the 29 carrier surahs in turn produced 29 positive reduced-population T values.

Removing any single surah does not reverse the positive sign of T.

This descriptive observation does not establish statistical significance or robustness to every subgroup exclusion.

Repeated-prefix-family sensitivities

The following family exclusions were specified before scoring:

Each exclusion retains the positive descriptive sign.

These values do not replace the primary assignment-null test and are not presented as new significant findings.

Equal-letter weighting sensitivity

The alternative equal-letter statistic first calculates enrichment for each distinct target letter and then gives those letters equal weight within each surah.

Its observed global statistic is:

T = +0.003031582262791358

This agrees with the positive descriptive direction of the primary statistic. It does not change the primary inferential classification.

Qaf/Sad/Nun exclusion sensitivity

The predefined QSN sensitivity removes surahs whose historical prefix contains Qaf, Sad, or Nun:

S7, S19, S38, S42, S50, and S68.

The remaining population contains 23 surahs.

The direction reverses under the predefined QSN exclusion.

The full-population positive descriptive sign is therefore QSN-sensitive. This is a subgroup-exclusion observation, not a demonstration that those letters causally produce the full-population statistic.

Prior art

A separate LAB-002 prior-art review examined computational, statistical, and historical work on muqattaat letters.

The closest identified partial precedent is Waiel5’s 2026 H17 positional-gradient analysis:

https://github.com/Waiel5/quran-decipherment/blob/main/findings/phase-b-hypotheses/muqattaat-positional-gradient.md

H17 examines the associated muqattaat letters inside the 29 carrier surahs after removing their literal openings. It uses verse-count quartiles, letter-density gradients, and within-surah verse-order permutations.

The broader within-surah positional question therefore predates LAB-002.

LAB-002 differs by using continuous normalized occurrence positions, an unweighted global statistic over the 29 surahs, and historical-prefix reassignment among the fixed stripped surah texts as its primary null.

No exact precedent for this specific combined methodology was identified in the sources examined. Absolute novelty is not claimed.

The reviewed H17 file bears an internal date of 2026-04-12; the earliest public Git commit identified for that file path in the review is dated 2026-04-29. These are distinct provenance dates.

The complete review is preserved at:

artifacts/lab-002/prior-art-review.md

The review was committed after the statistical verdict and does not retroactively change that frozen verdict.

Limitations

The primary result does not satisfy its frozen criterion.

A non-significant assignment-null result is not proof that the null hypothesis is true, and it does not exclude every other possible positional statistic or corpus convention.

The verse-order control and QSN sensitivity further limit the interpretation of the small positive full-population statistic.

The current prior-art review establishes only that no exact precedent was identified in the sources examined; it does not establish absolute historical novelty.

The available frozen verdict records summary statistics and provenance hashes. No complete permutation-distribution figure is claimed here. Any future visualization must be regenerated from the frozen engine and authenticated as a separate derived artifact.

Reproducibility and provenance

The scientific results are recorded in:

artifacts/lab-002/statistical-verdict.json

The frozen numerical and DATA-001 adapter implementations are at:

analysis/lab-002/core.mjs

analysis/lab-002/data001-adapter.mjs

The statistical verdict manifest retains its original priorArt.status: PENDING_FULL_REVIEW field because it was frozen before the separate prior-art review was completed. This article references the subsequent review without editing the earlier record.

Conclusion

LAB-002 tested a pre-specified hypothesis that the historical muqattaat letters are shifted toward earlier positions within their associated surahs.

The observed global statistic was slightly positive, but the primary historical-prefix assignment test did not satisfy the predefined criterion (p = 0.0536044731977634).

The observed statistic was also not unusual under the independent verse-order control (p = 0.24426751146497708), and the predefined Qaf/Sad/Nun exclusion reversed its direction.

LAB-002 is therefore classified as:

compatible-with-assignment-null

A prior-art review identified a strong partial precedent for the broader within-surah positional question, but no exact precedent for the specific combined LAB-002 methodology was identified in the sources examined.

No inference of intentionality, supernatural causation, statistical significance, or absolute historical novelty is made.

Observe. Verify. Test. Question. Reproduce.

Public evidence and reproducibility

The frozen LAB-002 evidence is publicly accessible:

• Evidence and reproducibility notice
• Frozen statistical verdict
• Prior-art review

These public files document the frozen result, scientific implementation, component tests, provenance, and review of prior work. The component tests do not constitute an independent rerun of the full historical permutation campaigns.