Mirror Surah Pairs and Divisibility by 59

Abstract

QMR-002 examines a numerical property of Quranic surah pairs whose numbers sum to 115.

Under DATA-001, six of the 57 canonical mirror pairs satisfy the rule:

abs(wordCount(A) - wordCount(B)) is divisible by 59.

The six DATA-001 pairs are:

The zero difference for 55 / 60 is mathematically divisible by 59 and is retained explicitly rather than silently excluded.

A separate external sensitivity check was then performed using published 2022 word counts from Hasan and Mamun.

Under those external counts, only 2 / 6 of the already-fixed pairs retain the divisibility-by-59 property.

QMR-002 is therefore recorded as an interesting structured observation, not as a robust or statistically significant discovery.

Research Question

For each canonical mirror pair:

A + B = 115

does the absolute difference between their word counts satisfy:

abs(W_A - W_B) % 59 = 0?

The retrospective reconstruction enumerates all 57 canonical pairs.

A second question is then asked without searching for new pairs:

Do the six DATA-001 matches retain the same property under an independently published set of surah word counts?

Dataset & Counting Rules

• Dataset: DATA-001
• Methodology: METHOD-001
• Corpus: Tanzil Quran Text - Simple Clean - Version 1.1
• Views: RAW and BODY
• Pair definition: A = 1..57, B = 115 - A
• Primary arithmetic rule: abs(wordCount(A) - wordCount(B)) % 59 === 0
• Zero difference: retained as divisible by 59

No approximate match is permitted.

No pair is omitted because its difference equals zero.

Deterministic DATA-001 Result

Exactly six mirror pairs satisfy the divisibility rule under DATA-001.

For these six pairs, the RAW and BODY match sets are identical.

The deterministic statement is therefore:

6 / 57 mirror pairs satisfy the fixed divisibility-by-59 rule under DATA-001.

This statement concerns the defined corpus and counting rules only.

External Word-Count Sensitivity

The six DATA-001 matches were frozen before the external counts were evaluated.

The external source is:

Md. Rashidul Hasan and Fazly Ealahi Mamun,
“Numerical Statements of the Holy Quran Based on Verses, Words, and Letters in Makki and Madani Sura”,
International Journal of Cultural and Religious Studies, 2022.

DOI:

10.32996/ijcrs.2022.2.2.3

The publication states that its numerical data were extracted from Quran Code software.

No new pair and no new modulus was searched during this control.

The result is:

Therefore:

DATA-001: 6 / 6 of the fixed QMR-002 matches retain the property.

External published word counts: 2 / 6 retain the property.

The two surviving pairs are:

• 13 / 102: difference 826 = 14 x 59
• 30 / 85: difference 708 = 12 x 59

Robustness Interpretation

The DATA-001 result is exactly reproducible under its registered counting rules.

However, the six-pair structure is not invariant across the tested word-count conventions.

The external sensitivity check shows that the result depends materially on the underlying textual representation and/or word-count convention.

This does not establish that one convention is uniquely correct.

It means only that QMR-002 must not be described as a corpus-independent numerical invariant.

For this reason the study is not classified as robust.

Statistical Analysis

The historical statistical procedure associated with this observation was not recovered with enough precision to reproduce it.

Earlier remembered values involving a fixed-59 test, a 99-module correction, or a larger family are therefore not treated as verified QMR-002 results.

No calibrated p-value is published for QMR-002.

The deterministic existence of six matches does not, by itself, establish statistical significance.

Multiple Testing

A numerical search can vary many choices:

• pair definitions;
• counting conventions;
• arithmetic operations;
• candidate moduli;
• corpus representations;
• inclusion or exclusion rules.

The exact historical search family that produced QMR-002 was not recovered.

Accordingly, Coran Codex does not assign a corrected significance level to this reconstruction.

Prior-Art Investigation

Numerical Quran research involving surah pairing, symmetry, word counts, and modular relationships predates Coran Codex.

During the present prior-art investigation, no earlier source was located that states the exact combined criterion:

A + B = 115

and

abs(W_A - W_B) congruent to 0 modulo 59

with the six DATA-001 pairs reported here.

This is not proof of novelty.

The novelty status therefore remains:

Investigating

Interpretation Standard

Fact

Under DATA-001:

• all 57 canonical mirror pairs were evaluated;
• six pairs satisfy the fixed divisibility-by-59 rule;
• the six RAW and BODY matches are the same;
• pair 55 / 60 has difference zero and is retained mathematically.

Under the Hasan-Mamun 2022 published counts:

• exactly 2 / 6 of those already-fixed pairs retain the rule;
• they are 13 / 102 and 30 / 85.

Statistical interpretation

No calibrated statistical significance is assigned.

The external control demonstrates substantial sensitivity to the tested word-count convention.

Claim

Coran Codex can reproduce the six-pair structure exactly under DATA-001.

The same six-pair structure does not remain intact under the tested external published word counts.

Not claimed

QMR-002 does not establish:

• statistical significance after a recovered multiple-testing correction;
• robustness across Quranic editions or tokenization systems;
• proof that the exact criterion is historically novel;
• a supernatural explanation;
• divine intent or theological significance.

No supernatural or divine conclusion follows from this result.

Limitations

The principal limitation is corpus sensitivity.

Word counts depend on textual representation, segmentation and tokenization rules.

The external control is also not a replication of DATA-001. It is a sensitivity analysis using another published numerical dataset.

The exact historical search process that led to the modulus 59 is unavailable.

Therefore the effective historical hypothesis space cannot presently be reconstructed.

Verdict

Status: Interesting

Evidence level: E1

Classification: Exploratory

Novelty: Investigating

Discovery: No

The deterministic pattern exists under DATA-001.

Its reduction from 6 / 6 to 2 / 6 under the tested external word counts prevents promotion to a robustness claim.

Reproducibility

External source data:

analysis/data/qmr-002-hasan-mamun-2022.json

Analysis:

analysis/qmr-002-external-sensitivity.mjs

Result:

analysis/results/qmr-002-external-sensitivity.json

Artifact SHA-256:

38C94983097C687850761FD32F08670B665044C3DB93541816C14E0BA26E0969

The external result was generated twice from the same frozen analysis.

The two files were verified as:

• SHA-256 identical
• byte-for-byte identical

before the temporary repeat artifact was removed.