The Golden-Ratio Verse Position 3854 and Quran 37:66

Abstract

QMR-009 examines a numerical observation recovered from the 2025 research record KS-Ω-2025-033.

Starting from the fixed 6,236-verse DATA-001 corpus, the golden ratio is defined as:

φ = (1 + sqrt(5)) / 2

Dividing the total number of verse records by φ gives:

6236 / φ = 3854.059953844344

Rounding to the nearest integer gives absolute verse position:

3,854

The 3,854th verse record in DATA-001 is:

Quran 37:66

فإنهم لآكلون منها فمالئون منها البطون

The positional calculation is deterministic and reproducible.

However, the historical precision reported for the corresponding fractional position does not reproduce exactly, and the core 3,854 → 37:66 observation was already publicly documented in 2011.

QMR-009 is therefore classified as a Previously Known structured observation, not as a Coran Codex discovery.

Research Question

Given the fixed DATA-001 corpus of 6,236 Quranic verse records:

1. What absolute verse position is obtained by calculating round(6236 / φ)?
2. Which Quranic verse occupies that position?
3. How close is the resulting discrete position to the exact fractional golden-section target?
4. Do the secondary textual measurements reported in the recovered historical record reproduce under the documented counting convention?

Corpus and Protocol

The analysis uses:

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

The corpus contains exactly:

6,236 verse identifiers

The positional protocol is:

1. calculate φ = (1 + sqrt(5)) / 2;
2. calculate 6236 / φ;
3. round the result to the nearest integer;
4. interpret that integer as a 1-based absolute verse position in DATA-001.

This yields:

6236 / 1.618033988749895 = 3854.059953844344

and therefore:

round(3854.059953844344) = 3854

The 3,854th DATA-001 record is Quran 37:66.

Deterministic Result

The recovered positional observation reproduces:

Thus:

golden-ratio rounded position 3,854 → Quran 37:66

This result follows directly from the fixed corpus size, the stated definition of φ and the stated rounding rule.

Correction of the Historical Precision Claim

The historical record represented the fractional position as approximately:

3854 / 6236 ≈ 0.618033...

The exact calculation on DATA-001 is instead:

3854 / 6236 = 0.618024374599102

while:

1 / φ = 0.6180339887498948

The relative difference is:

0.001555602%

Therefore the recovered historical statement that the relative error was below 0.001% does not reproduce under the standard relative-percent calculation.

This correction does not change the rounded positional result:

3854 remains the nearest integer to 6236 / φ.

It does change the numerical precision that may legitimately be reported.

Secondary Measurements of Quran 37:66

Under the literal counting convention recovered from the historical record, Quran 37:66 has:

• 6 words
• 32 Arabic letters
• traditional literal Abjad value 808

The Abjad calculation uses the recovered 28-letter TRAD_T1 mapping. Arabic letter variants that are not members of that literal mapping contribute zero to the Abjad total rather than being normalized to another letter.

These three measurements reproduce the corresponding historical values.

They are nevertheless secondary observations.

They are not inputs to the golden-ratio position calculation, and their presence after verse 37:66 has already been selected must not be treated as an independent confirmation of the positional result.

RAW and BODY

RAW and BODY both retain the same 6,236 verse identifiers.

Consequently, the absolute position calculation is identical in both analytical views:

position 3,854 = Quran 37:66

The BODY transformation affects opening Basmala text in 112 eligible surahs but does not remove verse identifiers.

Quran 37:66 is not one of those transformed opening records, so its reproduced measurements of 6 words, 32 Arabic letters, and 808 are also unchanged by the BODY transformation.

Prior Art

The core observation is Previously Known.

A public source by Ousman Ahmad, dated 7 April 2011, explicitly:

• states a total of 6,236 Quranic verses;
• divides 6,236 by the golden ratio;
• obtains approximately 3,854.05995;
• rounds this value to position 3,854;
• identifies the 3,854th verse as Quran 37:66.

This predates the recovered 2025 Coran Codex record by approximately fourteen years.

Accordingly, Coran Codex does not claim novelty for the relationship:

6236 / φ → 3854 → 37:66

The contribution of QMR-009 is the controlled reproduction, corpus fixation, numerical correction and explicit classification of the observation.

Statistical Interpretation

QMR-009 does not assign a probability of chance occurrence to this result.

The recovered historical record contained an extreme probability claim, but no sufficiently documented null model, preregistered target family, multiplicity treatment or reproducible calculation was recovered that would justify carrying that probability into the modern record.

The deterministic statement:

round(6236 / φ) = 3854, and verse 3854 is 37:66

is different from the statistical statement:

this correspondence is unlikely under chance.

Only the first statement is established here.

No statistical significance is claimed.

Interpretation Limits

QMR-009 establishes a reproducible positional calculation.

It does not establish that:

• the Quranic corpus was intentionally arranged according to φ;
• verse 37:66 was selected because of the golden ratio;
• the secondary word, letter or Abjad measurements are statistically exceptional;
• the semantic content of 37:66 has causal or statistical relevance to the positional calculation;
• the observation constitutes evidence of supernatural design.

Those questions would require separately defined hypotheses and appropriate statistical controls.

Reproducibility

The deterministic reconstruction is implemented in:

analysis/qmr-009.mjs

The frozen DATA-001 result is stored in:

artifacts/qmr-009/qmr-009-data001-report.json

The canonical source corpus SHA-256 is:

228df2a717671aeb9d2ff573002bd28d6b3f973f4bc7153554e3a81663d67610

The frozen artifact records:

• corpus size: 6,236;
• φ: 1.618033988749895;
• ideal position: 3854.0599538443444;
• rounded position: 3,854;
• verse: 37:66;
• observed fraction: 0.618024374599102;
• target fraction: 0.6180339887498948;
• relative error: 0.0015556022755739483%;
• word count: 6;
• Arabic-letter count: 32;
• literal TRAD_T1 Abjad value: 808.

Classification

Status: Observation Evidence: E1 — Structured Pattern Classification: Confirmatory Novelty: Previously Known Discovery: No Publication state: Published

QMR-009 records a reproducible historical observation together with its numerical correction and prior-art classification.