Lexical Frequency-Abjad Atlas

Abstract

QMR-015 examines the relationship between exact graphical word-form frequency and traditional Abjad value across canonical DATA-001.

The analysis asks three primary descriptive questions:

1. how many distinct exact word forms share the same corpus frequency;
2. how many share the same traditional Abjad total;
3. how many share both values simultaneously.

Two additional exploratory questions examine word forms whose own frequency equals their Abjad value and shared-verse occurrences among higher-frequency joint matches.

The resulting equalities are exact and reproducible under the declared corpus, tokenization and Abjad convention. The exploratory statistical controls do not show an unusual aggregate excess under the tested null models.

QMR-015 is therefore published as a descriptive and exploratory atlas, not as a confirmatory statistical result.

Corpus and lexical unit

The analysis uses:

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

Canonical SHA-256:

228df2a717671aeb9d2ff573002bd28d6b3f973f4bc7153554e3a81663d67610

The lexical unit is the exact whitespace-delimited graphical word form.

No stemming, lemmatization, root grouping or silent orthographic normalization is used.

BODY removes the exact opening four-token Basmala prefix from the first verse of 112 eligible surahs while preserving S1:1 and S9:1.

Abjad convention

QMR-015 uses:

ABJAD-TRADITIONAL-001

with traditional 28-letter values and the documented variant handling:

This convention is not identical to the literal TRAD_T1 convention used in QMR-009. Results from the two systems must not be silently interchanged.

Exhaustive RAW atlas

Same frequency

Across the 14,868 exact forms:

• 94 frequency groups contain at least two distinct forms;
• 14,791 distinct forms belong to such groups;
• those groups contain 41,683,473 unordered pairs.

The large pair count is dominated by low-frequency forms, especially forms occurring once.

Same Abjad total

The RAW inventory contains:

• 1,315 Abjad groups containing at least two forms;
• 14,625 distinct forms in those groups;
• 131,670 unordered pairs.

Same frequency and same Abjad

For the joint key (frequency, Abjad):

• 2,298 groups contain at least two distinct forms;
• 11,797 forms belong to those groups;
• the groups contain 45,552 unordered pairs.

These counts describe the exhaustive inventory. They are not, by themselves, evidence that the matches are statistically unusual.

BODY sensitivity

BODY produces:

The Abjad grouping is unchanged because Abjad is a property of the graphical form. Frequency-based differences arise from the BODY transformation.

Higher-frequency joint matches

Restricting the RAW inventory to forms occurring at least 10 times leaves:

• 21 joint frequency-Abjad groups;
• 43 distinct forms;
• 23 unordered pairs.

The highest-frequency pair is:

The threshold of 10 was selected after inspection of the descriptive results and is therefore exploratory rather than preregistered.

Frequency equal to own Abjad

Exactly two exact graphical forms satisfy:

frequency = own Abjad

in both RAW and BODY:

These are exact descriptive observations.

Shared-verse observation

Among the 23 higher-frequency RAW pairs, exactly one pair occurs in the same verse:

Shared verse:

Quran 23:115

The pair was identified after inspection of the joint inventory and is not an independently specified target.

Exploratory null calibration

Higher-frequency joint matches

The tested statistic is the number of joint frequency-Abjad pairs with RAW frequency at least 10.

The null model permutes observed Abjad totals among word forms having the same Arabic-letter count.

• simulations: 4,096
• seed: 20260922
• observed pairs: 23
• simulated mean: 22.56640625
• simulated median: 22
• simulated 5th percentile: 15
• simulated 95th percentile: 31
• simulated minimum: 8
• simulated maximum: 41
• simulations at least as large as observed: 1,938
• empirical upper-tail: 0.4732731266780571

The observed count is compatible with this tested exploratory null model.

Frequency equal to own Abjad

RAW:

• observed: 2
• simulated mean: 2.30908203125
• simulated median: 2
• empirical upper-tail: 0.6743958994386137

BODY:

• observed: 2
• simulated mean: 2.30126953125
• simulated median: 2
• empirical upper-tail: 0.6726873321942886

The observed self-equalities are also compatible with this tested exploratory model.

Positional control

Observed shared-verse events among the 23 higher-frequency RAW pairs:

1

Expected shared-verse events under the simplified positional model:

1.5158895774891188

The model preserves word frequencies by surah, verse token lengths and total token counts.

For the observed أنما / إلينا pair, its expected shared-verse count is:

0.11491863152130599

This is an expectation, not a p-value. No tail probability was calculated.

Independent reconstruction

A second implementation rebuilt the lexical inventory directly from canonical DATA-001 without importing the INDEX-001 analysis modules.

It independently reconstructed:

• 6,236 verse identifiers;
• 78,248 RAW tokens;
• 77,800 BODY tokens;
• 14,868 distinct exact graphical forms.

All 14,868 forms were compared with INDEX-001.

Mismatches:

0

It also reproduced the RAW and BODY totals, the 21 higher-frequency joint groups, the 23 corresponding pairs, the two self-equalities and the shared verse at Quran 23:115.

Verdict:

INDEPENDENT RECONSTRUCTION PASS

Prior-art context

The broader components of QMR-015 have precedent in Quranic lexical-frequency counting, Abjad calculation and numerical word analysis.

The QMR-015 review did not identify an exact precedent in the sources examined for the complete methodology combining exact graphical forms, exhaustive joint (frequency, Abjad) grouping, RAW/BODY analysis, exploratory null calibration, positional control and independent reconstruction against a cryptographically fixed corpus.

This statement is limited to the sources examined and is not proof of absolute novelty.

Interpretation

QMR-015 establishes an exhaustive and reproducible lexical inventory under a fixed corpus and declared Abjad convention.

The exact arithmetic matches remain exact observations.

The exploratory calibrations do not establish an unusual aggregate excess for the tested higher-frequency joint matches or for the frequency = own Abjad property.

Classification:

exploratory / descriptive / reproducible

Limitations

1. Results depend on DATA-001 and the declared exact-form tokenization.
2. Alternative Quranic orthographies can change forms and token counts.
3. Results depend on ABJAD-TRADITIONAL-001.
4. The frequency threshold of 10 was selected after descriptive inspection.
5. The null models preserve only specified structural features.
6. The shared-verse analysis is exploratory.
7. Prior-art searching cannot establish absolute novelty.

Public research archives

Complete inventories:

• RAW frequency-Abjad inventory (CSV)
• BODY frequency-Abjad inventory (CSV)

Machine-readable records:

• Deterministic summary (JSON)
• Exploratory calibrations (JSON)
• Research manifest (JSON)

The files are served directly from the frozen committed research artifacts.

Artifact integrity

Scientific research commit:

76017894524ee400f72ad9357d2afb661259275e

Merged through PR #7.

Research record

• docs/research/qmr-015-protocol.md
• docs/research/qmr-015-reproduction.md
• docs/research/qmr-015-prior-art.md
• artifacts/qmr-015/manifest.json

Canonical corpus:

Tanzil Project, Quran Text — Simple Clean — Version 1.1.