Twenty Quran transmissions: conditional compatibility

What the study covers

The full comparison inventory was retrieved from nQuran’s Shāṭibiyyah/Durrah view, which supplies the ten readers and their twenty principal transmitters. Source descriptions name their reader/transmitter groups, including an explicit “remaining transmitters” group. Unlisted cells were never filled with Ḥafṣ.

Measure	Count
Chapters retrieved	114
Source ten-verse groups	671
Comparison response pages	1266
Source feature blocks	33,602
Source features semantically coded	29,350 (87.3%)
Source features excluded	4,252
Variable analytic characters	33,306
Main fixed word-variant characters	1096
Main dependency blocks	586
Primary-source diagnostic cases checked	36
Transmitter-case checks matching	720

Full retrieval is not full semantic coverage. The numerical study uses 29,350 of 33,602 source feature blocks. The other 4,252 are retained with exclusion reasons. Their omission could alter the relationships and percentages. This is an exploratory study of the coded subset, not a final ranking of every documented reading difference.

A source block can contain multiple distinct dimensions, such as connected and stopping pronunciation. Those become separate characters when all groups explicitly specify the dimension; invariant components are omitted from the comparison. Accepted alternatives are retained as sets. No claim of exhaustive Ṭayyibah routes or a complete coherent performance path is made.

Agreement with reconstructions from the other nineteen

Every transmission is withheld before building its training tree. All eligible edge-root positions are considered. At every position, all minimum-change ancestral states are retained. Each target is compared with its own nineteen-transmission reconstruction, rather than one independently recovered archetype. A lower endpoint counts agreement that survives every permitted ancestral-state tie at that root, then takes the lowest result across roots. The upper endpoint permits any overlapping ancestral state, then takes the highest result across roots.

Twenty compatibility intervals across roots and ancestral-state ties

Transmission	Conditional agreement	Resolved exact agreement	Contradiction
Qālūn	49.1%–98.5%	49.1%–87.4%	1.5%–48.2%
Warsh	47.5%–98.5%	47.5%–87.4%	1.5%–49.7%
al-Bazzī	48.7%–99.4%	48.7%–87.5%	0.6%–47.1%
Qunbul	48.5%–99.3%	48.5%–87.5%	0.7%–47.6%
al-Dūrī (Abū ʿAmr)	46.0%–100.0%	46.0%–89.1%	0.0%–52.2%
al-Sūsī	46.0%–100.0%	46.0%–89.1%	0.0%–52.2%
Hishām	50.4%–98.2%	50.4%–80.9%	1.8%–47.0%
Ibn Dhakwān	51.0%–98.0%	51.0%–80.9%	2.0%–45.7%
Shuʿbah	54.9%–82.8%	54.9%–67.6%	17.2%–42.8%
Ḥafṣ	54.1%–83.8%	54.1%–67.5%	16.2%–40.0%
Khalaf (Ḥamzah)	44.8%–99.8%	44.8%–89.1%	0.2%–52.4%
Khallād	45.0%–100.0%	45.0%–89.1%	0.0%–52.2%
Abū al-Ḥārith	43.4%–100.0%	43.4%–87.9%	0.0%–52.8%
al-Dūrī (al-Kisāʾī)	43.4%–100.0%	43.4%–87.9%	0.0%–52.8%
Ibn Wardān	43.1%–99.8%	43.1%–85.2%	0.2%–53.0%
Ibn Jammāz	43.3%–100.0%	43.3%–85.2%	0.0%–52.8%
Ruways	45.1%–95.8%	45.1%–76.2%	4.2%–52.0%
Rawḥ	46.4%–96.9%	46.4%–76.2%	3.1%–50.5%
Isḥāq	48.1%–100.0%	48.1%–92.4%	0.0%–49.9%
Idrīs	48.1%–100.0%	48.1%–92.4%	0.0%–49.9%

The common denominator is 1096 fixed word-variant characters, carrying 586 total dependency-block units. The ranges are neither probabilities nor statistical confidence intervals. Minimum and maximum columns may occur at different roots and must not be added together. All twenty are shown in the stated reader/transmitter order, without forcing a rank.

Relationships and conflicting signals

Unrooted topology with resampling support

The tree is inferred from weighted differences using neighbor joining. Nonpositive internal NJ edges are contracted for the principal scoring, treating the resulting polytomies as hard constraints. This is a modeling choice, not evidence of simultaneous descent; scores on the uncontracted binary tree are retained as a sensitivity. Traditional reader labels were used to identify the requested transmissions and to define one pair-withholding sensitivity; they did not impose the tree. The drawing has no ancestral starting point and does not represent time.

Among 193 distinct nontrivial binary variant splits, 11,888 of 18,528 pairs conflict. Those characters cannot all arise by one change each on a single perfect tree. Reversal, convergence, exchange, source error, or coding choices could contribute; this count alone cannot identify the cause.

Similarity in this heatmap is symmetric. It does not establish which reading came first. The names Khalaf (Ḥamzah) and the tenth reader’s transmitters Isḥāq/Idrīs are kept distinct, as are the two al-Dūrīs.

How assumptions change the result

The table shows Ḥafṣ across the main coding and weighting scenarios. The accompanying workbook and machine-readable outputs give all twenty, all root-specific counts, and the joint-withholding results.

Scenario	Characters	Blocks	Ḥafṣ range
farsh fixed block	1096	586	54.1%–83.8%
farsh fixed site	1096	586	56.7%–84.9%
all block	33306	628	56.1%–84.2%
all site	33306	628	60.1%–99.3%
all fixed block	15215	623	55.9%–84.1%
all fixed site	15215	623	52.9%–98.5%
all envelope atomic accepted profiles	33306	628	55.9%–84.2%

Repeated general rules receive one unit per rule family in block-weighted analyses. Repeated word variants are grouped by reviewed lexical families or repeated displayed lexemes. These blocks approximate dependence and do not prove independence between blocks. Occurrence-weighted analyses test the consequences of counting every appearance separately. In this dataset, word variants carry 586/628 = 93.3% of the all-block weight, but only 1,096/33,306 = 3.3% of the occurrence weight. The two views therefore answer substantially different weighting choices.

Withholding Ḥafṣ and Shuʿbah together gives Ḥafṣ a 51.4–82.6% range on the same fixed word-variant subset. The study also withholds the other reader pairs together, withholds selected empirically supported groups, removes target-private positions from the scoring denominator, varies numerical tie resolution, and resamples dependency blocks. 200 bootstrap trees and 100 complete resampled leave-one-out refits were requested. Their actual completed counts are recorded in the output files. Accepted-set analyses measure marginal compatibility; they can allow combinations that no single transmitted path permits.

What this can tell us about an archetype

The data establish patterns of agreement and disagreement. Under the symmetric model used here, moving the root does not change the minimum number of changes. It therefore cannot choose a historical direction without an additional assumption. This is the same root-identification distinction discussed in the IQ-TREE rooting documentation; IQ-TREE itself was not used for these calculations.

Your concern about nineteen related readings is real. If nineteen share a derived state and one preserves the original state, withholding the lone preserver reconstructs the derived state and penalizes the original. Reversing that history produces the same unrooted observations. This counterexample is included in the executable review. A high agreement score can demonstrate consistency with the other readings without demonstrating historical priority.

Independent checks

A separate extraction from Ibn al-Jazarī’s al-Nashr supplied 36 diagnostic cases. All 720 transmitter-case assignments matched the source comparison, including the tested accepted alternatives. The cases were deliberately selected to exercise different phenomena; they are not a random error-rate estimate or an exhaustive validation. One contradictory-looking source phrase at 65:3 was explicitly adjudicated and recorded. This validates the extracted source at those cases. Only 15 of the 36 benchmark cases are fully represented in the numerical matrix; all 15 independently checked fixed-state partitions match. The other 21 cases are partial or excluded, so the 720 source checks must not be described as 720 validated matrix cells.

An independent implementation review checked 2,322 exhaustive state/root cases and caught a random-number-state leak between holdouts, which was fixed and regression-tested. Missing data, tied ancestral states, incompatible splits, and root-resolution effects were also checked. Reviews and exact code hashes accompany the data.

The institutional Corpus Coranicum export was inspected as corroboration. Its item-level source keys and Arabic subfields are empty in the retrieved snapshot, and direct data for Isḥāq/Idrīs are absent. It was therefore not substituted for a complete twenty-transmission matrix.

Reproducibility

The accompanying archive contains source retrieval manifests, parsed factual variant records, the complete coding inventory with exclusions, all twenty state columns, the method and review scripts, the study outputs, and the pre-analysis protocol. Each numerical character links to its source. The archive also includes 40,552 full-panel character/root state records and 21,920 heldout character/target sensitivity records; counts of root edges are not probabilities. The workbook provides a compact overview, every scenario’s intervals, and the fixed word-variant matrix. To reproduce the computation, follow README.md in the archive.