Coincidence is cheap: word-sum coverage of the Pentateuch tested against null models, and 8,629 classical gematria attestations from 834 works

A random text covers more gematria values than the Pentateuch does. That is the result of this record, and it runs against the direction gematria enthusiasm would predict. For every value 1-1500 we count in how many of the 54 weekly Torah portions some word has that letter-sum. 867 of the first 1000 values have at least one content word. On its own that number means nothing, so we measured what a text carrying no message at all would give: a corpus-wide permutation of all consonants (M1), a first-order Markov regeneration of every word at its own length and place (M2), and a reshuffling of the real words across portions (M3). 1000 replicates for M1 and M3, 300 for M2. Strict rule, values 1-1000: observed 867, against 946.9 +/- 4.9 (z = -16.4) for M1 and 938.1 +/- 5.1 (z = -14.0) for M2. Loose rule: observed 937 against 979.2 +/- 3.4 and 978.6 +/- 3.7. Not one replicate of any model fell to the observed level. The same holds for 1-1500 and for the count of values present in all 54 portions (observed 6, against 20.6, 24.1 and 31.6). The reason is ordinary: real language repeats itself, so a few thousand lemmas carrying eighty thousand word forms produce fewer distinct sums than a random letter stream of the same size. Coverage is therefore not evidence of design - it is below what chance alone delivers. Any claim of the form "the value X occurs in the text, therefore ..." rests on an event that is the normal case and is cheaper in a random text than in this one. Files: sapir861_coincidence_1500.csv gives values 1-1500 against the portions containing them, under a strict rule (noun, verb and adjective morphemes only, 59,633 forms) and a loose rule (every word form as written, 80,052 forms). coverage_vs_null_1500.csv gives every value its own null distribution - mean, standard deviation, z and empirical p - so any specific claim about any number can be checked rather than argued about. nullmodel_results.json is the summary for all three models under both rules. METHODS.md carries the definitions, corrections and limits. sapir861_code.zip regenerates the whole record from the public source text. Second dataset: sapir861_attested_gematria_v03.csv holds 8,629 gematria equalities actually asserted in classical works, rebuilt from the Hebrew Wikisource with our own code and recomputed by machine - 1,023 values, 834 works. 6,494 (75.3 percent) hold exactly; 2,135 (24.7 percent) require im hakolel, the plus-or-minus one allowance. The most kolel-dependent value is 110, where 90 of its 106 attestations need it. This records what authors wrote; it is not a claim that any equality is correct. On 861: under the strict rule it has no content word in the Pentateuch. The per-value null gives an expected 3.85 +/- 1.96 portions, so the observed zero sits at z = -1.97, with an empty result in 4.3 percent (M1) and 1.0 percent (M2) of replicates. Mildly unusual and nothing more - one value out of 1500. Under the loose rule 861 appears in 12 portions against an expected 11.5 +/- 3.2: entirely ordinary. Correction: an earlier build of ours truncated Exodus 20 at verse 23 and lost three verses; 21 of the 1500 rows were one portion too low. The files here are corrected and no headline figure changed. Not included: no comparison against other Hebrew corpora; no surrogate beyond first order; the attestation dataset has not been re-derived independently. No claim is made about the meaning of any equality, and none about any person. Version 3.0: the attestation dataset is now sapir861_attested_gematria_v04.csv, with two added columns, verification and verification_note. Two records were checked against the printed leaves they cite. The only attestation of 862 (Karnayim, Zholkva 1709, maamar 11) is withdrawn: the scanned leaf shows the printed phrase carries a different value, and our row came from a split at the word be-gematria during extraction. The 861 row (Bnei Yissaschar) is marked unverified — no scan of that edition is available on terms allowing reuse. A second file, sapir861_861_computed_v01.csv, gives 861-related counts computed directly from the Westminster Leningrad Codex, separate from what any author asserted. Open Scriptures Hebrew Bible, Westminster Leningrad Codex with morphology, CC BY 4.0, https://github.com/openscriptures/morphhbAttestations: Hebrew Wikisource, CC BY-SA 4.0.Method pages: https://sapir861.com/research/coincidence and https://sapir861.com/research/kolel