The Lexical Seam: The Zipf-Mandelbrot Residual Is a Boundary of Constant Width (1.2% of Vocabulary)

Fitted Zipf–Mandelbrot curves systematically miss on the most frequent words. This paper shows that miss is a boundary — the region where a text's small high-usage vocabulary gives way to the rest of the lexicon — and that the boundary has a width, a quantity prior two-regime accounts never assigned it. In linear rank that width is a constant fraction of vocabulary, s ≈ 0.012·V (R² = 0.97): invariant across 25 English corpora spanning five centuries, across the Brown corpus, WikiText and film dialogue, across forced concatenation of fourteen unrelated works, and across twelve languages once per-type sampling depth is matched. The constant is not universal across systems — constant-innovation growth gives 0.0101, US surnames 0.0185, an asteroid-size catalog 0.0166 — which makes it a fingerprint of the growth family rather than a fact about language alone. Two further results: Mandelbrot's shift parameter c measures sampling depth rather than style, so cross-corpus comparisons of it are confounded unless depth is matched; and a one-term extension, λ-ZM, beats ZM at exactly ZM's own parameter count on 32/32 corpora, because the correction's amplitude is stable enough to freeze — per-corpus optima run [14.2, 24.4] about a median λ* ≈ 20.6, and fixing it at that median on English still beats ZM, transferred unchanged, on Mandarin, Arabic and Russian. The estimator is calibrated from both sides: it recovers planted seams (ratio ≈ 1.03) and does not invent one from smooth single-regime data (2/75 in band for each of three seamless null families, against 23/23 for admissible real fits). Reported against interest: a one-component zero-truncated Poisson–lognormal — one population seen through the count floor — does reproduce the constant (56/59), which is why the width is presented as a shared invariant of the growth family and not as evidence for two populations; and information criteria are shown to be unusable on this objective, the rank curve's effective sample size being near 11 against a median V of 11,174. New in v6.4. The matched one-component null was recomputed after a parameter-selection defect and extended from 10 corpora to 25 (21/21 at median 0.0131 becomes 56/59 at median 0.0125; the conclusion is unchanged). Those same synthetic corpora were then tested on a second observable, and there the one-population account fails: real text carries a higher λ-ZM correction amplitude than its own matched null on 21 of 25 corpora (median 20.60 against 17.21, Wilcoxon p = 5×10−5). The gap survives matching on vocabulary (0.05%), sampling depth (0.001%) and fit quality, the test returns nothing when two independent nulls are compared with each other (p = 0.45), and the one-component model demonstrably fits the count histograms it is being faulted on (25/25 under a parametric bootstrap). The separation is size-dependent — decisive above a vocabulary of roughly 104 (12/13, p = 0.0005) and unresolved below it (9/12, p = 0.064) — and is reported on those terms. One null, two observables, opposite verdicts: a single population seen through the count floor accounts for the boundary's width but not for the curvature that produced it. This falsifies the sufficiency of the one-population account; it does not by itself establish that exactly two populations produce the curvature. v6.4.2 retitles the paper. The previous title led with "A Two-Population Account", which asserted in its opening words the very thing the paper declines to claim: §3.3 reports that the width does not establish two populations, and retired claim 5 relocates that case onto identity evidence. The new title names the measured object instead. Also corrects two rows of the claim map that still carried the superseded surname constant 0.0266 against the manuscript's 0.0185. v6.4.1 corrected one British spelling in a figure axis label. No data, statistic or conclusion has changed since v6.4. §4.2 documents eight claims this project retired, each with the experiment that killed it. Every quantitative claim maps to a versioned CSV in the accompanying repository. Unpublished and not peer reviewed; conducted with heavy AI assistance, disclosed in the acknowledgments.