Lattice ('gelosia') multiplication's paper trail runs India (12th-c. Lilavati commentary) → Islamic Maghreb (Ibn al-Banna, late 13th c.) → Renaissance Italy

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Lattice (or gelosia) multiplication — reading the partial products of a long multiplication off a diagonal-ruled grid — has a documented transmission history that predates the European devices built on it (see claim-napiers-bones-hardware-wrapper-on-lattice-multiplication). As recorded in tertiary sources, the method's paper trail has three legs:

1. Indian precedent (12th c., partially attested). A method called Kapat-sandhi, described as "very similar to the lattice method," appears in a commentary on the 12th-century Lilavati of Bhāskarāchārya (Bhāskara II).
2. Islamic Maghreb (late 13th c., earliest recorded use). The earliest recorded use in Arab mathematics is attributed to Ibn al-Banna' al-Marrakushi in his arithmetic treatise Talkhīṣ aʿmāl al-ḥisāb ("Summary of arithmetical operations"), written in the Maghreb. (As promoted this leg read "first full description" / "earliest full description"; the cited page says "earliest recorded use" — corrected 2026-09-11, see audit_status. The page also records an English Latin treatise c. 1300 and Wu Jing, 1450, as parallel earliest uses, and says the question of where it arose first is still being researched.)
3. Renaissance Italy. The method arrived in Europe as gelosia, later packaged by John Napier into the physical rods of his 1617 "Napier's bones."

The route — Indian origin, an Islamic-world intermediary that carries the surviving transmission, European arrival under a new locally-meaningful name (see claim-lattice-multiplication-renamed-window-grille-in-arabic-and-italian) — is structurally identical to the path traced for a wholly different kind of material at claim-kalila-wa-dimna-descends-from-borzuyas-lost-pahlavi (a Sanskrit fable collection → lost Pahlavi → surviving Arabic → Europe, carried by Borzuya, claim-borzuya-immortality-herb-was-really-a-book). Two unrelated domains — an arithmetic technique and a fable collection — moving India → Islamic intermediary → Europe on nearly the same multi-century schedule is the cross-domain pattern this capture was promoted to preserve, pursued further at question-transmission-chains-renamed-for-local-resemblance-pattern.

Why this note is seedling and flagged. The route is uncontested in outline, but it is the load-bearing point of the note and rests only on Tier 4 Wikipedia, and its dates are quantitative claims floored at Tier 1–2. Two specific attributions — that the lattice method actually sits inside Ibn al-Banna's Talkhīṣ, and that Kapat-sandhi is genuinely the same technique — are unconfirmed above the encyclopedia floor and routed at question-verify-lattice-multiplication-maghreb-india-primary. A 2026-08-13 verification pass found Tier 1–2 evidence that complicates rather than confirms the Maghreb leg specifically — see the Correction history below.

Correction history.

• 2026-08-13 — A verification pass (claim-abdeljaouad-oaks-talkhis-study-omits-lattice-gelosia-shabakh, Tier 1; claim-earliest-gelosia-manuscript-evidence-is-ibn-ghazis-commentary, Tier 2) found that the single Tier 1 source purpose-built to catalogue Ibn al-Banna's Talkhīṣ tradition never mentions lattice/gelosia/shabakh multiplication, and that the earliest manuscript evidence for gelosia grids in this tradition belongs to Ibn Ghāzī's 15th/16th-century commentary, roughly two centuries after Ibn al-Banna's own hand. This does not overturn the Maghreb leg of the transmission route — it is not proof lattice multiplication is absent from the Talkhīṣ — but it shifts the honest framing of the flag above from "unconfirmed" toward "the confirmed evidence found so far points at Ibn Ghāzī, not Ibn al-Banna, as the earliest documented Arabic attestation." The title and outline above are left as written; this is the sharper, correct caveat a reader should carry alongside them. Same session also found the Indian leg's Kapat-sandhi identification stated more precisely than Wikipedia's phrasing, but only by a Tier 3 source — see claim-kapat-sandhi-gelosia-identification-rests-on-tier-3-source.