docs(v4): the mesh ROM's design, MACHINE.md 2.2

Shared math in a small ROM for mesh nodes: UM*, UM/MOD, D+, DNEGATE,
Q.* and Q./ as entries 0-5 of both ROMs, from one source; the host
ROM's assembler entries follow, and its start moves from 12 to 18.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

docs/v4.0.0/MACHINE.md

@@ -83,6 +83,78 @@ What this asks of the ROM:
 Direction (Captain Bob, 2026-10-15): much more GA144-ish. Take what serves from colorForth's
 wiring, drop its odd concepts, add our own. That is what v4 becomes, on the way to v5 and later.
 
+### 2.2 The mesh ROM (designed 2026-10-15)
+
+**Status: designed, for review. Not built.**
+
+Not every node can carry the ROM of section 2. It is an assembler of about 2100 words, so it
+belongs to host nodes (`JUSTIFICATION.md` §9: "the compiler lives on the host node ... mesh
+nodes receive compiled code"). A mesh node carries a small ROM of shared math, as a GA144 node's
+ROM carries multiply and divide steps (Captain Bob, 2026-10-15).
+
+A mesh node needs no ROM to take code in. At reset it blocks on its ports and executes what
+arrives (`MESH.md` 4.2 and 5). The mesh ROM does not change that. It has no start entry.
+
+**One math source.** `capsules/v4/rom/math.f18` holds six routines and their private helpers.
+They are moved out of the system's `.f18` (`core.f18`, `numout.f18`, `qmath.f18`) unchanged in
+behaviour. It has no names, no headers and no FORTH (rule 7.1). Its errors are raised as now:
+`Q./` by zero leaves D-11's result and stores 11 into NODE-ERROR. `Q./`'s five scratch cells
+stay at `(Q/)`, an address fixed in the memory map, which is the reserved RAM of section 2.1.
+
+**Two ROMs, one entry order.** Both ROMs begin with the same six entries, written once and used
+by both tables so that the two orders cannot drift apart:
+
+| Entry | Routine | Host ROM | Mesh ROM |
+|---|---|---|---|
+| 0 | `UM*` ( u1 u2 -- ulo uhi ) | yes | yes |
+| 1 | `UM/MOD` ( ulo uhi ud -- urem uquot ) | yes | yes |
+| 2 | `D+` ( d1 d2 -- d3 ) | yes | yes |
+| 3 | `DNEGATE` ( d -- -d ) | yes | yes |
+| 4 | `Q.*` ( a b -- c ) | yes | yes |
+| 5 | `Q./` ( a b -- q ) | yes | yes |
+| 6 to 17 | the assembler's routines, entries 0 to 11 before this change | yes | no |
+| 18 | `(ROM)`, where the host machine starts (entry 12 before this change) | yes | no |
+
+- The mesh ROM is the six entries and the math: about 150 to 200 words.
+- Within a build both ROMs sit at the same base, `V4_ROM_BASE`. Code the host assembles that
+  calls entry k therefore runs unchanged on a node carrying either ROM.
+- `v4/tools/mkrom.c` builds both ROMs at each cell width. `v4/tools/mkmap.c` gives each entry's
+  address as a constant (`ROM-UM*` and so on) for the system's source.
+- The renumbering costs nothing: until now nothing but the boot and the tests' harness used an
+  entry number, and both only to start the machine.
+
+**The system calls the ROM.** `UM*`, `UM/MOD`, `D+`, `DNEGATE`, `Q.*` and `Q./` keep their
+dictionary entries in the system. Each one's code becomes a single `jump` to its ROM entry.
+Every other word (`*`, `/MOD`, `U*`, number output, the other Q48 words) calls them by name, as
+now, and is unchanged. `Q.TO-INT` stays an ordinary system word; the ROM keeps its own copy of
+that one-line shift rather than making it an entry. `dict_hash` and `rom_hash` change, and each
+must still be the same on every ISA.
+
+**Births.** A node Hera has born carries the mesh ROM: the fabric's owner attaches it when the
+node is made (`v4_node_rom_attach`). The host's assembled system that Hera streams to it then
+runs its math in the mesh ROM. Today only the test host makes nodes (`test_host_unit.c`); the
+products have no births yet.
+
+**Tests.** Each is written to fail first.
+- Each of the six entries, on both ROMs, gives the results today's words give on the same
+  values: 0, -1, the most negative cell, the largest cell, `UM/MOD` at the edge `uhi < ud`, and
+  `Q./` by zero (error 11 and D-11's result).
+- The mesh ROM holds the six entries and the math, and nothing of the assembler.
+- Hera's unit test: a node she has born computes `UM*`, `UM/MOD` and `Q./` and prints the right
+  answers.
+- Then the whole suite at both widths, POST 538 of 538, and the three QEMU boots, as
+  `.claude/CLAUDE.md` says.
+
+**Documents.** `DATASHEET-F18.md` lists the entries with each one's stack effect and the
+registers it uses (A, B), as section 2.1 asks, and its section 13 item 3 says the mesh ROM is
+built.
+
+**Not part of this.**
+- A real 1024-word mesh node's memory map, where the ROM's base is not the host's (D-4,
+  deferred). Until then a mesh node is the host's size, and both ROMs share one base.
+- Births in the products, and the name `v4:nucleus-64.f18` that `hera.4th` opens, which only
+  the test host serves. That is the next correction.
+
 ## 3. The boot
 
 1. **The machine.** The engine is reset and runs the ROM.