Merge branch 'next' into issue-7-webhook-delivery

Brings in the exact results past the range of a double. docs/TODO.md
conflicted: both Completed Steps lines are kept, the newer one first.

Model: opus-5-5

README.md

@@ -478,16 +478,23 @@ container.
   refused, exact powers are capped, and every number is held as a
   fraction, whole numbers too, under the 4096-bit limit below, so a
   message cannot make the bot do unbounded work. Whole numbers below
-  10<sup>21</sup> are written exactly; other results in the shortest
-  form that reads back as the same double, in exponent notation from
-  10<sup>21</sup> up and below 10<sup>-6</sup>. Refused as too large or
-  too small: any number whose numerator or denominator reaches 4096
-  bits, wherever it appears, as `go/constant` rounds a fraction that
-  grows that large (`1e-1300 + 1`); a power computed as a double whose
-  base or result is outside the normal range of a double, about 2.2e-308
-  to 1.8e308 in magnitude, where a double keeps all its digits
-  (`1e-400^0.5`); and a result other than zero outside that range, as it
-  is written through a double (`1e400`, `2^-1400`).
+  10<sup>21</sup> are written exactly. Other results inside the normal
+  range of a double, about 2.2e-308 to 1.8e308 in magnitude, where a
+  double keeps all its digits, are written in the shortest form that
+  reads back as the same double, in exponent notation from
+  10<sup>21</sup> up and below 10<sup>-6</sup>. Results outside that
+  range are written from their exact value in exponent notation, rounded
+  to 17 significant digits, the most the shortest form of a double
+  takes, with trailing zeros dropped: `2^1200` is
+  `1.7218479456385751e+361`, `10^400` is `1e+400` and `2^-1074` is
+  `4.9406564584124654e-324`. Refused as too large or too small: any
+  number whose numerator or denominator reaches 4096 bits, wherever it
+  appears, as `go/constant` rounds a fraction that grows that large
+  (`2^4095`, `1e-1300 + 1`); and a power computed as a double whose
+  result is outside the normal range of a double (`2^1500.5`). The base
+  of such a power may be outside that range: square roots taken from its
+  exact value bring it inside first, so `(2^1200)^0.5` is
+  `4.149515568880993e+180` and `1e-400^0.5` is `1e-200`.
 - **Failure is an exit.** If the chat client exits or the connection to
   it drops, the bot exits with an error and the container's restart
   policy starts both again. `SIGTERM` stops the bot, which stops the