diff --git a/context/adr/009-incremental-evaluation.md b/context/adr/009-incremental-evaluation.md
index 33e43cfe..44aeadcb 100644
--- a/context/adr/009-incremental-evaluation.md
+++ b/context/adr/009-incremental-evaluation.md
@@ -189,6 +189,22 @@ an **edge adapter**. So every edge has the same semantics:
   defined in `improvise-protocol`. The adapter converts to and from it, and `zset` stays
   free of serde. `CellKey` is not `Serialize`, so on the wire a cell is named by its
   tuple of ids, its position or an ADR 002 surrogate.
+- **The wire form is lossless.** Nothing is lost in transport, numeric precision above
+  all:
+  - a number never crosses as a JSON or JS double. A `numtower` `Num` crosses as its
+    canonical text (ADR 005). An f64 crosses as its exact bits, which keeps `-0.0` and
+    NaN payloads. That conflicts with today's `wire_f64` and with `numtower`'s `nan`
+    token, which both drop the payload, so the edge carries bits for every non-finite
+    value;
+  - integers wider than 2⁵³, including positions and counts, cross as strings;
+  - text crosses byte-exact, with no normalisation;
+  - the delta is the unit that crosses, never `ExactSum`'s limbs. A receiver that needs
+    a sum gets the host's exact read or rebuilds it from the exact deltas.
+
+  The stamp rule detects lost messages, but nothing would detect a lossy encoding. So
+  every element type has a round-trip property test, where encoding then decoding is
+  the identity for every value, including `-0.0`, NaN payloads, 28-digit decimals and
+  `i128`-wide fractions.
 - **Stamps compose end to end.** The host stamps each published batch (below), and an
   intermediate edge forwards the stamp unchanged. So a loss anywhere on the path shows up
   downstream as a gap.
@@ -245,8 +261,8 @@ maintained key, so it maps member keys through its own remap first. It then refe
 what moved. It refetches everything when it sees a publication gap, a new
 `document_generation` or host instance, its shape in the eviction list, or a notice it
 cannot read. A slow client may merge pending notices: the union of keys, the latest
-stamp, and axis changes kept in order. Outputs are consolidated under the wire's value
-identity, so every NaN counts as one value, because the wire spells every NaN `"nan"`.
+stamp, and axis changes kept in order. Because the wire is lossless, outputs keep the
+circuit's bit identity end to end.
 
 **What this replaces.** Today's per-session mirrors and pushed diffs (`Sessions`,
 `ClientSession`, `grid_updates`, `Projection`, `Dirty`). The host keeps no per-client