diff --git a/next/kernel/registry.erl b/next/kernel/registry.erl
new file mode 100644
index 00000000..5205325e
--- /dev/null
+++ b/next/kernel/registry.erl
@@ -0,0 +1,69 @@
+-module(registry).
+-export([new/0, kinds/0, register/4, lookup/3, list/2]).
+
+%% Pure-functional registry for the seven bootstrap kinds.
+%%
+%% State is a property list keyed by kind atom; each kind's value
+%% is itself a property list of {Name, Entry} pairs. Entry is
+%% opaque — typically a proplist with :cid, :schema, :semantics,
+%% :supersedes fields, but the registry doesn't enforce that here.
+%%
+%% A gen_server wrapper (Step 5b) will own the global registry
+%% process; the pure functions in this module remain the canonical
+%% API and are usable for tests and for offline projection-replay.
+%%
+%% Return shapes:
+%%   new/0            -> State
+%%   kinds/0          -> [Atom, ...]
+%%   register/4       -> {ok, NewState} | {error, unknown_kind}
+%%   lookup/3         -> {ok, Entry} | not_found | {error, unknown_kind}
+%%   list/2           -> [{Name, Entry}, ...] | {error, unknown_kind}
+
+new() -> [].
+
+kinds() ->
+    [activity_types, object_types, projections,
+     validators, codecs, sig_suites, audience].
+
+register(Kind, Name, Entry, State) ->
+    case is_valid_kind(Kind) of
+        false -> {error, unknown_kind};
+        true ->
+            Entries = kind_entries(Kind, State),
+            Updated = put_pair(Name, Entry, Entries),
+            {ok, set_kind_entries(Kind, Updated, State)}
+    end.
+
+lookup(Kind, Name, State) ->
+    case is_valid_kind(Kind) of
+        false -> {error, unknown_kind};
+        true ->
+            find_pair(Name, kind_entries(Kind, State))
+    end.
+
+list(Kind, State) ->
+    case is_valid_kind(Kind) of
+        false -> {error, unknown_kind};
+        true  -> kind_entries(Kind, State)
+    end.
+
+%% ── Internal ────────────────────────────────────────────────────
+
+is_valid_kind(K) -> lists:member(K, kinds()).
+
+kind_entries(Kind, State) ->
+    case find_pair(Kind, State) of
+        not_found -> [];
+        {ok, V}   -> V
+    end.
+
+set_kind_entries(Kind, Entries, State) ->
+    put_pair(Kind, Entries, State).
+
+put_pair(K, V, []) -> [{K, V}];
+put_pair(K, V, [{K, _} | Rest]) -> [{K, V} | Rest];
+put_pair(K, V, [P | Rest]) -> [P | put_pair(K, V, Rest)].
+
+find_pair(_, []) -> not_found;
+find_pair(K, [{K, V} | _]) -> {ok, V};
+find_pair(K, [_ | Rest]) -> find_pair(K, Rest).
diff --git a/next/tests/registry_pure.sh b/next/tests/registry_pure.sh
new file mode 100755
index 00000000..014ffe2c
--- /dev/null
+++ b/next/tests/registry_pure.sh
@@ -0,0 +1,135 @@
+#!/usr/bin/env bash
+# next/tests/registry_pure.sh — Step 5a acceptance test.
+#
+# Exercises the pure-functional registry API: new/0, kinds/0,
+# register/4, lookup/3, list/2. State threading is verified
+# by chaining register calls and inspecting the final state.
+# 13 cases.
+
+set -uo pipefail
+cd "$(git rev-parse --show-toplevel)"
+
+SX_SERVER="${SX_SERVER:-hosts/ocaml/_build/default/bin/sx_server.exe}"
+if [ ! -x "$SX_SERVER" ]; then
+  SX_SERVER="/root/rose-ash/hosts/ocaml/_build/default/bin/sx_server.exe"
+fi
+if [ ! -x "$SX_SERVER" ]; then
+  echo "ERROR: sx_server.exe not found." >&2
+  exit 1
+fi
+
+VERBOSE="${1:-}"
+PASS=0; FAIL=0; ERRORS=""
+TMPFILE=$(mktemp); trap "rm -f $TMPFILE" EXIT
+
+cat > "$TMPFILE" <<'EPOCHS'
+(epoch 1)
+(load "lib/erlang/tokenizer.sx")
+(load "lib/erlang/parser.sx")
+(load "lib/erlang/parser-core.sx")
+(load "lib/erlang/parser-expr.sx")
+(load "lib/erlang/parser-module.sx")
+(load "lib/erlang/transpile.sx")
+(load "lib/erlang/runtime.sx")
+(load "lib/erlang/vm/dispatcher.sx")
+
+(epoch 2)
+(eval "(get (erlang-load-module (file-read \"next/kernel/registry.erl\")) :name)")
+
+;; new/0 returns []
+(epoch 10)
+(eval "(get (erlang-eval-ast \"registry:new() =:= []\") :name)")
+
+;; kinds/0 has 7 entries
+(epoch 11)
+(eval "(erlang-eval-ast \"length(registry:kinds())\")")
+
+;; kinds/0 includes activity_types
+(epoch 12)
+(eval "(get (erlang-eval-ast \"lists:member(activity_types, registry:kinds())\") :name)")
+
+;; register + lookup round-trip
+(epoch 13)
+(eval "(get (erlang-eval-ast \"{ok, S} = registry:register(activity_types, create, [{cid, c1}], registry:new()), registry:lookup(activity_types, create, S) =:= {ok, [{cid, c1}]}\") :name)")
+
+;; lookup on empty registry returns not_found
+(epoch 14)
+(eval "(get (erlang-eval-ast \"registry:lookup(activity_types, anything, registry:new()) =:= not_found\") :name)")
+
+;; lookup on unknown kind returns {error, unknown_kind}
+(epoch 15)
+(eval "(get (erlang-eval-ast \"case registry:lookup(bogus_kind, foo, registry:new()) of {error, unknown_kind} -> ok; _ -> bad end\") :name)")
+
+;; register on unknown kind returns {error, unknown_kind}
+(epoch 16)
+(eval "(get (erlang-eval-ast \"case registry:register(bogus_kind, foo, bar, registry:new()) of {error, unknown_kind} -> ok; _ -> bad end\") :name)")
+
+;; list of empty kind returns []
+(epoch 17)
+(eval "(get (erlang-eval-ast \"registry:list(activity_types, registry:new()) =:= []\") :name)")
+
+;; Three registers + list returns 3 pairs
+(epoch 18)
+(eval "(erlang-eval-ast \"{ok, S1} = registry:register(activity_types, create, e1, registry:new()), {ok, S2} = registry:register(activity_types, update, e2, S1), {ok, S3} = registry:register(activity_types, delete, e3, S2), length(registry:list(activity_types, S3))\")")
+
+;; Re-registering same name overrides previous entry
+(epoch 19)
+(eval "(get (erlang-eval-ast \"{ok, S1} = registry:register(activity_types, create, v1, registry:new()), {ok, S2} = registry:register(activity_types, create, v2, S1), registry:lookup(activity_types, create, S2) =:= {ok, v2}\") :name)")
+
+;; Re-registering same name keeps list length at 1
+(epoch 20)
+(eval "(erlang-eval-ast \"{ok, S1} = registry:register(activity_types, create, v1, registry:new()), {ok, S2} = registry:register(activity_types, create, v2, S1), length(registry:list(activity_types, S2))\")")
+
+;; Different kinds are independent
+(epoch 21)
+(eval "(erlang-eval-ast \"{ok, S1} = registry:register(activity_types, x, 1, registry:new()), {ok, S2} = registry:register(object_types, x, 2, S1), {registry:lookup(activity_types, x, S2), registry:lookup(object_types, x, S2)} =:= {{ok, 1}, {ok, 2}}\")")
+
+;; list on unknown kind returns {error, unknown_kind}
+(epoch 22)
+(eval "(get (erlang-eval-ast \"case registry:list(bogus_kind, registry:new()) of {error, unknown_kind} -> ok; _ -> bad end\") :name)")
+EPOCHS
+
+OUTPUT=$(timeout 120 "$SX_SERVER" < "$TMPFILE" 2>/dev/null)
+
+check() {
+  local epoch="$1" desc="$2" expected="$3"
+  local actual
+  actual=$(echo "$OUTPUT" | awk -v e="$epoch" '
+    $0 ~ "^\\(ok-len " e " " { getline; print; exit }
+    $0 ~ "^\\(ok " e " "     { print; exit }
+    $0 ~ "^\\(error " e " "  { print; exit }
+  ')
+  [ -z "$actual" ] && actual="<no output for epoch $epoch>"
+  if echo "$actual" | grep -qF -- "$expected"; then
+    PASS=$((PASS+1))
+    [ "$VERBOSE" = "-v" ] && echo "  ok $desc"
+  else
+    FAIL=$((FAIL+1))
+    ERRORS+="  FAIL [$desc] (epoch $epoch) expected: $expected | actual: $actual
+"
+  fi
+}
+
+check  2  "module load name"                    "registry"
+check 10  "new/0 returns []"                    "true"
+check 11  "kinds/0 length"                      "7"
+check 12  "kinds/0 includes activity_types"     "true"
+check 13  "register + lookup round-trip"        "true"
+check 14  "lookup empty -> not_found"           "true"
+check 15  "lookup bogus kind"                   "ok"
+check 16  "register bogus kind"                 "ok"
+check 17  "list empty kind -> []"               "true"
+check 18  "three registers, list returns 3"     "3"
+check 19  "re-register overrides entry"         "true"
+check 20  "re-register doesn't grow list"       "1"
+check 21  "different kinds independent"         "true"
+check 22  "list bogus kind"                     "ok"
+
+TOTAL=$((PASS+FAIL))
+if [ $FAIL -eq 0 ]; then
+  echo "ok $PASS/$TOTAL next/tests/registry_pure.sh passed"
+else
+  echo "FAIL $PASS/$TOTAL passed, $FAIL failed:"
+  echo "$ERRORS"
+fi
+[ $FAIL -eq 0 ]
diff --git a/plans/fed-sx-milestone-1.md b/plans/fed-sx-milestone-1.md
index 1d439578..2688c6c1 100644
--- a/plans/fed-sx-milestone-1.md
+++ b/plans/fed-sx-milestone-1.md
@@ -337,6 +337,12 @@ created with a known stable CID.
 
 ## Step 5 — Registry mechanism + bootstrap dispatch
 
+**Sub-deliverables:**
+- [x] **5a** — Pure-functional `next/kernel/registry.erl`: `new/0`, `kinds/0`, `register/4`, `lookup/3`, `list/2`. State is a property list keyed by kind atom; per-kind storage is a property list of `{Name, Entry}`. Unknown kinds rejected with `{error, unknown_kind}`. `next/tests/registry_pure.sh` (14 cases).
+- [ ] **5b** — gen_server wrapper around the pure registry: `start_link/0`, registered name `registry`, the pure API delegated through `gen_server:call`.
+- [ ] **5c** — `bootstrap:load_genesis/1` (Step 4e) populates the registry from `read_genesis` output. Dispatches by section atom → kind.
+- [ ] **5d** — define-registry projection fold integration: incoming `Create{Define*}` activities are routed through the projection scheduler (Step 7) and update the registry.
+
 **Deliverables:**
 
 Registries are gen_servers, one per kind, each holding the active version map:
@@ -955,6 +961,7 @@ A few things still under-specified; resolve as work begins.
 Newest first. One line per sub-deliverable commit. Erlang conformance gate
 (`bash lib/erlang/conformance.sh`) must remain 729/729 on every entry.
 
+- **2026-05-28** — Step 5a: `next/kernel/registry.erl` — pure-functional registry. State is `[{Kind, [{Name, Entry}, ...]}, ...]` keyed by the same seven section atoms as Step 4c (activity_types, object_types, projections, validators, codecs, sig_suites, audience). API: `new/0`, `kinds/0`, `register/4`, `lookup/3`, `list/2`. Unknown kinds rejected with `{error, unknown_kind}`; missing names return `not_found`; re-registering the same name overrides without growing the list. `next/tests/registry_pure.sh` 14/14. Step 5 broken into 5a–5d on the plan. Erlang conformance 729/729.
 - **2026-05-28** — Step 4d: `bootstrap:build_genesis/1` + `verify_genesis/2` + `.cidhash` helpers in `next/kernel/bootstrap.erl`. Bundle CID delegated to host `cid:to_string` over `{genesis_bundle, Sections}` — deterministic, ~59 byte CIDv1 binary. `verify_genesis/2` returns `ok` on match, `{error, {cid_mismatch, Got, Expected}}` on drift. `write_cidhash`/`read_cidhash` persist the CID to a `.cidhash` sibling file (path hand-spelled `<<...,47,46,99,...>>` per the string-literal-in-binary substrate quirk). `next/tests/bootstrap_build.sh` 12/12. Erlang conformance 729/729.
 - **2026-05-27** — Step 4c: `next/kernel/bootstrap.erl` — Erlang module that enumerates the genesis bundle by walking seven hardcoded section subdirs via `file:list_dir/1`, filters `.sx` files via byte-pattern suffix match (`ends_with_sx/1`), reads each into a binary via `file:read_file/1`. Returns `{ok, [{Section, [{Name, Bytes}, ...]}]}`. Hits the same SX-parser substrate gap as Step 3b — kept the surface byte-only; parsing happens via SX-side helpers in later steps. Port gotchas: `fun name/arity` references unsupported (use anonymous fun wrappers); `<<"...">>` string-literal segments truncate to one byte (paths hand-spelled as integer-segment binaries). `next/tests/bootstrap_read.sh` 15/15. Erlang conformance 729/729.
 - **2026-05-27** — Step 4b-cod: bootstrap codecs + sig-suites + audience predicates complete. 3 `DefineCodec` files (dag-cbor + raw + dag-json, dag-cbor + dag-json deferring to host-codec primitive when wired), 2 `DefineSigSuite` files (rsa-sha256-2018 PEM-keyed, ed25519-2020 multibase-keyed, both :verify returning false as m2-deferred stand-in), 3 `DefineAudience` files (Public/Followers/Direct member-of predicates per design §16). Manifest now lists 26 bootstrap files across all eight sections; `next/tests/genesis_parse.sh` 50/50. Step 4b complete; remaining Step 4 is bundler code (4c–4e). Erlang conformance 729/729.