diff --git a/delphi/docs/CLJ-PARITY-FIXES-JOURNAL.md b/delphi/docs/CLJ-PARITY-FIXES-JOURNAL.md
index 8845b71e3..680d0b4ee 100644
--- a/delphi/docs/CLJ-PARITY-FIXES-JOURNAL.md
+++ b/delphi/docs/CLJ-PARITY-FIXES-JOURNAL.md
@@ -4470,3 +4470,16 @@ and bounded-distinct semantics (NaN rows, -0.0==0.0).
 - Bench FULL prod shape (33422x783x2.0M, scratch/vectorized_full.json):
   cold 28.15s, warm 26.66s — vs the ~31 min warm tick measured s6/s7
   (~70x). The largest prod conversation now ticks in under 30s.
+
+### Rename (Julien ruling, s7): the python poller is engine, not delphi
+
+Compose service delphi-math-poller → **math-python**, profile delphi-math
+→ **math-python**, env var DELPHI_MATH_ENV → **MATH_PYTHON_ENV** (default
+math_env value 'delphi' → 'python'; free rename — no rows exist yet
+anywhere). Living docs updated (runbook step 1, design §4, example.env);
+journal history left as written. Deploy reality recorded in the runbook:
+prod starts services BY NAME via scripts/after_install.sh role dispatch
+(SERVICE_FROM_FILE: server|math|delphi; profiles gate dev only), prod
+tracks branch `stable` — so the shadow wiring is one edit to the math
+role's compose-up line, deliberately NOT made yet (Julien weighing
+shadow vs clean replace).
diff --git a/delphi/docs/CUTOVER_RUNBOOK.md b/delphi/docs/CUTOVER_RUNBOOK.md
index 0ab51a878..7aa209435 100644
--- a/delphi/docs/CUTOVER_RUNBOOK.md
+++ b/delphi/docs/CUTOVER_RUNBOOK.md
@@ -82,17 +82,22 @@ equivalence evidence), CLOJURE_QUIRKS.md (Q1-Q19).
 
 ## Step 1 — shadow in prod (same day)
 
-Infrastructure already in compose (#2625): service `delphi-math-poller`,
-profile `delphi-math`, `MATH_ENV=${DELPHI_MATH_ENV:-delphi}` — distinct
+Infrastructure already in compose (#2625; renamed s7 per Julien — the
+math poller is engine, not delphi/UMAP): service `math-python`,
+profile `math-python`, `MATH_ENV=${MATH_PYTHON_ENV:-python}` — distinct
 from Clojure's env, rows invisible to the server (UNIQUE(zid, math_env)).
 
 ```
-docker compose --profile delphi-math up -d delphi-math-poller
-# env: DELPHI_MATH_ENV=delphi   (engine has one path since the mode collapse)
+docker compose --profile math-python up -d math-python
+# env: MATH_PYTHON_ENV=python   (engine has one path since the mode collapse)
+# PROD NOTE (deploy-script reality, s7): prod instances start services BY
+# NAME from scripts/after_install.sh per-role dispatch (profiles are a
+# dev-only gate) — shadow on the math role = add `math-python` to its
+# `docker-compose up -d math` line; prod tracks branch `stable`.
 ```
 
 Verify within minutes:
-- math_main rows appearing under math_env='delphi' with advancing
+- math_main rows appearing under math_env='python' with advancing
   caching_tick;
 - no errorconv dumps / parked zids in the poller log;
 - spot-compare a few active zids' blobs vs the clojure rows (the certify
diff --git a/delphi/docs/MATH_POLLER_DESIGN.md b/delphi/docs/MATH_POLLER_DESIGN.md
index d94a459fe..ca055e8bb 100644
--- a/delphi/docs/MATH_POLLER_DESIGN.md
+++ b/delphi/docs/MATH_POLLER_DESIGN.md
@@ -79,8 +79,9 @@ math_env string written), `VOTE_POLLING_INTERVAL` (ms, default 1000),
 
 ## 4. Cutover phases
 
-1. **Shadow (this PR):** new compose service `delphi-math-poller` (profile-gated,
-   `--profile delphi-math`) running next to the Clojure `math` service, writing under a
+1. **Shadow (this PR):** new compose service `math-python` (profile-gated,
+   `--profile math-python`; renamed s7 from delphi-math-poller) running
+   next to the Clojure `math` service, writing under a
    DIFFERENT `math_env` (e.g. `MATH_ENV=delphi` while Clojure writes `prod`/`dev`).
    `UNIQUE(zid, math_env)` makes the rows invisible to the prod server. No consumer
    change, zero production risk.
diff --git a/docker-compose.yml b/docker-compose.yml
index 2acca4cc9..a4dbfa8a9 100644
--- a/docker-compose.yml
+++ b/docker-compose.yml
@@ -147,12 +147,12 @@ services:
 
   # Python math poller — the eventual replacement for the Clojure `math`
   # container.  Profile-gated so it only runs when explicitly requested
-  # (`--profile delphi-math`).  Reuses the delphi build target and overrides the
+  # (`--profile math-python`).  Reuses the delphi build target and overrides the
   # command to run the poller CLI.  Defaults to SHADOW mode: writes under a
   # DISTINCT math_env (`delphi`) so its rows are invisible to the prod server
   # (UNIQUE(zid, math_env)) — zero production risk while parity is validated.
   # See delphi/docs/MATH_POLLER_DESIGN.md §4.
-  delphi-math-poller:
+  math-python:
     image: 050917022930.dkr.ecr.us-east-1.amazonaws.com/polis/delphi:latest
     build:
       context: ./delphi
@@ -166,7 +166,7 @@ services:
       - POSTGRES_CONNECT_TIMEOUT=${POSTGRES_CONNECT_TIMEOUT:-30}
       - LOG_LEVEL=${DELPHI_LOG_LEVEL:-INFO}
       # Shadow-mode math_env (distinct from the Clojure math service's MATH_ENV).
-      - MATH_ENV=${DELPHI_MATH_ENV:-delphi}
+      - MATH_ENV=${MATH_PYTHON_ENV:-python}
       # Poll cadences (ms) and boot window (days).
       - POLL_VOTE_INTERVAL_MS=${POLL_VOTE_INTERVAL_MS:-1000}
       - POLL_MOD_INTERVAL_MS=${POLL_MOD_INTERVAL_MS:-1000}
@@ -193,7 +193,7 @@ services:
           memory: ${DELPHI_POLLER_CONTAINER_MEMORY:-16g}
     restart: unless-stopped
     profiles:
-      - delphi-math
+      - math-python
 
   postgres:
     restart: always
diff --git a/example.env b/example.env
index 59c7e9209..548ac0a21 100644
--- a/example.env
+++ b/example.env
@@ -53,15 +53,15 @@ LOCAL_SERVICES_DOCKER=true
 # Leave empty for autodetection on AWS deployment. See delphi/DELPHI_AUTOSCALING_SETUP.md for configuring instance size in production.
 INSTANCE_SIZE=dev
 
-###### PYTHON MATH POLLER (delphi-math-poller, --profile delphi-math) ######
+###### PYTHON MATH POLLER (math-python, --profile math-python) ######
 # The Python replacement for the Clojure `math` container. Runs in SHADOW mode by
 # default: writes math_main/math_bidtopid/math_ptptstats under a DISTINCT math_env
 # so its rows stay invisible to the prod server (UNIQUE(zid, math_env)) while
 # parity is validated. See delphi/docs/MATH_POLLER_DESIGN.md.
 #
 # math_env the poller writes under. Keep distinct from the Clojure MATH_ENV while
-# shadowing; set equal to the server's MATH_ENV to cut over. Default: delphi
-# DELPHI_MATH_ENV=delphi
+# shadowing; set equal to the server's MATH_ENV to cut over. Default: python
+# MATH_PYTHON_ENV=python
 # Watermark boot window: start polling from N days ago. Default 10
 # POLL_FROM_DAYS_AGO=10
 # Poll cadences in ms. Defaults 1000/1000