Add .env.example for live-test provider keys

.env.example

@@ -0,0 +1,42 @@
+# SPDX-FileCopyrightText: Sudo Apt Holdings LLC
+# SPDX-License-Identifier: Apache-2.0
+#
+# Copy to .env and fill in the values. .env is ignored by git (.gitignore, checked by
+# scripts/plan_check.sh rule 9); this example file is the only one that is tracked.
+#
+# Load into a shell before running live tests or the app:
+#
+#   set -a; . ./.env; set +a
+#
+# The default test run blocks the network (test/support/network_guard.ex). Anything that
+# talks to a real provider is tagged :live and runs only with `mix test --only live`.
+# Keys never go in config files, commit messages, PROOF.md or NOTES.md.
+
+# ---- LLM providers for live tests (slice 011 onward) ------------------------------------
+# One hosted provider with a free tier is enough for the live suite. Both below speak the
+# OpenAI-compatible API, which req_llm drives through its openai_compatible provider.
+
+# OpenRouter: https://openrouter.ai/keys
+OPENROUTER_API_KEY=
+OPENROUTER_BASE_URL=https://openrouter.ai/api/v1
+
+# NVIDIA NIM: https://build.nvidia.com/ (API key from the account page)
+NVIDIA_API_KEY=
+NVIDIA_BASE_URL=https://integrate.api.nvidia.com/v1
+
+# Which provider and model the live suite uses. The model id must exist on the provider's
+# current list; check it there rather than here, since free-tier ids change.
+TRINITY_LIVE_PROVIDER=openrouter
+TRINITY_LIVE_MODEL=
+
+# ---- Local inference, optional --------------------------------------------------------
+# Ollama or LM Studio through the same openai_compatible provider. Leave empty to skip.
+OLLAMA_BASE_URL=http://localhost:11434/v1
+OLLAMA_MODEL=
+
+# ---- App runtime (config/runtime.exs reads these; all have defaults) ------------------
+# PORT=4000
+# DATABASE_PATH=
+# SECRET_KEY_BASE=
+# PHX_HOST=
+# TRINITY_AUTHORITY=local