docs: draft COGS tweet — cost of a grounded answer (Hermes ~9c, Qwen ~16c per 1k)

Main tweet + follow-up (Merkle cache hit skips GPU, doesn't increment the
per-1k). Numbers are the measured claim_lattice figures from the energy
report; note attached to hold the arbitrage/forcing-function framing until
the value side is hardened (higher N + blinded judge).

docs/posts/cogs-tweet.md

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+# COGS tweet — cost of a grounded answer (arborist)
+
+Draft social post. Numbers are the measured claim_lattice figures from
+`docs/energy-cogs-benchmark.md` (n=30, $0.33/kWh, real GPUs: Hermes-8B on
+a 3090, Qwen-27B on a 4090). Hold the bigger "arbitrage / forcing
+function" framing until the value side is hardened (higher N + blinded
+SOTA judge) — see that report's §5.5 + §9.
+
+## Main tweet
+
+What does a *grounded* answer actually cost in GPU electricity? We
+measured it on real cards:
+
+- arborist + Hermes-3-8B → **~9¢ per 1,000 answers**
+- arborist + Qwen-27B → **~16¢ per 1,000**
+
+No reasoning chains (those burn 4–6×). Read the evidence cheap, write a
+short answer locked to a claim lattice, stop.
+
+## Follow-up
+
+And if an answer's already hot, it never even joins that 1,000 — it's a
+Merkle-bound cache hit that skips the GPU entirely. Zero joules, zero
+cents. You pay GPU only for *new* questions; the cached answers are free
+forever, and provably the same answer.
+
+---
+
+**Source numbers (claim_lattice, $0.33/kWh):**
+- Hermes-3-8B + substrate: $0.085 / 1,000 grounded answers (~9¢)
+- Qwen-27B + substrate: $0.158 / 1,000 (~16¢)
+- quote mode is cheaper (Hermes $0.070, Qwen $0.121) — less context prefilled
+- thinking/reasoning mode measured 4–6× the energy for the same answer
+- cache hit (Merkle-bound providence record) returns the answer with no
+  LLM call → 0 GPU joules, does not increment the per-1k cost