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docs: rename the working name "hotpath" to peltier.io in README and the book

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The project ships as peltier.io; "hotpath" was the placeholder working name
(CLAUDE.md: "Rename freely; nothing depends on it"). Replaces the product
name in the README front page and every mdBook source chapter — book title,
nav header, and prose ("Peltier profiles…", "Peltier sells…") — plus the
theme CSS comment.

The metaphor is unchanged (a Peltier device is a thermoelectric cooler:
"spot cooling for hot paths"), and the literal noun phrase "hot paths"
stays. Two code identifiers are intentionally left as-is because they are
not prose: the `agent/hotpath_agent/` Python module path and the
`HOTPATH_ISOLATION` env var — renaming those is a code change, not a docs
one.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EcKPWQ3MQD4NdEHwar96u2
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# hotpath
# peltier.io
> Spot cooling for hot paths. A profile-guided optimization agent that
> only ships wins it can prove.
hotpath profiles real binaries and services, isolates hot paths, proposes
Peltier profiles real binaries and services, isolates hot paths, proposes
optimizations, and accepts a change **only** when two independent bars are
cleared: **behavioral equivalence** (upstream tests + byte-identical golden
replay + differential fuzzing + sanitizers) and **statistical significance**
(the speedup's bootstrap 95% CI lower bound clears a threshold on
calibrated hardware). A change without both is discarded and logged.
Consultants sell surveys; compilers sell flags. hotpath sells **verified
Consultants sell surveys; compilers sell flags. Peltier sells **verified
deltas with the methodology attached** — a stopwatch on pinned hardware, a
proof of equivalence, and an ROI figure whose confidence interval survives
hostile review.
📖 **Full documentation: the [hotpath book](https://bdbrown4.github.io/peltier.io/)**
📖 **Full documentation: the [peltier.io book](https://bdbrown4.github.io/peltier.io/)**
· Design spec: [SPEC.md](SPEC.md) · Charter: [CLAUDE.md](CLAUDE.md)
## Verified results