Snapshot WIP: solver HP epic progress, BPHX/HX physics, BMAD skill refresh.

Capture uncommitted solver robustness work (regularization, domain errors, linear solver lifecycle, tube DP/MSH), web workbench updates, and synced BMAD skills across IDE agent folders before starting BPHX pressure-drop.

Co-authored-by: Cursor <cursoragent@cursor.com>

.agents/skills/bmad-architecture/assets/spine-template.md

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+---
+name: '{name}'
+type: architecture-spine
+purpose: build-substrate    # build-substrate (default) · discussion · report · deck
+altitude: feature           # initiative (keeps features) · feature (keeps epics) · epic (keeps stories)
+paradigm: '{named design pattern, e.g. hexagonal, layered, pipes-and-filters, actor}'
+scope: '{what this spine governs}'
+status: draft               # draft · final
+created: '{date}'
+updated: '{date}'
+binds: []                   # capability / unit IDs governed (from the driving spec; at epic altitude, also the inherited parent AD ids)
+sources: []
+companions: []
+---
+
+# Architecture Spine — {name}
+
+<!-- TEMPLATE GUIDE — act on these comments, then delete them; never emit a comment in the finished spine. This is a shape, not a script: keep only the sections this spine needs and cut the rest (no empty headers). A small intent may be just paradigm + a few ADs + conventions; a platform earns more. An inherited epic spine is usually mostly Inherited Invariants + a thin Deferred. Decisions, not rationale (rationale lives in the memlog). Carry shape in diagrams; prose only where it must. -->
+
+## Design Paradigm
+
+<!-- Name the pattern (a known one loads a whole model for free) and map its layers to namespaces/directories. The smallest, most durable thing here. -->
+
+## Inherited Invariants
+
+<!-- Only when this spine inherits a higher-altitude parent. The parent's ADs/conventions/paradigm that bind here, by their ORIGINAL ids — read-only, never renumbered, not re-derived. A local decision that contradicts one is a conflict to surface, not an override. Cut this section otherwise. -->
+
+| Inherited | From parent | Binds here |
+| --- | --- | --- |
+| {AD-id / convention} | {parent spine} | {what it constrains in this scope} |
+
+## Invariants & Rules
+
+<!-- The durable heart: calls a future builder can't read off compliant code. One block per decision: stable ascending id (never reused/renumbered), Binds, Prevents (the divergence), Rule (enforceable). Tag [ADOPTED] when the user or existing reality settled it. Include a dependency-direction diagram (who may depend on whom) — it IS a rule; author it as valid mermaid, never an empty graph. -->
+
+### AD-1 — {decision}
+
+- **Binds:** {capability / unit ids / fr/nfr's, areas, or `all`}
+- **Prevents:** {the divergence this stops}
+- **Rule:** {the constraint downstream must follow}
+
+## Consistency Conventions
+
+<!-- Defaults that bind where independent builders would drift. Cut rows that don't apply; add rows the project needs. -->
+
+| Concern | Convention |
+| --- | --- |
+| Naming (entities, files, interfaces, events) | |
+| Data & formats (ids, dates, error shapes, envelopes) | |
+| State & cross-cutting (mutation, errors, logging, config, auth) | |
+
+## Stack
+
+<!-- SEED — verified current at authoring; the code owns this once it exists. Name + version only; the why lives in the memlog. One row per language, framework, key dependency, platform, or chain that's pinned. -->
+
+| Name | Version |
+| --- | --- |
+| {language / framework / key dep / platform / chain} | {pinned version} |
+
+## Structural Seed
+
+<!-- The shapes worth fixing at cold-start — not a fixed list. Include only what's non-obvious at this altitude, and use as many diagrams as convey it, each as VALID mermaid (never a placeholder or empty graph). Candidates: system/container/context view; DEPLOYMENT & ENVIRONMENTS and external provider/infra topology (cover the operational envelope here when this altitude owns it — don't let it fall through); core-entity ERD (names + relationships only; an attribute that's itself an invariant is an AD, not a diagram); a minimal source tree. The code owns the detail — this is scaffold, not a mirror to maintain. -->
+
+```text
+{root}/
+  {dir}/   # {what lives here}
+```
+
+## Capability → Architecture Map
+
+<!-- Present when a spec drove this run. Bridges the spec's capabilities to where they live + what governs them; the consistency auditor's checklist. Cut otherwise. -->
+
+| Capability / Area | Lives in | Governed by |
+| --- | --- | --- |
+| {CAP-id / area} | {component / module} | {AD-id, convention, paradigm} |
+
+## Deferred
+
+<!-- Decisions intentionally pushed down, each with the reason it can wait — including whole dimensions this altitude doesn't own yet. The half of the contract that keeps the spine lean. -->