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-spec/assets/headless-schemas.md

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+# Headless JSON Response
+
+The default invocation is headless: input goes in, JSON comes out. The contract is intentionally tiny — return the outcome and the files touched. Anything else a caller needs is inside those files (SPEC.md, companions, `.memlog.md`).
+
+## Success
+
+```json
+{
+  "status": "complete",
+  "files": [
+    "_bmad-output/specs/spec-quarter-drop/SPEC.md",
+    "_bmad-output/specs/spec-quarter-drop/glossary.md",
+    "_bmad-output/specs/spec-quarter-drop/.memlog.md"
+  ]
+}
+```
+
+`files` lists every file written or modified in this run, in any order. The spec folder, kernel filename, memlog location, capabilities, companions, and verdict are all readable from those files; no need to re-encode them in the response.
+
+## Blocked
+
+```json
+{
+  "status": "blocked",
+  "error_code": "insufficient_intent",
+  "reason": "Input was a one-line idea with no surrounding context; too thin to distill. Suggest bmad-prd to draw the vision out first."
+}
+```
+
+Defined `error_code` values:
+
+- `insufficient_intent` — input too thin to distill into a kernel.
+- `missing_slug` — input is sparse or multi-source and no slug was provided by the caller or derivable from a source path.

.agents/skills/bmad-spec/assets/spec-template.md

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+---
+id: SPEC-{slug}
+companions: []     # files downstream MUST read alongside SPEC.md. Paths may point inside the spec folder (spec-authored) or outside it (adopted from an upstream skill).
+sources: []        # files fully absorbed into the SPEC (audit only; downstream does NOT read these). Never the memlog.
+---
+
+> **Canonical contract.** This SPEC and the files in `companions:` are the complete, preservation-validated contract for what to build, test, and validate. Source documents listed in frontmatter are for traceability only — consult them only if you need narrative rationale or prose color this contract intentionally omits.
+
+# {Spec Title}
+
+## Why
+
+{One paragraph naming the force behind this work. A spec can exist for any of:
+  - **a pain to solve** — a user or operator is stuck on a specific gap;
+  - **an opportunity to capture** — something newly possible we want to claim;
+  - **a vision to realize** — a thing we want to make exist because we want it to exist;
+  - **a mandate to meet** — a regulation, deprecation, deadline, or contractual obligation.
+
+Name which (or which combination) applies, who is affected, and the backdrop that makes it matter now. This is the anchor every downstream trade-off resolves against.}
+
+## Capabilities
+
+- **CAP-1**
+  - **intent:** {One sentence. "User or system can do X to achieve Y." WHAT, not HOW.}
+  - **success:** {Testable or demonstrable criterion. Something a test or a real demonstration can decide.}
+
+## Constraints
+
+- {A non-negotiable that bends design. If it doesn't rule anything out, it doesn't belong.}
+
+## Non-goals
+
+- {Explicit out-of-scope item. At least one. Stops downstream from filling the vacuum.}
+
+## Success signal
+
+- {One or two sentences. World-change moment, not dashboard. Concrete enough to write a test or run a demonstration against.}
+
+## Assumptions
+
+<!-- Optional. Omit this section entirely if empty. Inferred calls made without direct confirmation from the input. -->
+
+- {Statement of fact the Spec proceeded under, e.g. "Assumed mobile-first since input mentioned GPS but no platform."}
+
+## Open Questions
+
+<!-- Optional. Omit this section entirely if empty. Gaps the input did not resolve that need a human decision before downstream skills consume the Spec. -->
+
+- {Question phrased so a human can answer it, e.g. "Is offline playback in scope for CAP-2?"}