feat(amicode): system card renders the recorded Hamiltonian, and stops inventing one

packages/ui/src/amicode/amicode.css

@@ -760,6 +760,31 @@
 [data-component="amicode-system-view"] .amc-c-lvl { color: var(--v2-text-text-muted); font-size: 0.8rem; }
 [data-component="amicode-system-view"] .amc-c-params { color: var(--v2-text-text-base); font-size: 0.8rem; }
 [data-component="amicode-system-view"] .amc-ev-formula { margin-top: 4px; }
+/* Provenance on a section header. A RECORDED Hamiltonian is shown bare; an
+   inferred one — the canonical form for the platform, which nobody stated —
+   has to say so, or the card is asserting physics it guessed. Sits before the
+   ::after rule so the hairline still fills the remaining width. */
+[data-component="amicode-entity-view"] .amc-ev-sec-note {
+  font-size: 9px;
+  letter-spacing: 0.04em;
+  text-transform: none;
+  color: var(--v2-text-text-faint);
+  font-style: italic;
+}
+/* The "no model recorded" placeholder reads as a prompt, not as an equation. */
+[data-component="amicode-system-view"] .amc-ev-formula.is-empty {
+  color: var(--v2-text-text-faint);
+  font-size: 0.82rem;
+  font-style: italic;
+  background: transparent;
+  border-style: dashed;
+}
+/* Conventions the recorded terms assume (frame, units, basis ordering). */
+[data-component="amicode-system-view"] .amc-ev-formula-note {
+  margin: -2px 4px 4px;
+  font-size: 0.72rem;
+  color: var(--v2-text-text-faint);
+}
 
 /* ---- Formulation hero (spec §6.2): mode badges + objective + constraints ---- */
 [data-component="amicode-formulation-view"] { display: flex; flex-direction: column; gap: 8px; }

packages/ui/src/amicode/problem.ts

@@ -513,11 +513,22 @@ export interface SystemProjection {
   topology?: string
   components: { id: string; role: string; levels?: number; params: Record<string, number> }[]
   couplings: { between: string[]; kind: string; params: Record<string, number> }[]
+  /** The model the researcher CONFIRMED, term by term (amicode_set_model's
+   *  `hamiltonian`). Present → the card renders exactly this; absent → it falls
+   *  back to a canonical form for the platform and labels it as inferred. */
+  hamiltonian?: { terms: HamiltonianTermProjection[]; notes?: string }
   notes?: string
   /** false = a legacy FLAT entity read-collapsed to N=1 (no couplings). */
   isComposite: boolean
 }
 
+export interface HamiltonianTermProjection {
+  kind: string
+  latex: string
+  acts_on?: string[]
+  label?: string
+}
+
 const asNumberRecord = (v: unknown): Record<string, number> => {
   const out: Record<string, number> = {}
   if (typeof v === "object" && v !== null) {
@@ -526,6 +537,24 @@ const asNumberRecord = (v: unknown): Record<string, number> => {
   return out
 }
 
+/** Recorded Hamiltonian, tolerant of raw JSON: a term without usable `latex` is
+ *  dropped rather than rendered as a hole, and an empty result reads as "nothing
+ *  recorded" so the card falls back to inference instead of showing `Ĥ/ℏ = `. */
+const asHamiltonian = (v: unknown): SystemProjection["hamiltonian"] => {
+  if (typeof v !== "object" || v === null) return undefined
+  const raw = v as Record<string, unknown>
+  if (!Array.isArray(raw.terms)) return undefined
+  const terms = (raw.terms as Record<string, unknown>[])
+    .filter((t) => t && typeof t.latex === "string" && t.latex.trim() !== "")
+    .map((t) => ({
+      kind: typeof t.kind === "string" ? t.kind : "drift",
+      latex: t.latex as string,
+      ...(Array.isArray(t.acts_on) ? { acts_on: (t.acts_on as unknown[]).map(String) } : {}),
+      ...(typeof t.label === "string" ? { label: t.label } : {}),
+    }))
+  return terms.length === 0 ? undefined : { terms, ...(typeof raw.notes === "string" ? { notes: raw.notes } : {}) }
+}
+
 /** Structured projection for the entity view (spec §3 point 3). Composite → read
  *  through; legacy flat → collapse to N=1 in place (role from platform: rydberg→atom
  *  else qubit — mirrors normalizeSystem without importing it). Never throws. */
@@ -550,6 +579,7 @@ export function systemProjection(input: Record<string, unknown>): SystemProjecti
         kind: str(cp.kind) ?? "?",
         params: asNumberRecord(cp.params),
       })),
+      ...(asHamiltonian(entity.hamiltonian) ? { hamiltonian: asHamiltonian(entity.hamiltonian) } : {}),
       ...(typeof entity.notes === "string" ? { notes: entity.notes } : {}),
       isComposite: true,
     }