feat(course): course three -- GoldenFloat, 27 modules (20 done, 7 pending)

[gHashTag]

Closes #1469

Course three, GoldenFloat (arXiv:2606.05017), route #/goldenfloat, share path learn/goldenfloat/. Built by a bee that read only trinity's AGENTS.md "New course to open a topic" and specs/course_recipe/{course-27,roadmap}.t27 from PR #1465, as a test of whether that recipe is self-sufficient. Answer: not yet -- see Recipe gaps.

What is in it

• specs/course/goldenfloat.t27 + goldenfloat-ru.t27 + i18n/goldenfloat.ru.json; registered fourth in specs/course/courses.t27.
• 27 of 27 lessons done, in 9 modules of 3 lessons (owner's decision 2026-10-07): a unique tool widget each (specs/widgets/golden-*.t27, public/widgets/golden-*/, card 1200x630) and a lesson spec that compiles clean in the site's wasm compiler.
• The 7 lessons that were pending (2, 4, 5, 9, 11, 15, 16 -- phi ratio, split optimality, radix economy, GF8, GF12, GF24, GF32) now open their own spec (phi_ratio, phi_split_optimality, radix_economy, gf8, gf12, gf24, gf32). The vendored copies under public/t27/files/specs/ carry the smallest compile fix, proposed upstream as spec(numeric,math): the GoldenFloat lesson specs compile clean and say only true things t27#7496. Every table number is a constant, a test value or arithmetic of that spec; where a comment and the code disagree (gf8 max_value comment 15.5 vs computed 31; gf12 test named ..._lowest asserts only < 0.05 while GF14 sits at 0.007; gf32 comment "second after GF12") the lesson says which is which. Their public/term/golden-*/ placeholders are deleted and the gallery entries are tools.
• courses.t27 set to MODULES_PER_COURSE 9, LESSONS_PER_MODULE 3 -- the same values as the courses 0-2 work on fix/course-nine-modules, so that merge is trivial.
• 27 widgets inserted at index 90 of gallery.t27 (end of the compiler run, before game); shifted index tests (wars 117, race-the-bee 121, gatle 122).
• TS (hence owner-approved-foreign): routes in main.tsx, COURSE_ROOTS in GlobalStarfield.tsx, a Navigation.tsx entry, blog post course-three-goldenfloat (EN body + RU ruBody) registered in posts.ts/index.ts, regenerated course.generated.ts/queenWidgets.generated.ts. course-from-spec.test.mjs mutation target moved 3->4 courses.
• No tri casts run on the Mac; no paid services.

Recipe gaps

1. AGENTS.md lists fields to rename when copying a course spec, but omits RU_CONTRACT and GENERATED.
2. No card.png generator for widgets; I rendered via headless BrowserOS, which never exits (needs timeout + SIGKILL + PNG check).
3. No recipe/generator for pending placeholders (term page, meta.json pending, session.cast, card), yet the gates require a real gallery entry per lesson.
4. A pending lesson still needs a clean LESSON_SPEC; many roadmap specs are dirty, so "pending" has no honest spec to point at.
5. Silent on whether two lessons may share a lesson spec, or a spec already used by another course (gf4 is in ai-numbers too).
6. Gallery tests hard-code WIDGET_COUNT and specific indices; tri widget gallery-add is only mentioned in a gallery comment.
7. Gate list omits test:widgets-spec, check:widget-pages, tsc, and running onboarding-from-spec.
8. Format count must come from t27 tools/gen_formats_catalog.py, outside trinity.
9. No harness to test the recipe itself (a dry-run course).
10. Branch suffix -3 is ambiguous (course index vs attempt).
11. No recipe for an infographic widget spec; inferred from basics-*.
12. Work-report JSON format lives only in PR feat(course): course 0 -- t27 basics in 27 modules with infographics #1463.
13. TS edits (main.tsx routes, GlobalStarfield COURSE_ROOTS, Navigation PAGES) are not in the recipe.
14. No generator for pending cast pages.
15. roadmap.t27's 9 topic parts did not map onto 27 single-lesson modules (now 9 modules of 3).
16. The family spec has GF20 but the roadmap has no part for it.
17. WIDGET_CATEGORIES must be one contiguous run per category in CATEGORY_IDS order, so a new compiler course must be inserted mid-gallery, shifting hard-coded index tests -- appending fails.
18. Card rendering tool missing (see 2) -- the hang costs minutes per batch.
19. Blog registration (posts.ts import + map, index.ts entry + RU block) is not in the recipe.
20. course-from-spec.test.mjs hard-codes the current course count in a mutation test (COURSE_COUNT = 3); adding a course breaks test:course until it is bumped.
21. The RU bundle checker demands the same digit multiset as English and bans superlatives ("first", "only") -- correct, but undocumented; spelled-out numbers ("sixteen-bit") fail it.
22. The widget card generator lives only on feat/widget-cards-from-spec (5bdcf8e); cards here were drawn with a temporary copy of it, not committed.

{
  "version": 1,
  "head_sha": "cc806047ccbed37d7eb6ccb3c18908dbc233a9fb",
  "summary": "Course 3, GoldenFloat: 27 of 27 lessons real in 9 modules of 3 on the phi-split float family, each with a unique widget and a lesson spec that compiles clean; built from the PR #1465 recipe, 22 recipe gaps found.",
  "changes": [
    "apps/website/specs/course/goldenfloat.t27, goldenfloat-ru.t27, i18n/goldenfloat.ru.json: the course in 9 modules of 3, its Russian contract and bundle",
    "apps/website/specs/course/courses.t27: four courses, goldenfloat fourth; MODULES_PER_COURSE 9, LESSONS_PER_MODULE 3",
    "apps/website/specs/widgets/golden-*.t27 and public/widgets/golden-*/: 27 tool widgets with cards; the 7 public/term/golden-* placeholders deleted",
    "apps/website/public/t27/files/specs/{numeric,math}: 8 vendored lesson specs with the smallest compile fix, same as gHashTag/t27#7496",
    "apps/website/specs/widgets/gallery.t27: 27 widgets inserted at index 90 inside the compiler run; count 123; shifted index tests",
    "apps/website/src: routes, starfield root, nav entry, blog post course-three-goldenfloat (EN + RU, 9 modules of 3, no pending lessons), generated catalogs",
    "apps/website/scripts/course-from-spec.test.mjs: catalog mutation target follows the course count (4 -> 5)"
  ],
  "tests": [
    {
      "command": "npm run check:widgets, test:widgets-spec, check:widget-pages, check:onboarding, check:play",
      "result": "123 widgets, spec tests 10 asserts 37 hold; 81 tool pages, spec tests 282 asserts 970 hold; widgets-spec 5 of 5; onboarding spec tests 10 asserts 55 hold",
      "status": "passed",
      "evidence": "local runs, rc 0 each, on f94130df"
    },
    {
      "command": "npx tsc --noEmit -p apps/website; node --test scripts/blog-cover-*.test.mjs",
      "result": "tsc rc 0; blog tests 12 of 12",
      "status": "passed",
      "evidence": "local runs on f94130df"
    },
    {
      "command": "npm run check:course, test:course, check:course-pages",
      "result": "rc 0 after merging fix/course-nine-modules (trinity#1472) and rerunning every generator; check:widgets, test:widgets-spec, check:widget-pages, check:onboarding, check:play, check:subpath-urls and tsc also rc 0",
      "status": "passed",
      "evidence": "local run on cc806047"
    },
    {
      "command": "mutant: specs/widgets/golden-gf8.t27 K_TABLE_ROWS 5 -> 6; specs/course/goldenfloat.t27 LESSON_WIDGETS[1] == golden-phi-ratiox",
      "result": "widget: check:widget-pages rc 1, the_cells_fill_whole_rows assert #1 false; course: 7 problems incl. every_lesson_opens_its_own_spec assert #20 false; after git checkout -- both back (rc 0; 6 catalog problems)",
      "status": "passed",
      "evidence": "local runs after commit f94130df"
    },
    {
      "command": "lefthook pre-commit and commit-msg",
      "result": "language contracts pass, subject is English ASCII",
      "status": "passed",
      "evidence": "hook output on f94130df"
    }
  ],
  "limitations": [
    "Stacked on trinity#1472 (courses 0-2 to 9 x 3); lands after it",
    "The 7 lesson specs are fixed in vendored copies; upstream gHashTag/t27#7496 is open, not merged",
    "public/t27/manifest.json stats were not regenerated for the vendored specs",
    "The browser compiler runs only constant asserts of a spec, not its function tests; function results in the lessons come from the specs' own test values",
    "Pages were not opened in a browser; cards were checked as images",
    "No tri casts were recorded",
    "Stacked on feat/course-t27-basics-0; merge after it"
  ],
  "tags": [
    "t27",
    "course",
    "goldenfloat"
  ],
  "blog": {
    "title": "Course 3: GoldenFloat in 9 modules of 3 lessons",
    "summary": "A course on the phi-split float family from arXiv:2606.05017: 27 lessons in 9 modules of 3, each with a widget and a lesson spec that compiles clean.",
    "outline": [
      "GoldenFloat gives every width the same rule: the exponent takes round((N - 1) / phi^2) of the bits after the sign, so E / M stays near 1 / phi.",
      "The course walks the family from GF4 to GF1024 and the ternary GF-T formats in 9 modules of 3 lessons, each lesson with one widget and one spec.",
      "Seven lesson specs did not compile clean in the browser compiler; each got the smallest fix, proposed upstream as t27 PR 7496, before its lesson went live.",
      "Where a spec's comment and its code disagree, as with the largest GF8 value, the lesson says which is which instead of quoting the comment.",
      "The course was built by an agent that read only the recipe, and the post lists the twenty-two places where the recipe left it guessing."
    ]
  }
}

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