paper-claims widget and blog post: 45 numbers from three format papers, recomputed exactly #1689

gHashTag/t27#10392 added specs/numeric/paper_claims.t27, which recomputes 45 numbers printed in the GoldenFloat (arXiv:2606.05017), Golden Ruler (arXiv:2606.09686) and TNF papers in exact integers: 34 fit, 8 do not, 3 cannot be checked. tri papers (gHashTag/t27#10401) and the MCP tool t27_paper_claims (gHashTag/t27-mcp#23) run it. The site does not show the result yet.

Boundary

• apps/website/specs/widgets/paper-claims.t27 (new widget spec) and apps/website/public/widgets/paper-claims/ (tool.js import, card.png, generated page)
• apps/website/specs/widgets/gallery.t27, apps/website/specs/course/goldenfloat.t27 and the generated gallery/course outputs
• apps/website/src/data/blog/ (one new post: body, index entry, posts map entry)

Out of scope: correcting the papers, the t27 spec itself, any change to infographic.js.

Scenarios

• A reader opens t27.ai/widgets/paper-claims/ and sees all 45 rows: paper, location, claim, printed value, recomputed value, verdict.
• A reader of lesson 1 of the GoldenFloat course is offered the widget.
• A reader opens the blog post and sees the per-paper totals table, the table of the 8 misfits and two figures, in English and in Russian.

Requirements

• Every row and count in the widget is copied from one t27_paper_claims answer; the spec names that source in DATA_SOURCES.
• The widget spec's tests check that the cells fill whole rows and that the per-paper counts add up to 34 / 8 / 3.
• tool.js holds no words: it imports ../infographic.js, which draws the spec's SAY_TABLE_* and SAY_FLOW_*.
• The blog post has an EN body and an RU ruBody; its figures are static SVG strings.

Criteria

• node scripts/widget-pages-from-spec.mjs --check, widgets-from-spec.mjs --check, course-from-spec.mjs --check and widget-logic.mjs --check pass.
• node scripts/blog-bodies-check.mjs passes.
• CI on the PR is green.