Display histogram bin label

The dollar label printed under each ending-balance histogram bar.

Field: Histogram bin center label Unit: US dollars Basis: nominal dollars Computed by: UI transformation Status: Complete chain

Appears in: monte-carlo-page (Ending balances histogram x-axis labels (histRows))

Calculation records

• Histogram bin centres Formula record, justified by derivation

  Purpose: The dollar amount each bar of the ending balance histogram is labelled with.

  Statement: montecarlo/run.ts#histogramFor publishes, on every histogram aggregateMonteCarlo builds, binCenters[i] = min + (i + 0.5) × binWidth in that association, or min for every bin when every value is equal, where binWidth is only a placeholder of 1 and the one value the sample holds is the only amount it can show. A histogram with min $100,000 and binWidth $50,000 has centres $125,000, $175,000 and so on to $1,575,000; endings [0, 20, 40, 80, 100] in 4 bins have centres 12.5, 37.5, 62.5 and 87.5; four paths all ending at $0 have every centre $0, where the page used to label the bars $1 to $30. Units: the histogram's dollars (nominal ending values). Rounding: none; the page formats compactly.

  Formula: c_i = min + (i + 0.5) · binWidth when max > min, else c_i = min

  • min, max: Smallest and largest value of the sample (unit: usd) (domain: finite; 0 and 0 for an empty sample)
  • binWidth: (max − min) / bins, or 1 when every value is equal (unit: usd) (domain: > 0)
  • i: Bin index (unit: 1) (domain: 0 to bins − 1)

  Timing: once per aggregation

  Rounding: none

  Limits:

  • The last bin is closed (it holds the maximum), so its centre is the midpoint of a closed interval.
  • With every value equal the other bins are empty and their centres carry no information; at the page's defaults this happens on 3 of the 29 example plans as the library opens them on the default seed (every path runs out; 5 on the plan-id seed it replaced).

  Provenance: derived by claude, implemented by claude-subagent.

  Independent review: codex

  Gates (6 of 6 pass): fixture registers a test: pass; pins resolve: pass; families exist: pass; worksheet exists: pass; mutation receipt exists: pass; provenance independent: pass

  Worksheet: display-histogram-bin-label.md Mutation receipt: display-histogram-bin-label.mutation.md

  Evidence tests: run.binCenters.evidence.test.ts

  Implemented in: run.ts

  Is the number of: display-histogram-bin-label

Transformations

• The engine's histogram publishes binCenters (min + (i + 0.5) × binWidth, or min when every value is equal); the page formats each compactly (format.ts#histogramBars), and when every centre is one value it draws one bar at that value holding every path.