“What did this product cost?” has two honest stories. Assay prints both and names which.

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Tree product

Placement on the objective tree. What the work was for. Spend follows the first episode at the winning source. See Objectives and Framing. Dashboard → Products. Each trunk is a product. Unknown sittings are their own card, not a fake root named other.

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Path product

Derived from path mentions in the harness’s own session documents. Not from project (that field is seating). 
assay products
assay attribute products    # write the overlay (sweep already does this)
Every surface that prints this story shows two cost columns:
ReadingWhat it is
InclusiveWhole spend of every sitting that mentioned the product. Upper bound. Sessions may overlap. Does not partition.
WeightedSitting spend × share of that sitting’s workspace refs. Does partition. Residuals must reconcile to priced spend.
A breakdown you cannot tie back to the total is a breakdown nobody should trust. The weighted column plus every residual population adds up.

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Residuals (named, never merged)

BucketMeans
No evidenceThe sitting was read. It referenced no workspace path.
UnscannedThere was no source document to read.
UnknownAnything else that did not land on a product.
A measured zero is not folded into unknown. Every figure names its counting unit. Default is line-distinct (one line that names a component is one reference). An older unit stays reproducible and is never mixed into the default.

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The products map

A product name is a business fact. Config groups workspace folders: 
{
  "products": {
    "workspaceRoots": ["~/code"],
    "groups": {
      "website": ["marketing-site", "docs-site"]
    }
  }
}
KeyMeaning
workspaceRootsWhere a component lives. The next path segment under a root is the component. Default ["~/code"].
groupsProduct name → the components it is made of. Unnamed components stay products of their own.
A component may belong to at most one product. Overlap would count the same refs twice and weighted would stop being a partition. Assay refuses that config at load. groups is a read-time roll-up. The overlay is stored at component grain. Edit groups and every report relabels immediately. Nothing is re-derived. Changing workspaceRoots changes the measurement. The next attribute products pass writes a new measurement. With no products block the feature still works: each component is its own product.

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Filter

The console’s ?product= scope is the inclusive reading. Panels that do not apply it say so in words.

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CLI

assay products
assay products --product website