Chapter 15. The Derived Stack

Five chapters have scored seven columns between them, and every column holds a failure. One column remains, scored on the same seven rows: the stack Part III revealed. An audit that stopped here, one column short, would have exempted exactly the technology the book argues for; this chapter removes the exemption. It is the audit with the least new work in it, and that is the finding: every cell below carries a citation to a result already proved. So where the other columns needed scoring, this one needs collecting.

When Chapter 11 scored the SPA, the scores were assessments — argued in prose, each naming the property it rested on, so a dispute had an address. The cells below assert nothing new: R2’s check is the union law (5.1), proved before the stack had a name; S2’s is Theorem 8.2, proved before this part began. The part’s opening rule is that a score is rejected only by striking a row. That rule reaches its hardest case here: striking any of the column’s rows means refuting a proved result, and each cell names which one.

The three R-cells are the derivation itself, taken in the order the propositions arrived. R2 is the union law (5.1): merge is set union — total, order-free, idempotent, the only composition the coordination-free laws leave. R3 is (5.3): the first two positions of every fact lie in I, so reference is global by type rather than by discipline. R1 is Proposition 5.2 with Theorem 5.4: triples encode any domain, and any arity-minimal model satisfying all three requirements is this one up to isomorphism. Chapter 5 argued the requirements against the reader’s alternatives, not against the stack’s competitors; the stack inherits the checks because Chapter 8 proved it is the model, renamed.

The four S-cells draw on the two halves of Part III’s meeting point. From the analysis half, S1: it holds by construction of the factorization (4.3). From the synthesis half, S2 and S3: each factor denotes a term in a language with closed, cited semantics — SPARQL’s algebra, XSLT-over-canon, CSS — and terms with closed semantics substitute per factor (8.3). S4 draws on both halves: the factorization requires every stage value to be addressable (4.3), and the stack delivers it by construction — the graph, the query result, and the document each dereference (8.3). One honest asterisk carries over with the theorem: the completeness class for arrange excludes smuggling — a transform qualifies only if it is generic, invariant under URI renaming (B.8). The S2 and S3 checks are checks on that class, not on arbitrary code.

What would make the column suspect is not who scored it but what the scoring left out, and Chapter 9 already filed the omissions. Four mismatches, then: where do they land on the rows? The two that belong to the model land nearest. Blank nodes graze R2: idempotence holds up to logical equivalence rather than syntactic identity, priced exactly (Prop. 9.1). The row holds over ground facts on the nose, and the composition laws survive. The fourth position adds a requirement rather than striking one: the web demands R4 — attribution — and the column meets it as quads, merge still union (Prop. 9.2). R4 is not a row below because no column in this part was scored on it; it is Chapter 9’s addition, and the quad model carries it.

The two that belong to the platform strike no row, because no row scores maintenance. The abandoned seam and the write-side last mile are deployment failures, and deployment failure is what this part has priced in every other column’s compensating industry. The pricing is symmetric: no other column’s row was struck for deployment either, because the industries corroborated failures the rows had already scored. The stack’s own deployment bill is itemized in Chapter 9, mismatches three and four. The mismatches do not soften the column. They are why it can be trusted: Chapter 9 filed all four in the open before this audit began, and every cell below cites a result that carries its own caveats with it.

Column: Derived stack.

	Derived stack
R1	✓ — encodes any domain; the model is forced (5.2, 5.4)
R2	✓ — merge is set union: total, order-free, idempotent (5.1)
R3	✓ — reference is global by type: the first two positions lie in I (5.3)
S1	✓ — factor boundaries by construction (4.3)
S2	✓ — each factor a term with closed, cited semantics (8.3)
S3	✓ — terms substitute per factor (8.3)
S4	✓ — every stage value dereferences (4.3, 8.3)

Seven cells, none of them this chapter’s judgment: every check predates the audit that collects it. What remains is to put the columns side by side.