The DQS Mathematical Model: Flat-Cost Suppressions and Deterministic Gates

The Documentation Quality Score (DQS) is an integer from 0 to 100. Given the same repository state, it always produces the same number. v0.8.0 changed two things: it closed a gate paradox where CI-blocking codes had zero DQS weight, and it replaced the allowance-based suppression model with a flat-cost model.

The Gate Paradox¶

Before v0.8.0, the scoring engine had two separate tables: CODE_SARIF_LEVELS (used by the CI gate) and a penalty table (used by the DQS calculator). These tables were maintained independently. The invariant — that a CI-blocking code must also deduct from the score — was not enforced.

Three codes broke that invariant:

Code	Name	SARIF Level
Z103	ORPHAN_LINK	`error`
Z111	VIRTUAL_ROUTE_BROKEN	`error`
Z113	AUTHOR_KEY_COLLISION	`error`

The observable consequence: a repository with 50 ORPHAN_LINK findings would fail the CI gate (exit code 1) but report a DQS of 100. The gate and the score were contradicting each other.

v0.8.0 established a single source of truth: CodeDefinition, a NamedTuple that stores severity, penalty, and category for each code in one place. CODE_SARIF_LEVELS is now derived from it. Structural registration is impossible without a penalty — the paradox cannot recur.

The three paradox codes received their penalties in the migration:

Code	Name	Penalty	Category
Z103	ORPHAN_LINK	2.0 pts	Structural
Z111	VIRTUAL_ROUTE_BROKEN	8.0 pts	Structural
Z113	AUTHOR_KEY_COLLISION	2.0 pts	Structural

From Allowance to Flat-Cost¶

The previous suppression model was allowance-based:

\[ \omega_{\text{debt}} = \max(0,\; n - \text{cap}) \]

Suppressions up to suppression_cap were free. Only excess suppressions generated debt. The cap served two roles simultaneously: it was a governance allowance boundary and a hard-fail threshold.

That dual role was the problem. A project with suppression_cap = 30 and 30 active suppressions had: score impact = 0, exit code = 0. Suppressions were invisible in the DQS.

The v0.8.0 model decouples the two roles:

\[ \omega_{\text{debt}} = n \]

Every suppression deducts 1 point. The cap is exclusively a hard-fail threshold:

When \(n \leq \text{cap}\): score is reduced by \(n\) points. Exit code is determined by the score gate.
When \(n > \text{cap}\): zenzic score exits with code 1 immediately, before score gate evaluation.

The Complete DQS Formula¶

Assembling all five stages:

\[ DQS = \begin{cases} 0 & \text{if } \sum_{c \in \mathcal{S}} n_c > 0 \quad \text{(Security Override)} \\[8pt] \max\!\left(0,\; S_{\text{gravity}} - n\right) & \text{otherwise} \end{cases} \]

where \(\mathcal{S} = \{Z201, Z202, Z203, Z204\}\), \(n\) is the total active suppression count, and:

\[ S_{\text{gravity}} = \begin{cases} \min\!\left(S_{\text{base}},\; 70\right) & \text{if } \text{cat\_pts}_{\text{brand}} = 0 \\ S_{\text{base}} & \text{otherwise} \end{cases} \]

\[ S_{\text{base}} = 100 - \sum_{i \in \text{tiers}} \min\!\left(\text{Cap}_i,\; \sum_{c \in \text{tier}_i} \text{penalty}_c \times n_c\right) \]

Or, expanding the full pipeline into a single expression:

\[ DQS = \max\!\left(0,\; S_{\text{gravity}} - \left| F_s \right| \times \text{DebtCost}\right) \]

where \(\left| F_s \right|\) is the total suppression count and \(\text{DebtCost} = 1\).

Numerical Properties¶

Maximum achievable score is now \(100 - n\), where \(n\) is the active suppression count. A project with 10 suppressions cannot exceed 90, regardless of finding counts.

Monotonicity: \(DQS\) is non-increasing in \(n\). Adding a suppression never improves the score.

Score/gate coupling: the CI gate threshold (configured via --fail-under) and the hard-fail suppression threshold (suppression_cap) are now independent. A project with a score of 80 and 29 suppressions (cap = 30) passes both. A project with a score of 95 and 31 suppressions (cap = 30) fails the cap gate regardless of the score.

Closing the Mapping Gap¶

The CodeDefinition single source of truth was established to prevent gate/score divergence. But the initial migration targeted only the three paradox codes (Z103, Z111, Z113). A subsequent audit identified four additional codes that the engine could emit (causing Exit 1) while carrying a penalty of 0.0 in the penalty table. The same paradox, at a smaller scale.

Three of the four received penalties in the migration:

Code	Name	Penalty	Category	Notes
Z401	MISSING_DIRECTORY_INDEX	2.0 pts	Navigation	Directory reachable but no index page present
Z403	MISSING_ALT	1.0 pt	Content	Image with missing `alt` attribute (`is_warning=True`)
Z404	CONFIG_ASSET_MISSING	3.0 pts	Brand	Favicon or OG image declared in config but absent on disk

The fourth — Z602 (I18N_PARITY) — remains frozen at 0.0 by architectural decision. I18N_PARITY acts as a governance gate: it enforces language parity between documentation trees and triggers Exit 1 when parity fails. Assigning it a DQS penalty would conflate two independent quality dimensions (translation completeness vs. link health / content quality) into a single number, making the score harder to interpret. A separate ADR is required to add Z602 to the DQS formula. For now, it is excluded from the penalty table, listed in FROZEN_CODES, and defined in CODE_DEFINITIONS with penalty 0.0.

Migration Impact (v0.7.x → v0.8.0)¶

Projects with active suppressions will see their DQS decrease. The magnitude is exactly the active suppression count:

\[ \Delta DQS = -n \]

For a project with 10 suppressions previously scoring 75 (under allowance model with \(n \leq \text{cap}\)), the new score is \(75 - 10 = 65\).

The suppression audit output in the CLI is unchanged. The label semantics for [MANAGED DEBT] and [EXTENDED DEBT] describe governance posture, not score exemption.