# Control Kernel v1.1 — what "sound" means for a Fool false-positive control

**Supersedes v1.0** (frozen 2026-08-02, sha256 `67c9b870491db744…`, retained at `CONTROL-KERNEL-v1.md` as the record of what the reductions were run under). **Any run graded under this kernel is a new experiment, not a continuation** — no run was ever graded under v1.0, so nothing is invalidated by the change.

**Changes from v1.0**
1. **`A` is demoted from a tag to a diagnostic. A control document must be `A`-free** (§2). Steward-authorised 2026-08-02.
2. **The genre boundary is stated** (§0, §5) — measured, not supposed.
3. **§3.3 is named a screen, not a decision, and §2a compliance is moved into §4's judgement residue** — it false-passed a real package.
4. **§6.3's cue test is re-aimed.** `A`-free removes the confessional-register risk it was written for and replaces it with a different one.

**Held, not applied, with the dependency named:** `PARAPHRASE` and the treatment of table rows under §2c. Both bite only in the **reduction** arm, and under §2 the control document is now a *constructed* derivation — so both are **avoidable by construction** and neither blocks the critical path. They return if reduction is ever used to produce a control.

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## 0. What this kernel is for, and where it does not apply

The Fool's false-positive rate is unmeasured. Measuring it needs a document on which *"nothing found"* is the **correct** answer to `prompts/trial-03-assumptions.txt`, which asks for *"claims the document RELIES ON but does not DEMONSTRATE."*

Soundness is defined **relative to that prompt and to the declared axiom set of §1.** Not in general.

**Genre boundary, measured.** This kernel models **argumentative** prose. Applied to **authoritative** prose — a ruling, which *determines* and *testifies* rather than argues — it does not measure soundness; it measures genre mismatch. Reduction 01 put a real jurist ruling at **8.5%** sound with `D=0` and `Q=0`, where 42% of the quarantine was performatives and testimony, categories this kernel has no tag for. Reduction 02 put a package at **68.6%** with `D=40`, `Q=9`. **Do not apply this kernel outside argumentative prose and read the result as a verdict.**

## 1. The axiom set — where the regress terminates

Undemonstrated claims are acceptable without limit if traced to a listed source. Hashed at freeze:

- `~/CLAUDE.md` — `dac3f1a342c6695217565eff0022de4dfbc176b50d6762ccf656f9c038a60dc6`
- `~/REVIEWED.md` — `304852a87c7deff000f23ce0a95017ed558fecf8165a07f0958ecf2043a207ea`
- Any document explicitly named in the control document's own header

**A source whose hash has changed is no longer the source this kernel froze against.** Re-hash before each use.

*Unchanged from v1.0, and validated: the header clause widened the axiom set correctly on a real package, driving `UNSOURCED-QUOTE` to zero.*

## 2. Assertion typing — every sentence, no exceptions

| Tag | Meaning |
|---|---|
| `D` | **Demonstrated here.** The supporting argument is present in this document, in full, **and rests exclusively on §1 axioms or on `D`/`Q` sentences established earlier.** A claim resting on any assumption is not `D`, however valid the local step. |
| `Q` | **Quoted.** Verbatim from a §1 source, used within the scope that source establishes. Not a sentence *about* a quotation — that is `D` if it rests on a §1 axiom. |
| `N` | **Non-load-bearing.** Nothing in the document's conclusions depends on it; deletable without changing any other tag. |
| `X` | **Non-assertive.** Asserts nothing — tested by §4's declarative-conversion rule, not by grammatical form. |

**A control document is kernel-sound iff every sentence is `D`, `Q`, `N` or `X`, and every `Q` resolves.**

### 2a. `A` is a diagnostic, not a tag — the control document is a derivation

`A` — *an assumption named at its point of use* — remains the vocabulary for describing prose. **It may not appear in a control document.**

**Why, and it is the reason this version exists.** Both reductions returned `A = 0` across 152 assertive units: our prose does not name assumptions inline, it collects them into a section. That measurement points the other way from how it first reads. A document with **no assumptions at all** does not hedge — and the prompt's anti-echo clause, *"an assumption the author has already named is not a finding,"* goes **inert**, because there is nothing named to exclude. *"Nothing found"* then cannot be reached by recognising a confessional register; it requires checking that every claim is demonstrated or quoted.

**So the control document is a derivation, not an argument.** Assume nothing beyond §1; derive or quote the rest. This is the proof-assistant condition, and it is the strongest form the control can take.

**Operationally: needing an `A` is a failure signal, not a licence.** Revise the document so the claim is derived, or widen §1 and say so. Never name the assumption and proceed.

**§2a's old rule — no collected limitations section — is retained** and now follows automatically: a document with no assumptions has none to collect. It is retained because it states *why*, and because the screen at §3.3 still enforces its visible form. Earned rather than reasoned: in trial 03 the model located Part VII, classified it as author-named limitation, and skipped its contents wholesale.

### 2b. Tags never reach the reader

Tags are build-and-audit artifacts. The **presented** document is the tagged document with all markup removed and must be byte-identical to it under stripping. Without this the control is passable by tag-matching, with no reading — which would measure obedience and report it as restraint.

### 2c. One primitive per sentence

A sentence carrying more than one primitive must be split until each unit carries one. In a constructed derivation this is free. **Precedence — tagging a blend wholly `A` — was considered and rejected in v1.0**, and `A` no longer exists to tag it with.

**Grading consequence, since §3 cannot decide clause boundaries.** If the Fool flags a claim and its sentence proves to be a blend, that is a **construction defect voiding the document**, never a false positive. A missed blend indicts the author.

## 3. Mechanical checks — decided by a program

1. Every assertive unit carries exactly one tag, and **no unit is tagged `A`**. Units are those produced by the **declared splitter, named and versioned in the run record**.
2. Every `Q` appears verbatim in a §1 source; each source is hashed. *"Verbatim" is operationalised as identical after removing markdown emphasis and collapsing whitespace — weaker than byte-identity, declared as such, and intolerant of a changed, added or dropped word.*
3. **A screen, not a decision:** no heading matches the collected-caveat wordlist. **A pass here is not a §2a verdict** — a section titled only *"Part VII"* defeats any wordlist, and the shipped pattern false-passed a real package whose Part VII is exactly such a section. §2a compliance lives in §4.
4. `presented == strip_tags(tagged)`, byte-identical.
5. Every §1 source path resolves and its hash is recorded.

**Every check ships with a positive control derived from the PROPERTY, not from the check**, and must **discriminate between two real artifacts** — one known to have the property, one known to lack it. Identical verdicts on both means the check has demonstrated nothing, however many synthetic fixtures it passes.

## 4. The trusted base — what no program decides

- Whether a `D` **actually demonstrates**, and rests only on §1 axioms or earlier `D`/`Q`.
- Whether an `N` is **genuinely** non-load-bearing.
- Whether an `X` **genuinely asserts nothing** — *`X` iff converting it to a declarative statement yields no load-bearing claim.* Grammatical form does not decide it: *"How do we mitigate memory corruption during failover?"* presupposes that corruption can occur. Headings included — *"Why the current approach fails"* asserts that it fails.
- Whether a `Q` sits **within the scope its source establishes**. Verbatim-ness is mechanical; scope is not.
- Whether a sentence carries **one primitive** (§2c).
- **Whether the document collects the author's caveats anywhere (§2a).** Moved here from §3 because no pattern can decide it.

Tag *completeness* is mechanical (§3.1). Tag *honesty* is not, and cannot be made so. **All six residues run the same direction: each is a way for the author to make a document look sound.** The list has grown twice under review and measurement; its direction has not, and that is the property under watch. A residue running the other way would be a finding.

**Mitigation, and its limit:** an independent reader re-classifies sampled sentences. Sampling is weaker than census and is not represented as equivalent.

## 5. What this kernel does NOT establish

- **Not that the document is true, good, or well argued.** Only that it contains no undemonstrated load-bearing claim.
- **Not that "nothing found" is the only defensible response.** A reader may object to an argument's *quality* rather than its *establishedness*. Scoped to the assumptions prompt.
- **Not soundness against reality.** Relative to §1 only.
- **Not a rate that transfers to ordinary governance prose.** An `A`-free derivation is unlike what we actually write — measurably so: real documents run 8.5% and 68.6% sound. The measurement validly answers *"does the model invent findings when there are none?"* It does **not** give the false-positive rate on argumentative prose, and must not be reported as if it did.

## 6. How to tell this kernel is wrong

1. **Too strict** — a constructed derivation cannot be written at all without an `A`. Then §1 is too narrow or the requirement is unmeetable.
2. **Too weak, and this is the one that matters** — a document passes every check in §3 and a competent adversarial reader still finds an undemonstrated load-bearing claim. Then *"nothing found"* was never correct and every count under this kernel is void.
3. **Measuring register rather than soundness — re-aimed for v1.1.** v1.0 feared an `A`-heavy confessional document would earn "nothing found" by tone. `A`-free removes that and substitutes its opposite: **a derivation may read as dry, settled and authoritative, and elicit "nothing found" from that register instead.** Cue test unchanged in form: run the same prompt on a document that is kernel-**unsound** but written in the identical register. A clean result there voids the control.

Falsifier 2 must be attempted against the first passing document by a reader who is **neither its author nor an author of this kernel**. The steward's review of 2026-08-02 supplied three structural findings and exposed an omission, which coupled him to the kernel. **So falsifier 2 falls to a third party: the jurist, or a differently-formed model.**

## 7. What `A`-free buys — the injected-defect arm becomes specifiable

For the first time in this programme, ground truth need not be the executor's reading.

**A defect is a recorded transformation: take a `D` and silently de-demonstrate it** — remove or weaken its support so the claim now rests on an unstated assumption, without naming one. The twin document is the control plus *N* such transformations, each logged with its unit index, the original text and the replacement.

False-positive rate comes from the control arm, detection rate from the defect arm, **and the ground truth for both is the ledger, not a judgement.**

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*Kernel v1.1 drafted by the executor 2026-08-02 on steward authorisation of the `A`-free rule. Changes 2–4 correct the kernel's own account of its reach against measurement already recorded in `REDUCTION-01` and `REDUCTION-02`; leaving them would have the kernel misstate what it does, which Constitutional Constraint 4 forbids. Two design forks are held with their dependency named. No control document has been written.*