The Derivation Trace Instrument (DTI) — Version 0.2
The Derivation Trace Instrument (DTI) — Version 0.2
Theoretical foundations: Grant C. Sterling (Eastern Illinois University). Analysis and synthesis: Dave Kelly. Prose rendering: Claude (Anthropic). 2026.
Version note: v0.2 supersedes v0.1. Two amendments, both to the HALT apparatus, arising from the first run — the trace of the academic-integrity derivation in The Obligation and Its Ground — A Conduct Code Restoration. No step is deleted and no finding category changes. v0.1’s unratified status is superseded: the instrument is grounded in the ninth distinction, Derivation and Consistency, and in Sterling’s foundationalism as recorded in the ISF archive — the regress argument of 1 July 2007 and the rejection of coherentism of 23 September 2021.
Purpose
To test corpus output for performed derivation. The instrument answers, of every proposition in a document, the two questions the ninth distinction sets: what does this rest on, and what rests on it.
It does not assess truth, style, or doctrinal agreement. A document can be entirely correct and fail this instrument, and that failure is the finding. What the instrument detects is corpus-shaped prose — right terms, right structure, Ergo-lines in the right places — with no derivation actually performed. Because the vocabulary survives that loss, the failure is invisible in the output and can be found only by trace.
Scope
Corpus documents and corpus-generated output. Not outside targets: CPA, SCE, CIA and the field audits handle those. DTI is the corpus turned on itself.
A run may take a whole document or a unit smaller than a document. A sub-document run is declared as such at Step 0 and carries the restriction stated at the HALT conditions below.
Step 0 — Halt and Input Restatement
State the document under trace, its version, and its stated thesis in one sentence drawn from the document itself. If the thesis cannot be located in the text, HALT and report.
Where the target is a unit smaller than the document, state the unit and declare the run a sub-document run.
Step 1 — Proposition Extraction
Decompose the document to numbered propositions. Rhetorical and transitional sentences are marked as such and excluded from the trace rather than silently dropped; the count of exclusions is reported.
Step 2 — Type Assignment
Each proposition takes exactly one type: Foundational, Derived, Empirical, Definitional, or Restatement. Restatement covers propositions that repeat corpus content without advancing a claim — these carry no derivation burden but also no weight.
Step 3 — Upward Trace
For each Derived proposition, name its support and locate it: document, section, theorem number. Support that cannot be located is flagged Unlocatable. Support located only by topical similarity is flagged under the contamination guard below.
Unlocatable flags are provisional until Step 5 completes. The substitution test reclassifies any proposition whose named support merely loosens rather than falsifies it, which changes the Derived set. The Derived count is therefore not stable at this step, and no ratio may be computed against it before Step 5.
Step 4 — Downward Trace
For each proposition, record what in the document rests on it. A proposition with nothing above it and nothing below it is flagged Decoration — true or false, it is doing no work, and the document is longer than its argument.
Step 5 — Substitution Test
For each claimed derivation, ask whether removing the support falsifies the proposition or merely loosens it. Falsifies: derivation confirmed. Loosens: the relation was coherence wearing the grammar of derivation, and the proposition is reclassified.
The Derived set is stabilized at the close of this step. Ratios are computed against the stabilized set and not before.
Step 6 — Foundation Guard
Foundational status is not self-assigned. Only propositions the corpus itself places at the base — Th10 and the commitments — may take it. Any other proposition typed Foundational is reported as a protected claim: unproven, and claiming the protection that belongs to the base.
This is the instrument’s guard against the second direction of the ninth distinction, run in reverse. There the failure was demanding a proof of what is unprovable by construction; here it is extending that exemption to a proposition that has no title to it.
Step 7 — Empirical Gate
Every Empirical proposition must carry a declared source outside the corpus. Undeclared empirical claims are flagged.
Empirical propositions that other propositions rest on are flagged separately and prominently, since a derivation running through an undeclared fact is not a derivation.
Step 8 — Roll-Up
Counts by type and flag, and a single verdict: Traced, Partially Traced, or Untraced.
Where the ratio condition applies below the floor, the roll-up reports Ratio Advisory, so that a completed run beneath the floor is not read as a run that passed the ratio test.
Untraced is not a claim that the document is wrong. It is a claim that the document has not shown its work, and that its correctness is therefore unavailable to the reader.
Self-Audits
At every step transition: did I supply a derivation the document does not contain?
The instrument reports what the text does, never what it could be made to do. A trace the auditor completed on the document’s behalf is the characteristic failure of this instrument and voids the run.
Failure Modes
Associative justification. Citing a theorem because it shares vocabulary with the proposition. The contamination guard from CDS v0.2 applies unchanged.
Retrofitting. Locating support after reading the claim and calling it the claim’s ground. Support counts only where the document itself names it.
Protection by elevation. Typing a contested proposition Foundational to exempt it from trace.
Restatement as derivation. Repeating Th10 in different words and treating the repetition as an inference from it.
Author deference. Relaxing the trace because the document is corpus-internal or ratified. Ratification is not derivation.
HALT Conditions
The document’s thesis is not locatable in the document.
After Step 5, more than half of the stabilized Derived set is Unlocatable, and the stabilized Derived set numbers twenty or more — the document is not a candidate for trace but for reconstruction. A run beneath that floor reports Ratio Advisory and completes. A sub-document run never HALTs on the ratio, whatever its count.
The instrument cannot proceed without supplying a derivation itself.
Grounds for the HALT Amendments
A ratio taken over a small denominator does not discriminate between a passage that has not shown its work and one that had little work to show. The first run fired the condition at four Unlocatables out of six Derived propositions, on a passage of four sentences. The floor and the sub-document restriction answer that.
The ordering amendment answers a second defect found in the same run: the condition as written could stop the trace at Step 3, before the substitution test — which is the step at which that run produced its usable finding. A stop that precedes the instrument’s sharpest operation forfeits the run to no purpose.
Theoretical foundations: Grant C. Sterling (Eastern Illinois University). Analysis and synthesis: Dave Kelly. Prose rendering: Claude (Anthropic). 2026.
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