First Edition · July 2026 · Doctex Research Division
This Lexicon defines the terminology of Deterministic Structural Measurement (DSM) as practised by Doctex Research Division. Every term describes a measurable structural property of a document. None imply qualitative judgment, normative assessment, or evaluation of correctness. All structural metrics are deterministic: identical source text produces identical output.
The structures described here have been observed across a diverse corpus including legal instruments, corporate filings, government reports, academic papers, literary works, sacred texts, and commercial agreements. Several of these phenomena have not been formally described prior to this work.
Structure 1 — Terminal State
Structure 1
Terminal State
The dominant structural signature that a section (or document) propagates toward neighbouring sections as part of the engine's terminal resolution pass. Terminal state is not a summary of content — it is a structural attractor that shapes how adjacent sections interact. The overall document terminal state is the value that dominates after propagation converges.
Structural Criteria: Determined by the engine during the terminal resolution pass of the DSM graph propagation algorithm. No semantic analysis is involved. Terminal state assignment is fully deterministic.
Observed Terminal States
The DSM engine has observed the following eighteen terminal state values across analysed documents. The list is not closed — additional states may be identified as the corpus expands.
Interpretation Note: A terminal state of destabilizing does not indicate a flawed document. It indicates that the section's structural signature disrupts the document's dominant terminal propagation. Whether this disruption is intentional, beneficial, or problematic is a domain-specific judgment made by the reader — not by the DSM instrument.
Structure 2 — Recursive Density
Structure 2
Recursive Density
A measure of the frequency and intensity with which structural patterns revisit earlier regions of the document. Recursive density captures the degree to which a document refers back to its own structural positions — not semantically, but in the topology of its graph representation. Elevated recursive density is associated with complex, multi-threaded argument structures. Low recursive density is typical of linear, single-pass documents.
Structural Criteria: Computed as a weighted sum of recursive edge traversals during graph propagation, normalised by document length and section count. Values below 2,000 are considered low; values above 50,000 are considered elevated; values above 90,000 are considered exceptionally high. Thresholds are derived from the observed corpus and may be refined as the corpus expands.
Observed Range: 153 (short-form commercial agreement) to 92,326 (state consolidated annual report). The range spans approximately three orders of magnitude across the analysed corpus.
Structure 3 — Density Gradient
Structure 3
Density Gradient
The rate and direction of structural density change across consecutive sections. A positive gradient indicates increasing structural concentration as the document progresses. A negative gradient indicates thinning. A flat gradient indicates uniform structural distribution. The density gradient is one of the primary inputs to the Classification System's coherence gradient check.
Structural Criteria: Computed as the sequence of inter-section density deltas, normalised by the document mean. A gradient is considered "declining" when the trailing sections exhibit sustained density below the document mean and the terminal section falls below the opening density.
Structure 4 — Section-Level Terminal Shift
Structure 4
Section-Level Terminal Shift
The degree to which terminal state assignments vary across adjacent sections. High shift volatility indicates a document whose structural character changes frequently — typical of argumentative, multi-perspective, or dialectical texts. Low shift volatility indicates structural consistency — typical of expository, procedural, or template-driven documents.
Structural Criteria: Measured as the count of distinct terminal state transitions between consecutive sections, weighted by the structural distance between the states involved. Documents with 6 or more distinct terminal states across 10 or fewer sections are considered to exhibit high shift volatility.
Related Structures: Structure 1 (Terminal State), Structure 3 (Density Gradient), Structure 7 (Coherence Gradient). Section-Level Terminal Shift is a primary input to the Classification System's shift volatility check.
Structure 5 — Linear Topology
Structure 5
Linear Topology
The dominant organisational form of the document's structural graph. Linear topology describes a document whose sections propagate sequentially — each section passes structural influence primarily to its immediate successor. This is the most common topology observed across the corpus and is the default expectation for prose documents. Non-linear topologies (branched, networked, radial) are theoretically possible but have not been observed at sufficient resolution in the current corpus.
Structural Criteria: Determined by analysing the edge weight distribution of the document's structural graph. A document exhibits linear topology when the dominant edge pathway follows sequential section ordering and non-sequential edge weights fall below the significance threshold.
Note: Linear topology does not imply simplicity. Many structurally complex documents — including legal judgments, legislative texts, and multi-part financial reports — exhibit linear topology with high recursive density. Topology describes the shape of structural propagation, not the intensity or depth of structural content.
Structure 6 — Single-Section Collapse
Structure 6
Single-Section Collapse
A boundary condition in which the document lacks sufficient internal segmentation for section-level analysis. All DSM metrics apply to the document as a whole. Single-Section Collapse is not a defect — it is a measurement constraint indicating that the document is structurally indivisible at the current resolution of measurement.
Structural Criteria: Triggered when the engine's section-chunking pass produces exactly one section. This occurs when the document is shorter than the minimum segmentation threshold or when the document's structural graph fails to exhibit internal boundaries above the segmentation confidence threshold.
Observed Instances: Short-form commercial agreements (4,000–6,000 words), single-page policies, template-driven documents with uniform structure. Also observed in anomalous cases where a large document (100,000+ words) exhibits structural uniformity sufficient to defeat the segmentation algorithm — see Classification System, Class IV-b (Dense Monolith).
Structure 7 — Coherence Gradient
Structure 7
Coherence Gradient
A composite measure of structural stability across the document's full span. The coherence gradient integrates density gradient, terminal shift volatility, and recursive density decay to produce a single directional indicator. A positive or flat coherence gradient indicates structural stability or building coherence. A negative coherence gradient — in which structural intensity, terminal stability, or recursive engagement decline across the document — is the primary signal for Class III (Declining) classification.
Structural Criteria: Computed as the weighted sum of three normalised sub-measures: terminal state stability across the trailing sections (weight 0.4), density trajectory from opening to closing sections (weight 0.35), and recursive density distribution across the document span (weight 0.25). A coherence gradient below the negative threshold triggers Class III classification.
Related Structures: Structure 1 (Terminal State), Structure 3 (Density Gradient), Structure 2 (Recursive Density), Structure 4 (Section-Level Terminal Shift). The Coherence Gradient is the primary structural input to the Classification System decision tree.
Structure 8 — Destabilizing Close
Structure 8
Destabilizing Close
A structural pattern in which the final section or sections of a document exhibit terminal state values associated with structural disruption — most commonly destabilizing, but also resistant or oscillatory — following a sequence of stable or resolved sections. The Destabilizing Close is structurally distinct from a Declining Coherence Gradient: in a Destabilizing Close, the body of the document may be structurally coherent, but the conclusion introduces structural turbulence. This pattern is observed in documents whose concluding sections introduce new structural elements, unresolved tensions, or abrupt shifts in register.
Structural Criteria: Identified when the final section (or final two sections, if the document has more than five sections) carries a terminal state of destabilizing, resistant, or oscillatory, and the preceding sections do not exhibit a sustained decline in coherence. The Destabilizing Close is a trigger for the +V (Unresolved) overlay in the Classification System.
Observed Instances: Legal agreements with contentious closing clauses. Academic papers whose conclusions introduce limitations that structurally disrupt the preceding argument. Literary works with ambiguous or unsettling endings. Government reports whose final recommendations structurally conflict with the body of analysis.
How often the structure revisits its own prior configurations
153 to 92,326 (observed range)
3
Density Gradient
Distribution of structural weight across sections
Flat, positive, or negative
4
Section-Level Terminal Shift
How terminal state changes from section to section
Low (0–2 distinct states) to high (6+ distinct states)
5
Linear Topology
The overarching sequential architecture of the document
Linear (all observed documents); non-linear theoretically possible
6
Single-Section Collapse
Boundary condition: document structurally indivisible at current resolution
Present or absent
7
Coherence Gradient
Trend in structural integrity across the document's length
Flat, positive, or negative (declining)
8
Destabilizing Close
Structural endpoint that disrupts what preceded it
Present or absent; triggers +V overlay
Methodological Note: This Lexicon describes structural phenomena as observed by the DSM engine. The engine is deterministic and closed-source. Identical source text produces identical output. The boundary between public observation and confidential implementation is defined in the Doctex Methodology (First Edition, July 2026). All terminology defined herein is value-neutral and describes measurable structural properties only.