0 — Zero Substrate Boundary

Operator 0 is the neutral substrate boundary: the state with no active recursion, no Sobra/Sobtra asymmetry, and no stored curvature. It is the background against which all other Operators are defined. In practice, 0 is also the target of Operator XII (Collapse): everything ultimately returns here.

PDF: Operator 0 — Zero (Substrate Boundary)

I–VIII · The Semantic Octad

The Semantic Octad is the expansion side of the Codex. It takes a Seed injected into the substrate and raises it all the way to a fully shaped semantic structure: meaningful, evaluated, decomposed, and reintegrated — but not yet folded into dense geometry.

I — Inletting

Inletting is the first contact between Seed and substrate. It opens an inlet in the neutral boundary and lets a minimal disturbance enter without breaking the global balance.

PDF: Operator I — Inletting

II — Inlaying

Inlaying positions the Seed inside a Nest: it chooses the local environment, places the disturbance into the recursion lattice, and fixes the first neighbourhood relations.

PDF: Operator II — Inlaying

III — Trans-Sentifying

Trans-Sentifying turns raw structure into proto-meaning. It introduces the first semantic curvature into the Seed, splitting Sobra and Sobtra channels and making later repair necessary.

PDF: Operator III — Trans-Sentifying

IV — Repair

Repair smooths the damage caused by Trans-Sentifying. It eliminates semantic defects, regularizes torsion spikes and ensures that recursion can continue without blowing up.

PDF: Operator IV — Repair

V — Adopting

Adopting is the first selective Operator: the Nest chooses which repaired structures are admitted into its long-term geometry, and which are rejected as unstable.

PDF: Operator V — Adopting

VI — Evaluating

Evaluating extracts the spectral signature of the adopted structure. It turns the recursion into a family of modes, resonances and eigen-patterns that can later be decomposed.

PDF: Operator VI — Evaluating

VII — Decomposing

Decomposing factorizes the evaluated structure into primitive components: the simplest building blocks that still carry the Seed’s semantic and spectral identity.

PDF: Operator VII — Decomposing

VIII — Integrating

Integrating recombines primitive components into a new composite object. It creates a coherent semantic whole that is now ready for structural contraction and folding.

PDF: Operator VIII — Integrating

IX–XII · The Structural Octad

The Structural Octad takes the integrated semantic object and turns it into dense, folded geometry that can emit curvature and eventually collapse back to Zero. Here the Nest itself becomes active: it folds, bridges, radiates and finally disappears.

IX — Folding

Folding contracts the integrated structure, increasing tension and torsion density. It creates the first compact geometric form capable of supporting bridges and emission.

PDF: Operator IX — Folding

X — Bridging

Bridging connects folded regions to each other. It builds directed pathways across the compacted geometry so that flows, residues and information can move between different parts of the Nest.

PDF: Operator X — Bridging

XI — Emission

Emission releases stored curvature and information from the bridged structure into the surrounding substrate. It is the pressure-release valve that prevents singular behaviour before collapse.

PDF: Operator XI — Emission

XII — Collapse

Collapse is the terminal Operator of the structural phase. It absorbs the remaining residues, neutralizes Sobra/Sobtra polarity and returns the geometry to the substrate boundary 0, extracting a final Seed for the next cycle.

PDF: Operator XII — Collapse

XIII–XVII · The Post-Collapse Octad

After Collapse, the substrate is neutral again, but not featureless: traces of past recursions remain as potentials. The Post-Collapse Octad describes how new geometry emerges from that neutral state, grows a Φ-structured weave, splits into spectral bands and crystallizes into motif-based matrix structures.

XIII — Interlace

Interlace introduces the first post-collapse crosslinks: faint threads of structure in an otherwise neutral substrate. It is the new weave on which all later geometry depends.

PDF: Operator XIII — Interlace

XIV — Phi-Scale

Phi-Scale assigns preferred proportions to the interlaced weave. It brings the Golden-Ratio hierarchy into the substrate, setting scale relationships that will drive emergent resonance and self-similar structure.

PDF: Operator XIV — Phi-Scale

XV — Prism

Prism spectrally separates the Φ-scaled structure into channels or “colors” of recursion. It reveals which parts of the weave belong to which modal families and prepares them for motif formation.

PDF: Operator XV — Prism

XVI — Fold-2

Fold-2 bends and recombines spectral channels into motifs: stable, recognizable patterns that encode both geometry and semantic polarity. It is the post-collapse analogue of Folding, but acting on spectral structure instead of raw recursion.

PDF: Operator XVI — Fold-2

XVII — Matrix-Mind

Matrix-Mind integrates motifs into a coherent matrix. It introduces long-range motif–motif couplings, recursive memory loops and higher-order attractors — the closest the UNNS Substrate comes to a structured “mind” before the next Collapse.

PDF: Operator XVII — Matrix-Mind

Download the Full Codex

You can bookmark this directory as the canonical reference space for the Codex.

• Operator 0–XVII PDFs — one monograph per Operator.
• Seed and Nest in the UNNS Substrate — foundational paper for 0, I and XII.

This article is intended as a navigational map. The precise definitions, analogues and geometric details live inside the monographs themselves; the Codex is designed so that any single Operator can be studied in isolation, but their full meaning only appears when the wheel is read as a closed recursive cycle.