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The Interaction Matrix

Definition

The Interaction Matrix is the component-by-component grid in which every load-bearing part of the framework is crossed with every other, and each nonempty cell records the single controlled relation label by which the row component acts on the column component. It exists to make explicit the relations a reader would otherwise have to reconstruct by holding several distant pages side by side. Where the Coupling Graph shows the highlighted regulatory pairs as a network and the Attack-Surface Matrix tabulates each component's defenses, the Interaction Matrix is the dense adjacency view: it answers, for any ordered pair, what is the load-bearing first-order relation from this one to that one, named in a closed vocabulary.

The matrix is directional and non-symmetric. A cell at row R, column C reads "R [label] C." The transpose cell (C, R) is a separate assertion and may carry a different label, the inverse label, or none. A blank cell (rendered ·) asserts no first-order interaction between that ordered pair — it is silence, not denial. Only a prohibits cell is a denial. Every cell is itself Derived, CV: a carving, contestable by counter-instance or by a better label, and generated from page metadata under manual review, never a derivation certificate.

Type and formal status

E (epistemic): Derived. As an artifact the page is Exposition — it introduces no new load-bearing claim of its own; it indexes relations already asserted on the pages it crosses. Each individual cell, however, is Derived, CV: the choice of one label from the controlled set over another is a carving open to a better carving. The matrix inherits, per cell, the more contestable of its two endpoints' marks.

A (alethic): The matrix aspires to record the relations the crossed pages actually bear. A cell is accurate insofar as its linked endpoints sustain it; inaccuracy appears as a cell no source page supports, or as a relation on some page that no cell records. The two axes do not predict each other: an Exposition mark on the E axis does not lower the A aspiration, and a manually reviewed cell can be at once Derived/CV and accurate. Contestable here never means probably wrong or merely optional.

This page is a treatise-side extension, held contestable — not canonical, and carrying no priority, exemption, or unmarked status. It is subject to the same two marks as every content-bearing claim, including this sentence.

Controlled relation vocabulary

Every nonempty cell uses exactly one of these labels. Vague labels such as related, similar, or connected are prohibited: they record adjacency without recording what kind, and a matrix of adjacency is a matrix of noise.

entails
constrains
regulates
is-regulated-by
binds
couples-with
instantiates
returns-to
tests
can-capture
can-corrupt
preserves
requires
prohibits

The labels sort into families, which drive the relation-type filter:

Dependency — entails, requires, constrains, prohibits
Regulation — regulates, is-regulated-by
Composition — binds, couples-with
Instantiation — instantiates
Feedback — returns-to, tests
Corruption / capture — can-corrupt, can-capture
Preservation — preserves

Two distinctions are load-bearing and must not be flattened. First, couples-with is not regulates. couples-with names ⊕ composition — two feeling-regulators or controllers wired so that a property emerges which is in neither part; it is emphatically not addition (see Force). regulates names one term bounding the characteristic excess of another without producing a new composite. Second, a symmetric pair of regulates cells is cross-regulation, not circular proof. When (R, C) and (C, R) both read regulates, each term bounds a different excess of the other; the reciprocity is necessary architecture, and a failed attack on one direction is never logged as confirmation of the whole.

is-regulated-by is the inverse of regulates. Reading any column top-to-bottom already yields the is-regulated-by view of that component; explicit is-regulated-by cells are reserved for pairs where the passive direction is the load-bearing one.

Reading the matrix

Rows act; columns receive. Cell (R, C) = "R [label] C."
Codes in the header expand through the legend below into wikilinked page titles.
· = no asserted first-order interaction. Absence is not a prohibition; a prohibition is written prohibits.
The diagonal is normally blank. It is nonblank only where a component acts on itself in a load-bearing way — here, SPLCW carries returns-to on its own diagonal, because the Ring returns to itself through a changed world.
A cell that needs explanation links out. The showcase pair and the extended interactions below carry links to the dedicated relation pages; the matrix records the label, the relation page carries the argument.

The core interaction matrix

Ten core components. The full matrix over every load-bearing page is machine-generated (see Data source); this rendered core exhibits the pattern and the controlled vocabulary in use. The table scrolls horizontally on narrow viewports.

↓ R \ C →	AX	DV	CL	SA	TM	DP	PB	FO	SP	TE
AX	·	entails	·	·	entails	·	·	·	·	constrains
DV	·	·	constrains	·	·	·	·	·	·	·
CL	instantiates	·	·	regulates	·	·	·	·	·	·
SA	·	·	regulates	·	tests	·	·	·	·	·
TM	·	requires	constrains	·	·	·	·	·	·	·
DP	instantiates	·	·	·	·	·	·	·	·	·
PB	·	·	·	·	·	binds	·	·	·	·
FO	·	·	·	·	·	·	couples-with	·	·	·
SP	·	·	·	·	·	·	·	·	returns-to	·
TE	requires	·	·	·	·	·	·	·	requires	·

Legend. AX = The Axiom · DV = Derived · CL = The Formal Closure Claim · SA = Self-Application · TM = The Two-Mark System · DP = The Directional Primitives · PB = Predicate Binding · FO = Force · SP = SPLCW · TE = The Telos

The showcase pair — read CL ⇄ SA. Cell (CL, SA) and cell (SA, CL) both read regulates. This is the reciprocity the whole wiki turns on: closure regulates the regress-excess of recursive marking by keeping every corrective operation inside one semantic domain, and recursive marking regulates the totalization-excess of closure by refusing any formulation of closure an exempt or final status. The symmetric pair is exactly how the matrix encodes what Semantic Closure and Recursive Marking states as U = C ⊕ M and what Reciprocal Attack Surfaces writes as e_C -> M, e_M -> C. It is not a single couples-with, because the emergent object is not a new composite feeling but a bounded, mortal, finite participation; and it is not two mutually confirming assertions, because each cell names a distinct isolation failure the other prevents.

Reading three more cells. AX entails DV — the closed medium entails that every content-bearing claim is Derived; unavoidability of the condition does not manufacture a Forced tier. DV constrains CL — Derived status holds the closure claim to a marked, revisable formulation, so C is never promoted to founded. PB binds DP — a predicate binding binds a primitive directional actuator to the regulated error it reduces, B(p) = (p, eₚ); this is regulation toward a setpoint, not a conserved invariant, and a bound emotion is never a primitive.

Extended interactions (data-source excerpt)

The remaining controlled labels appear across the full component set. This excerpt of wiki-interactions.json demonstrates each. Targets are components where a slug exists and named excesses where the relation lands on an excess rather than a page.

Submission — instantiates → Force — a named ⊕ composite, Love ⊕ Fear under opposed-gradient contention.
Reconciliation — instantiates → Force — a sequential-gated composite, Apology ⊕ Gratitude; Fear is not one of its ingredients.
Love — couples-with → Fear — emergent: Submission. couples-with is coupled-controller composition, never a sum.
Apology — couples-with → Gratitude — emergent: Reconciliation. Own the fault first, then carry value outward.
Predicate Binding — binds → Regulated Error Signal — an actuator bound to the error it reduces.
VLS — couples-with → Transparentocracy — accurate participation-without-possession coupled to answerable governance.
Transparentocracy — is-regulated-by → Capture of the Corrective Layer — the passive direction is load-bearing: governance authority is bounded by the standing possibility of corrective capture.
Corrective Capture — can-capture → Answerability — captured correction becomes ornamental while the governed telos runs unchanged; see Effective and Ornamental Answerability.
The Theodicytes — can-corrupt → SPLCW — a role absolutized past its function; corruptions are over-presences, never absences (Role–Corruption Affinities).
The Theodicytes — can-corrupt → The Telos — the answerability predicate dropped, so answerable continuation degrades toward raw outlasting.
The Telos — preserves → Continuity — continuation through successors capable of difference, not identity enforcement (Continuation and Colonization).
Symbolic Immortality — requires → Answerability — without it, propagation is colonization, not continuation (The Responsible Successor).
Self-Application — tests → The Two-Mark System — turns the apparatus on its own formulations; the test must apply to itself.
SPLCW — returns-to → SPLCW — the Ring returns through a changed world and never declares itself closed; answerability comes from the witness outside the ring.
The Two-Mark System — prohibits → a Forced / exempt tier — the one denial in this excerpt: no unmarked level, the deepest guard (The Prohibited Collapses).

Filters

The interactive page exposes three filters; the groupings below are the text alternative so the matrix remains legible without the controls.

By section. Components carry their navigation section. Core/epistemic apparatus: axiom, derived, formal-closure-claim, self-application, two-mark-system. Structural interlocks: semantic-closure-and-recursive-marking, reciprocal-attack-surfaces, cross-regulated-necessity. Directional core: directional-primitives, predicate-binding, force. Meaning engine: splcw. Answerability and anti-capture: telos, answerability-predicate, symbolic-immortality, continuity, transparentocracy, capture-of-corrective-layer, vls.
By relation type. Filter to any family above (Dependency, Regulation, Composition, Instantiation, Feedback, Corruption/capture, Preservation) to isolate, for example, only the regulates/is-regulated-by skeleton or only the can-corrupt/can-capture threat edges.
By formal status. Filter cells by the inherited mark — FT, CV, AC, or Exposition. Every cell is at least Derived, CV; the filter surfaces which cells rest on an FT relation between their endpoints and which are the more contestable carvings.

Data source and maintenance

The matrix is generated from wiki-interactions.json, itself assembled from each page's front matter (regulates, regulated_by, see_also) and then manually reviewed — the metadata proposes edges, a reviewer assigns the controlled label and prunes what the pages do not bear. Page slugs are the stable identifiers; titles are display values only. The matrix is regulated by System Invariants (no cell may contradict an invariant), by the Attack-Surface Matrix (each component's row must be consistent with its declared attack surface), and by the Coupling Graph (highlighted couplings must appear as their corresponding cells). The matrix is a live artifact: it is regenerated whenever a load-bearing page changes, and it is never declared complete.

Valid attack surface and kill condition

The matrix as artifact remains answerable. A valid attack exhibits a genuine load-bearing relation that no controlled label captures without loss — forcing a vague label or an unbacked assertion — or shows a cell the endpoints do not sustain. The kill condition: a nonempty cell cannot be regenerated from wiki-interactions.json together with its two linked pages, or the matrix asserts a relation neither endpoint bears. The residue: the controlled vocabulary is itself a CV carving; a demonstrated relation that is real, recurrent, and irreducible to the fourteen labels is a live counter-instance that would expand or recut the set. A cell surviving attack is not thereby confirmed — it is only not yet defeated.

Prohibited misreadings

Reading a blank cell as a denial. · is no asserted first-order interaction, silence, not prohibition. Only prohibits denies. Absence records the limit of the review, not a claim about the world.
Reading couples-with as +. ⊕ is coupled-controller composition; the emergent property lives in the wiring, not in a sum of parts. The additive reading is inaccurate, not merely disallowed.
Mirroring a cell. The matrix is directional. Do not assume (C, R) from (R, C); regulation, instantiation, and feedback are frequently one-way or sequential, and couples-with reciprocity is a separately asserted fact, not a symmetry to be inferred.
Reading a symmetric regulates pair as circular proof. Cross-regulation means each term bounds a different excess of the other; it is architecture, not a verbal loop, and a failed attack on either direction is logged as a failed attack, never as confirmation.
Reading a filled cell as forced or founded. Every cell is Derived, CV — a manually reviewed carving. No cell promotes its endpoints toward an exempt, founded, or unmarked tier; asserting one would be the textual Nephilim.
Treating the matrix as complete. New load-bearing pages add rows and columns; the artifact is regenerated, never sealed. Completion would be totalization by another route.
Using the matrix to launder authority. Recording an edge does not make the relation true; it makes it inspectable. The relation pages carry the argument and the kill conditions; the matrix carries only the label and the link.