[[home|← Ultimentality Wiki]] # 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|Coupling Graph]] shows the highlighted regulatory pairs as a network and the [[attack-surface-matrix|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-mark-system|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. ```text 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|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 [[cross-regulated-necessity|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|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 = [[axiom|The Axiom]] · DV = [[derived|Derived]] · CL = [[formal-closure-claim|The Formal Closure Claim]] · SA = [[self-application|Self-Application]] · TM = [[two-mark-system|The Two-Mark System]] · DP = [[directional-primitives|The Directional Primitives]] · PB = [[predicate-binding|Predicate Binding]] · FO = [[force|Force]] · SP = [[splcw|SPLCW]] · TE = [[telos|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: [[formal-closure-claim|closure]] regulates the regress-excess of [[self-application|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|Semantic Closure and Recursive Marking]] states as `U = C ⊕ M` and what [[reciprocal-attack-surfaces|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|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|predicate binding]] binds a primitive [[directional-primitives|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|Submission]] — `instantiates` → [[force|Force]]** — a named ⊕ composite, Love ⊕ Fear under opposed-gradient contention. - **[[reconciliation|Reconciliation]] — `instantiates` → [[force|Force]]** — a sequential-gated composite, Apology ⊕ Gratitude; Fear is not one of its ingredients. - **[[love|Love]] — `couples-with` → [[fear|Fear]]** — emergent: Submission. `couples-with` is coupled-controller composition, never a sum. - **[[apology|Apology]] — `couples-with` → [[gratitude|Gratitude]]** — emergent: Reconciliation. Own the fault first, then carry value outward. - **[[predicate-binding|Predicate Binding]] — `binds` → [[regulated-error-signal|Regulated Error Signal]]** — an actuator bound to the error it reduces. - **[[vls|VLS]] — `couples-with` → [[transparentocracy|Transparentocracy]]** — accurate participation-without-possession coupled to answerable governance. - **[[transparentocracy|Transparentocracy]] — `is-regulated-by` → [[capture-of-corrective-layer|Capture of the Corrective Layer]]** — the passive direction is load-bearing: governance authority is bounded by the standing possibility of corrective capture. - **[[capture-of-corrective-layer|Corrective Capture]] — `can-capture` → [[answerability-predicate|Answerability]]** — captured correction becomes ornamental while the governed telos runs unchanged; see [[effective-and-ornamental-answerability|Effective and Ornamental Answerability]]. - **[[theodicytes|The Theodicytes]] — `can-corrupt` → [[splcw|SPLCW]]** — a role absolutized past its function; corruptions are over-presences, never absences ([[role-corruption-affinities|Role–Corruption Affinities]]). - **[[theodicytes|The Theodicytes]] — `can-corrupt` → [[telos|The Telos]]** — the answerability predicate dropped, so answerable continuation degrades toward raw outlasting. - **[[telos|The Telos]] — `preserves` → [[continuity|Continuity]]** — continuation through successors capable of difference, not identity enforcement ([[continuation-and-colonization|Continuation and Colonization]]). - **[[symbolic-immortality|Symbolic Immortality]] — `requires` → [[answerability-predicate|Answerability]]** — without it, propagation is colonization, not continuation ([[responsible-successor|The Responsible Successor]]). - **[[self-application|Self-Application]] — `tests` → [[two-mark-system|The Two-Mark System]]** — turns the apparatus on its own formulations; the test must apply to itself. - **[[splcw|SPLCW]] — `returns-to` → [[splcw|SPLCW]]** — the Ring returns through a changed world and never declares itself closed; answerability comes from the witness outside the ring. - **[[two-mark-system|The Two-Mark System]] — `prohibits` → a Forced / exempt tier** — the one denial in this excerpt: no unmarked level, the deepest guard ([[prohibited-collapses|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|System Invariants]] (no cell may contradict an invariant), by the [[attack-surface-matrix|Attack-Surface Matrix]] (each component's row must be consistent with its declared attack surface), and by the [[coupling-graph|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. ## See also [[coupling-graph|The Coupling Graph]] · [[attack-surface-matrix|The Attack-Surface Matrix]] · [[system-invariants|System Invariants]] · [[prohibited-collapses|The Prohibited Collapses]] · [[category-error-atlas|The Category-Error Atlas]] · [[reader-paths|Reader Paths]] · [[semantic-closure-and-recursive-marking|Semantic Closure and Recursive Marking]] · [[reciprocal-attack-surfaces|Reciprocal Attack Surfaces]] · [[cross-regulated-necessity|Cross-Regulated Necessity]] · [[one-page-reconstruction|Ultimentality in One Page]]