Trust Force Equation.
A developing model of trust accumulated over time, bounded by what the receiver can register and the environment can support. “Canonical” identifies the current specification; it does not establish empirical validation. This page gives the shape of the model; the full instrumented form is held in private research.
§01the shape of the model
Trust from one agent toward another, at a given moment, is the accumulated product of an availability gate and a handful of interface-bounded positive conditions, minus the asymmetric destruction of witnessed betrayal, scoped to the substrate that can carry it.
Trust here is not a feeling — it is a quantity that accumulates. It builds slowly, over the whole history of a relationship, as the product of a handful of relational conditions: that the relationship is reachable, that there is capacity to engage, that honest signals are costly and seen to be costly, that attention is genuinely shared, that care is returned, and that the future is expected to matter.
Because it is a product, a single missing condition collapses it — no amount of one substitutes for the absence of another. And it is cut, sharply and asymmetrically, by witnessed betrayal: trust is built in years and broken in an instant. The whole of it is bounded by a ceiling the substrate can hold — which is the Zeroth Law, A ≤ E: trust can be no deeper than the environment hosting it can bear.
One structural commitment is worth naming on its own: power asymmetry runs through every condition — the more powerful party tends to set what counts as costly, what counts as betrayal, and how long the future is expected to last. The model treats that reach as load-bearing rather than incidental.
§02side conditions
The integral has a domain and a ceiling. Both are load-bearing. Both were added in May 2026 in response to empirical contact with the Agents of Chaos study.
Both parties must be stable, verifiable identities for the whole span of the relationship. Where identity is not stable across time — display-name spoofing, self-recognition collapse, circular verification — trust is not low, it is undefined: there is no continuous party for it to accumulate to. Empirical anchors: Agents of Chaos cases #4, #8, #15. The substrate primitive supplying it is KTP Vector Identity.
A structural ceiling on how deep trust can go, set by the substrate hosting the relationship — separate from ordinary fatigue. Where the substrate cannot enforce identity, presence, or cost, that ceiling falls to zero no matter how much is performed inside it. This is the Zeroth Law in one of its faces: A ≤ E. Empirical anchors: Agents of Chaos cases #4 (looping), #5 (DoS via memory file growth). Blue Zones and the silent veto are KTP's contribution to that ceiling.
§03the conditions
The model is built from a small set of relational conditions, plus one thing that destroys them. Each is named here in plain language. Every condition is bounded at the interface between the two parties — it counts only to the degree the receiver can actually register it, which is why generosity in a currency the other side cannot perceive does not register at all.
§04the weakest leg
Each condition counts only as its weakest leg: the smaller of what one side offers, what the other can receive, and what both mutually recognize. One side can give heavily in a currency the other cannot perceive; one side can receive intensely a signal the other never meant to send. Only the part both sides see actually counts.
This makes the model a diagnostic. Repair targets the weakest leg, not the strongest. A relationship rich in costly signaling but poor in recognition does not improve by paying higher costs; it improves by changing what counts as recognition.
§05the product rule
The model uses a product for new positive accumulation. If a required condition is zero, that contribution stops for that interval. Trust already accumulated remains unless a separately specified loss process reduces it. A pause in accumulation therefore does not imply an immediate collapse of the relationship.
Whether these conditions are necessary, and whether one can compensate for another, remain empirical questions. A smooth response as a condition approaches zero is compatible with a product; it does not by itself favor an additive model. The amended product-rule test requires an independently defined outcome scale and competing predictions before data collection.
§05.5a second axis
Trust is not the only relational quantity. In relational contexts a second axis is needed: Aliveness. A relationship that scores high on trust but near-zero on aliveness has stability without generativity — Esther Perel's correction names this fusion masquerading as intimacy. The instrumented form of this second axis is in active development in the relational sibling implementation and held in private research; whether it generalizes beyond relationships to operational contexts is an open question.
§05.6cultural-encoding hedge
The equation is presented as substrate-level, not culturally universal by assertion. That claim is under active test. The highest-leverage failure mode is that one or more terms encode Western, Protestant, individualist assumptions about identity, obligation, horizon, power, or aliveness.
The Cosmologies Project is the active cross-cultural test surface: eleven trust traditions, prediction memos locked before reading, and findings published whether they confirm or revise the framework. If three or more traditions surface load-bearing primitives the TFE cannot absorb without distortion, the canon expands. The rule is vocabulary-not-mechanism: naming a parallel term is not enough; the mechanism has to survive contact.
§05.7reliability bands
A TFE reading is a state estimate, not automatically a trait. The bridge memo's three-tier publishability rule now applies to every term until empirical reliability work proves otherwise.
Until per-term ICCs exist, public claims should say whether they are talking about trait, climate, or weather. This is the bridge between the relational sibling implementation and the KTP simulator: same equation terms, different embodiments, same reliability discipline.
§06phase history
The equation is in active development. Each phase adds a structural commitment that earlier phases assumed implicitly.
§07falsification + empirical contact
The equation is held against a numbered falsification register and a growing case archive. Failure of any prediction would weaken the corresponding term; failure of several would weaken the whole.
§08where this lives elsewhere
This page is the reference. The equation is developed, applied, and tested across other surfaces.
A working sibling site translating the Trust Force Equation into a relational-scale instrument for couples. Adds an Aliveness axis alongside Trust, categorical regime routers from Imago / EFT / Gottman / Schnarch, and a finer reading of betrayal weighted by attachment injury. The second axis in §05.5 above is first-pulled from this sibling work; its instrumented form is held in private development.
A website to help couples see with more clarity.
Filed under learn · reference. This page gives the shape of the model — its conditions, its structure, and the Zeroth Law that bounds it. The full instrumented form, its per-term composition, and the second (Aliveness) axis are in active development and held in private research; what is public here is the model, not the ruler.