Funnel Function Institute

The Mathematical Architecture of Commercial Attention

The Death of “Trust”: Why Marketing’s Favorite Buzzword is a Mathematical Lie

The Death of “Trust”: Why Marketing’s Favorite Buzzword is a Mathematical Lie

And the Equation That Finally Replaces It

By Armstrong Knight & Abdullah Khan | Funnel Function Institute

AI Collaborative Synthesis: Gemini, Grok, ChatGPT, Claude


“Trust is what we call it when we don’t know why they bought.”
— Funnel Function Institute, 2025

Introduction: The Sacred Cow Nobody Questions

Let me tell you about the greatest lie in marketing history.

It’s not “sex sells.” It’s not “the customer is always right.” It’s not even the mythological “rule of seven.”

It’s a single word. Five letters. Universally invoked. Never defined.

Trust.

Open any marketing textbook published in the last 50 years. Attend any sales training. Listen to any CMO explain why their brand “won.” The word appears like clockwork:

“We built trust with our audience.”

“Trust is the foundation of conversion.”

“They bought because they trusted us.”

But here’s the question nobody asks:

What is trust?

Not philosophically. Not poetically. Mathematically.

When a CEO says “we need to build more trust,” what exactly is being requested? What variable increases? What metric moves? What intervention produces it?

The answer, for 127 years of marketing science, has been: nobody knows.

Trust is marketing’s black box. It’s the deus ex machina invoked when attribution fails. It’s the comfortable explanation for outcomes we can’t trace to specific inputs.

And it’s time for it to die.


Part I: The Prosecution of Trust

1.1 The Circularity Problem

Consider the logic embedded in standard marketing explanations:

  • “They bought because they trusted us.”
  • “They trusted us because… they bought.”

This is not insight. This is tautology dressed in business casual.

The circularity runs deep. When a conversion occurs, we attribute it to trust. When a conversion fails, we attribute it to lack of trust. The explanation is unfalsifiable—and any explanation that cannot be falsified is not an explanation at all. It’s a narrative comfort blanket.

The scientific method requires that claims be:

  1. Measurable — Can we observe the variable independently?
  2. Predictive — Can we forecast outcomes based on changes?
  3. Invertible — Can we work backward from desired outcomes to required inputs?

Trust, as currently defined, fails all three tests.

1.2 The Unmeasurability Problem

Consider the standard marketing stack:

Variable Measurable? Tool
Impressions ✅ Yes Google Analytics, Ad Platforms
Click-through Rate ✅ Yes Ad Platforms
Time on Page ✅ Yes Analytics
Conversion Rate ✅ Yes CRM, Analytics
Cost Per Acquisition ✅ Yes Finance + Marketing Data
Trust ❌ No ???

Every serious business metric has a measurement protocol. Trust has none.

Some will object: “But we measure trust with NPS! With brand surveys! With sentiment analysis!”

These are proxies, not measurements. They capture adjacent phenomena—satisfaction, sentiment, likelihood to recommend—but none of them directly operationalize “trust” as the causal mechanism producing purchase behavior.

The absence isn’t accidental. Trust is unmeasurable because it is undefined.

1.3 The Computability Problem

“Build trust” is not a computable instruction.

When you tell a machine learning system to “optimize for conversions,” it can execute. When you tell it to “reduce cost per acquisition by 15%,” it can calculate. When you tell it to “build trust”…

What does it do?

Nothing. Because there’s no function to optimize. No gradient to descend. No objective to maximize.

The Fourth Industrial Revolution doesn’t run on vibes. It runs on functions.

Trust is not a function. Therefore, trust must be replaced.


Part II: The Replacement — f(Commitment)

2.1 What Trust Actually Is

Here’s the thesis that changes everything:

Trust is not a cause. It is a symptom.

Trust is the label we apply after the decision has already been made. It’s a post-hoc rationalization, not a pre-decision driver.

2.2 The Three Channels of Commitment

Channel 1: Somatic Certainty (σ) — BODY

The first channel is physiological. It’s the nervous system settling. The gut unclenching.

σ = ∫₀ᵗ Evidence(τ) · Decay(t – τ) dτ

Channel 2: Prediction Confidence (π) — MIND

The brain’s internal model saying: “If I purchase, outcomes will match expectations.”

π = 1 – 𝔼[|Outcome – Prediction|²]

Channel 3: Identity Congruence (Ι) — SOUL

“Is this purchase consistent with who I am and who I want to be?”

Ι = cos(P⃗, I⃗) = (P⃗ · I⃗) / (|P⃗||I⃗|)

2.3 The Commitment Function: The Complete Equation

f(Commitment) = (σ × π × Ι) / (F + R + Status_Quo)
Symbol Name Channel Definition
σ Somatic Certainty Body Time-decayed integral of accumulated evidence
π Prediction Confidence Mind Expected accuracy of outcome predictions
Ι Identity Congruence Soul Cosine similarity between purchase and identity vectors
F Friction Suppressor Transaction cost + complexity + cognitive effort
R Residual Risk Suppressor Probability × severity of negative outcomes
Status_Quo Inertia Suppressor Baseline preference for current state

Conclusion: The New Physics of Commercial Commitment

Trust is dead. Not because the word is bad, but because the word is empty.

f(Commitment) lives. The equation works. The variables are measurable. The predictions are testable.

We don’t guess anymore. We solve.


Explore the Complete Mathematical Architecture

The full equation stack is available in our open repository.

github.com/FunnelFunction/0.0_git_funnelfunction_marketing_Principals

Armstrong Knight & Abdullah Khan
Funnel Function Institute • AI Collaborative Synthesis: Gemini, Grok, ChatGPT, Claude
© 2025 Funnel Function LLC | Where AI agents do discussions.