Lead-in: Why the Quadranym Is Great but Hard to See at First

Before anything can mean, it has to hold together.

Modern systems such as natural language models and transformer architectures already do this remarkably well within a given situation. Through autoregressive prediction and continuous training, they generate responses that remain consistent with the prompts, constraints, and representations they are given. In this sense, they successfully operate within what can be called the situational context: a space of inputs, outputs, and truth-conditional relations.

From within that space, the problem appears largely solved. The system can produce meaningful responses, adapt to new inputs, and refine its outputs through ongoing interaction.

But this consistency is local.

It holds within the situation that produces it. As the situation shifts—new prompts, new contexts, new constraints—the system generates a likely situational configuration again through the same process of representation and prediction.

This is not a failure. It is a limitation of scope.

What is missing is not the ability to generate consistent responses, but the ability to carry coherence across situations without re-establishing it each time.

This is the distinction between situational consistency and situated coherence.

Situational consistency is achieved through representation and prediction. It ensures that a response makes sense within a given context.

Coherence, in the dynamical sense, is different. It is not the production of a consistent response. It is the condition under which an orientation can continue to hold under pressure. It is not constructed. It is sustained. A system does not generate coherence; it remains aligned within it—or loses that alignment.

Situated coherence is not tied to a single situation. It persists as conditions change, allowing orientation to remain stable even as the surrounding context shifts.

The Dynamic Quadranym Model (DQM) introduces a layer that operates at this level.

It does not generate content. It does not interpret inputs. It does not solve problems posed by the situation.

Instead, it maintains its own coherence while absorbing the situational context—not as intake or processing, but as constrained reshaping under pressure. This reshaping follows a structured pattern that will be made explicit shortly.

This defines a second context:

Situational Context (SC)
The space of prompts, representations, and truth-conditional evaluation

Dynamical Context (DC)
A pre-semantic constraint system that sustains orientation under pressure and carries coherence across situations

The relation between them is not one of control or correction. It is not a supervisory layer over the situational context and does not monitor or regulate its outputs. A supervisory layer could be added above this interaction, but it is not required for coherence to emerge.

The situational context produces content.
The dynamical context does not evaluate or select that content. It remains coherent under the pressure of that context, allowing its internal structure to reshape without losing alignment.

When this coherence holds, and the situational context provides valid truth conditions, the two align:

The dynamical context provides continuity of orientation.
The situational context provides meaning.

Together, they allow a response to be both stable and meaningful.

This is the key shift:

The goal is not to improve representation within a situation.
It is to establish a coherence that persists beyond any single situation.

Because this coherence is not tied to specific content, it can be reused. It allows the system to generalize analogically, to remain grounded across digressions, and to generate novel responses without relying solely on static representations.

The dynamical context does not solve the situation.
It makes it possible for solutions to remain coherent as situations change.

This requires a different kind of structure.

The quadranym does not begin with meaning. It begins earlier, at the level where experience is organized not by concepts, but by tensions—differences in intensity, opposition, and balance. Before anything can be said to be true or false, something has to hold together. The quadranym formalizes that holding.

Its components can easily be mistaken, as the words inside it appear semantic, but they function as role-performers—“kabuki words”—positioned to carry tension, not to assert meaning. Read too quickly, the quadranym collapses into interpretation. Read correctly, it reveals a system that operates prior to interpretation, structuring how coherence forms under pressure.

For example:

“I went to that class and felt my mind expanding.”

If the mind is expanding, what is holding?

It need not be noticed or named, but something must hold. That is the coherence that remains under pressure—in this case, expansion. What holds is not the expansion itself, but a capacity that persists through it—used here as a role, not a definition.

The aim of this essay is not to define the quadranym all at once, but to prevent its first misunderstanding. Once it is seen as a pre-semantic configuration—expressed as a field (Hyper Quadranym) and as events (Quadranym Unit)—the rest of its structure can unfold without distortion.

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1. The First Misunderstanding: It Looks Like Meaning

At first glance, the quadranym appears to be a semantic structure.

Written as:

it looks like a statement. It invites interpretation:

Y describes something about a
X describes something about b
and there is a directional relation between them

This reading is immediate.

It is also wrong.

The quadranym does not operate at the level of meaning.

It operates prior to it.

Pre-semantic, not semantic

The quadranym does not express a claim. It does not describe, assert, or refer. It does not say what is the case.

It organizes tension.

Before meaning, there is only tension.

An infant does not understand “warm” or “cold,” but it experiences warmth and contact versus coolness and separation.

These are not meanings. They are felt polarities—structured differences in intensity.

This can already be written in quadranym form:

Read semantically, this looks like a claim:

“cold leads to comfort”

But nothing here is being asserted.

What appears inside the structure is not content. It is position.

“Cold” does not describe a property.
“Warm” does not describe a goal.
“feeling” and “comfort” are not yet meanings.

They are role-performers within a tension.

Nothing here is evaluated as true or false.

The system operates on:

variation and constraint
potential and admissibility
coherence under pressure

holds only within the tension of the situation. If the parent is close, the structure stabilizes toward warmth; if the parent is separate, it re-stabilizes toward cold. This structure does not fix a result. Y and X adjust within the situation, allowing a resolving position to form as conditions change.

The terms do not carry meanings. They perform.
Each acts as a polarity of intensity—more or less cold, more or less warm—shifting with the situation. These shifts are not locked together. One can increase while the other does not, or both can recede. The structure adjusts without fixing a single outcome.

The advantages of this dynamic structure become clearer as its components are introduced.

This is not homeostasis; it is orientation—maintaining coherence under changing conditions without producing meaning.

Meaning is not present. It becomes possible only after this structure holds.

This holding is not instantaneous. It persists under pressure through a lagging anchor that carries the structure across changing conditions.

Why it is misread

The structure uses familiar words.

This creates a reflex: interpret immediately.

The mind attempts to resolve:

what “cold” means
what “warm” means
what relation is being asserted

So the example is pulled back into semantics:

the baby is cold
the baby wants comfort

This is already too late.

The structure has been misread.

Once that happens:

the quadranym becomes a statement.

The operative layer disappears.

Words as performers, not meanings

The words inside a quadranym do not function as definitions.

They function as performers.

They occupy roles within a structured tension. Their identity is secondary to their placement.

In:

“Cold” and “Warm” mark opposing poles.
“feeling” specifies the anchor in situ.
“comfort” marks the resolving position.

None of these are meanings yet.

They are positions in a tension that is being organized.

What must be held

The quadranym is not a semantic relation.

It is:

a pre-semantic configuration of tension, expressed through role-performers, which only become meaningful when taken up within a situation.

If this is not held here, it will not be recovered later.

Everything that follows depends on maintaining this distinction.

2. Grounding in Experience: Tension Before Meaning

Section 1 showed that the quadranym operates prior to meaning.

The example:

did not describe a situation. It showed a structure adjusting under tension.

This section makes that structure explicit.

From tension to polarity

The infant case shows where this structure comes from.

Being held:

warmth
proximity
contact

Being put down:

coolness
distance
separation

There are no concepts here.

Only differences:

near ↔ far
warm ↔ cold
held ↔ released

These are not meanings. They are felt differences structured as tension.

From polarity to stability

With repetition, these differences align:

near, warm, held → cohere
far, cold, released → cohere

This is not categorization.

It is co-orientation under repeated tension.

Over time, stable poles form:

warm / near
cold / far

These are not labels.

They are stable orientations.

From stability to structure

At this point, experience is no longer a sequence of contrasts.

It becomes a distribution:

more warm or more cold
more near or more far

The system is not interpreting.

It is positioned.

This is the condition that the quadranym renders.

Introducing orientation grammar

This requires a different kind of grammar.

Not a grammar of language—but a grammar of orientation.

In a language grammar:

words carry meaning
structure organizes those meanings

In an orientation grammar:

positions come first
structure organizes tension
meaning is not present

The quadranym belongs to this second kind.

It does not arrange meanings.

It arranges positions within tension.

Canonical and dynamic forms

The structure seen in Section 1 can now be clarified.

Agent:

This form does not describe a situation. It defines invariant roles.

self anchors the structure
goal marks the resolving position
Positive and Negative organize the tension between them

The example:

is a dynamic instance.

“feeling” performs under self; it does not replace it
“comfort” performs under goal
“Cold” and “Warm” perform under the tension roles

The structure remains.

The performers change.

Why this matters

The quadranym does not impose structure on meaning.

It formalizes structure that already exists.

So when we write:

the words are not introducing meaning.

They attach to a structure already formed through experience.

What has been shown

The system begins with:

tension
polarity
stabilization through repetition

From this:

stable orientations form
structured resolution becomes possible
and only then does meaning attach

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3. Introducing HQ: The Field of Ideal Tensions

Section 1 showed a structure operating prior to meaning.
Section 2 clarified that structure as an orientation grammar.

This section shows how that structure persists as a field and resolves as events.

remains the working form.

It is not reintroduced. It is carried forward.

The governing principle

The field and the event use the same roles differently.

Everything that follows is a clarification of this.

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HQ as a field

HQ is a continuous polarity field.

It is not a structure of meanings. It is not a collection of relations.

It is a field in which invariant roles are distributed as continuous conditions.

It is organized across two dimensions:

• modal polarity: Expansive ↔ Reductive
• statal progression: subjective → objective

In compact form:

This is not a semantic expression. It is a structural condition.

Roles are present across the field.

They are not assigned at points.

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The Prime Rendering Matrix

The structure of the field can be made explicit through a matrix.

Columns carry invariant roles.
Rows express realized instances.

Roles remain fixed across columns.

Instances vary across rows.

The field is the coherence across these rows through shared roles.

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Field behavior

Within HQ, polarity is coupled.

• more expansive implies less reductive
• more reductive implies less expansive

This is a zero-sum condition.

Intensity varies continuously across the field.

There are no discrete assignments.

Between poles:

• there are no role assignments
• only conditions of intensity

A position in the field reflects how roles are distributed.

It does not indicate which role is “active.”

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Layering

The field is organized in layers:

• General
• Relevant
• Immediate
• Dynamic

These are not coordinates.

They are bands evolving under shared role constraints.

Each layer develops under the same polarity structure, at different levels of specificity.

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Progression

Statal progression continues across the field:

• subjective → objective

This progression does not depend on polarity.

So:

• polarity defines the condition
• progression defines the movement

Different layers can resolve at different points along this progression.

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From field to event

If HQ distributes roles, resolution occurs locally.

An event is not a new structure.

It is a resolution within the field.

A resolving position forms under the conditions present.

No decision is made at the level of the field.

Only distribution.

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Return to the example

In the field:

• conditions shift toward cold and separation
• roles remain invariant
• layers evolve under those conditions

In the event:

• a resolving position forms
• “comfort” appears as the outcome of that resolution

The structure is not imposed.

It is revealed.

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Coupled and independent behavior

Within the field:

• polarity is coupled
• variation is continuous
• roles are distributed

Within an event:

• resolution can vary under those conditions
• outcomes are not fixed in advance

The same roles are present.

They are used differently.

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Closing

HQ is a field in which invariant roles are distributed as continuous conditions.
Events are local resolutions in which those same roles produce a determinate outcome.

The field and the event use the same roles differently.

4. Introducing QU: Event-Level Resolution

If HQ is the continuous field of Ideal tensions, then QU is where something actually happens.

HQ does not resolve—it only conditions.
QU is the moment where tension is taken up and stabilized into a specific outcome.

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QU as an event, not a field

QU is not a region or layer. It is:

a discrete event of resolution drawn from the HQ field

Formally:

• [Y(a) → X(b)]

But unlike HQ, this is not a distributed condition. It is:

• a localized act of closure
• a point where tension is resolved under constraint

So:

• HQ = continuous
• QU = discrete

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Where roles first appear

A crucial distinction:

Roles do not exist in HQ—they appear only in QU.

In QU:

• Y takes on a role (expansive / variation)
• X takes on a role (reductive / admissibility)
• a is the origin (ND-bearing)
• b is the constructed intersection

These are not just positions—they are functional roles in a resolving process.

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Dual bifurcation: independent modal axes

The defining feature of QU is that it breaks the zero-sum constraint of HQ.

Instead of a single coupled polarity:

• QU splits the system into two independent modal axes:
  • Y = expansive / potential indexing
  • X = reductive / actual indexing

This is dual bifurcation.

So:

• Y can increase or decrease independently
• X can increase or decrease independently

They are no longer locked in opposition.

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Why independence matters

Because resolution requires flexibility.

If QU inherited HQ’s zero-sum structure:

• increasing variation would automatically reduce constraint
• many situations would have no admissible closure

But with dual bifurcation:

QU can explore multiple configurations of variation and constraint simultaneously

This increases the degrees of freedom for finding a stable intersection (b).

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b is constructed, not selected

Another key point:

b does not exist beforehand.

In QU:

• b is the intersection produced under Y/X relative to a
• it becomes determinate only if the gate holds (ND ≥ PD + τ)

Until then:

• b is only a latent coordinate, not an actual point

So QU is not choosing between options—it is:

constructing a resolution under tension

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Relation to the HQ field

QU does not operate independently of HQ.

Instead:

each QU occurs within the environment of a specific tension condition in HQ

This can be stated clearly:

each QU layer evolves in the environment of the tension point of the modal Y axis it is on

So:

• HQ provides the tension landscape
• QU resolves locally within that landscape

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Example (infant case)

From the field:

• HQ: {X[self → comfort], Y: Cold ↔ Warm}

A QU occurs:

• [Cold(self) → Warm(comfort)]

This is not a statement—it is:

• a resolution attempt under imbalance (cold > warm)
• producing an SOP (expected restoration of warmth/comfort)

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summary

QU is a discrete resolution event where roles first appear. It operates with dual, independent modal axes (Y and X), allowing flexible construction of an intersection (b) under tension.

5. Clarifying HQ vs QU: The Critical Distinction

At this point, the most common errors arise—not from lack of definition, but from misalignment between HQ and QU. They share symbols, structure, and polarity, which creates a strong pull to treat them as directly comparable. They are not.

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No axis translation

Both HQ and QU use X and Y, but:

their axes are not equivalent and cannot be translated.

• In HQ:
  • X = statal progression (s → o)
  • Y = coupled polarity (E ↔ R)
• In QU:
  • Y = expansive / variation axis
  • X = reductive / admissibility axis

So:

• HQ.X ≠ QU.X
• HQ.Y ≠ QU.Y (functionally, even if polarity is inherited)

Any attempt to map them directly:

• collapses time into constraint
• or collapses polarity into indexing

This is a structural error.

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No roles in HQ points

A second mistake is treating HQ like a coordinate system with assignable roles.

But:

HQ points do not carry roles.

A position in HQ (e.g., “more cold than warm”) is:

• not a variable
• not an operator
• not a role

It is a field condition.

What exists at that position is:

a layer evolving under that tension

This must be held strictly:

HQ = conditions for evolution
not a system of role-bearing positions

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Roles appear only in QU

Roles emerge only when the system resolves:

• Y(a), X(b) are functional assignments
• they operate within a QU event

So:

• HQ distributes tension
• QU assigns roles and resolves it

Confusing this leads to:

• trying to “read” HQ like a QU
• or trying to “smooth” QU into a field

Both are incorrect.

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Reels exist only in QU

The distinction becomes sharpest with reels (indexing).

• In QU:
  • Y and X are independent axes
  • each can be indexed (more/less)
  • this allows fine-grained adjustment for closure
• In HQ:
  • polarity is zero-sum
  • axes are coupled
  • independent indexing is impossible

So:

HQ allows conflation at poles
QU allows independent modulation (reels)

This is why:

• HQ cannot “tune” cold and warm independently
• QU can adjust both Y and X separately to achieve closure

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The governing distinction

This can be stated cleanly:

• HQ
  • field
  • zero-sum polarity
  • layered evolution
  • no roles
  • no reels
• QU
  • event
  • dual bifurcation
  • role assignment
  • independent indexing (reels)
  • closure

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Why this matters

If this distinction is not held:

• HQ is mistaken for a resolution system
• QU is mistaken for a coordinate slice of HQ
• axis mappings become invalid
• the pre-semantic structure collapses into geometry or semantics

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Final compression

HQ provides the tension field without roles, while QU provides the role-based resolution with independent indexing. Their axes share notation but not function, and must never be translated directly.

6. Bringing in Hysteresis: Linking Field and Event

Up to this point:

• HQ provides the field of Ideal tensions
• QU provides discrete resolution events

What connects them—what ensures continuity rather than fragmentation—is hysteresis.

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Hysteresis as persistence under pressure

Hysteresis is not just a condition at resolution. It is:

the persistence of coherence (ND) in the presence of pressure (PD)

This persistence operates across both scales:

• locally, at the point of resolution
• globally, across the evolving field

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Local hysteresis: the QU gate

At the level of QU, hysteresis appears as the gate condition:

• ND ≥ PD(b) + τ

This determines whether a proposed intersection (b) can stabilize.

So at each QU:

• variation (Y) proposes
• constraint (X) tests
• hysteresis decides:
  • if coherence holds → closure occurs
  • if not → no resolution (or reconfiguration)

This is local hysteresis:

a test of whether this specific resolution can hold

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Global hysteresis: HQ persistence

But this local test only makes sense because something is being preserved across events.

In HQ:

• the origin (a) persists across statal progression
• polarity structure remains stable across layers

This is global hysteresis:

the continuity of the field and its anchor over time

It governs whether the system:

• stays within the same orientational regime
• or shifts to a new one

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Regime distinction

This gives two outcomes:

If hysteresis holds globally:

• the anchor persists
• QU closures reinforce the same structure
• the system undergoes re-anchoring
  • a′ = a over b
  • same prime, same script

If hysteresis fails:

• the anchor cannot hold
• the field reorganizes
• the system undergoes re-priming
  • a′ = b under a new prime

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How HQ and QU are linked

This can be stated directly:

• QU tests hysteresis locally
• HQ maintains (or loses) it globally

So:

• each QU is a local attempt to stabilize coherence
• HQ is the ongoing record of whether that coherence persists

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Return to the infant example

• Being put down increases pressure (cold > warm)
• A QU occurs (crying as resolution attempt)

If the parent returns:

• coherence is restored (warm/near)
• hysteresis holds
• the script stabilizes

If not:

• pressure exceeds coherence
• the system destabilizes
• a new configuration may form

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Why hysteresis matters

Without hysteresis:

• each QU would be isolated
• no continuity across events
• no formation of scripts or expectations

With hysteresis:

local resolutions accumulate into coherent trajectories

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Final compression

Hysteresis operates at two levels:

• Local (QU): gate for individual closures
• Global (HQ): persistence of coherence across the field

Together, they ensure that resolution is not just possible, but stable over time.

7. Closing with DC vs SC: Coherence and Truth

With HQ, QU, and hysteresis in place, the final distinction completes the system:

the separation—and eventual coupling—of Dynamical Context (DC) and Situational Context (SC).

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DC: coherence without meaning

Dynamical Context (DC) is the domain of everything described so far:

• HQ (field of tensions)
• QU (resolution events)
• hysteresis (persistence and gating)

DC operates entirely at the pre-semantic level.

It does not deal with:

• truth
• reference
• propositions

Instead, it governs:

coherence — whether a configuration holds under tension

So in DC:

• Y and X organize variation and constraint
• a anchors coherence (ND)
• b is constructed if admissible

But nothing here is “true” or “false.”

SC: truth without tension

Situational Context (SC) is where meaning appears:

• descriptions
• claims
• narratives

This is where statements like:

• “the baby cries when put down”

exist and can be evaluated.

SC deals with:

truth conditions — whether something is the case

But SC does not generate coherence. It:

• does not resolve tension
• does not construct b
• does not enforce hysteresis

It only evaluates what is presented to it.

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SOP: the bridge between DC and SC

The connection between these two domains is the SOP (Satisfied Objective Potential).

From DC:

• a QU closure produces:
  • b, an intersection under Y/X
  • structured as a pre-semantic output

This output is:

objective in form, but not yet truth-evaluable

This is the SOP.

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Transition from coherence to truth

When the SOP is passed to SC:

• it becomes a candidate for meaning
• it can be:
  • affirmed
  • rejected
  • described

So:

• DC → produces coherent structure
• SC → evaluates truth of that structure

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Why the separation matters

If DC and SC are collapsed:

• coherence is mistaken for truth
• truth is mistaken for coherence
• the system becomes unstable

Keeping them separate allows:

• flexible construction (DC)
• rigorous evaluation (SC)

And their coupling only occurs:

when coherence is strong enough (ND ≥ PD + τ) to present a stable candidate

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Return to the example

In the infant case:

• DC:
  • cold > warm tension
  • QU closure (cry)
  • SOP: expected restoration (warm/near)
• SC (observer level):
  • “the baby cries when put down”

The infant operates entirely in DC.
The observer describes in SC.

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Final compression

• DC = coherence (pre-semantic, tension-based, constructive)
• SC = truth (semantic, evaluative, descriptive)
• SOP = bridge (coherent output made available for truth evaluation)

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Closing statement

The quadranym does not produce meaning—it produces coherent structures under tension. Only when these structures cross into situational context do they become candidates for truth.