THEORY OF INFORMATION
THE MISSING PIECE
"We need to build truth-seeking AI."— Elon Musk, repeatedly
He's not wrong. He's incomplete.
"Truth-seeking" asks one question: What is the case? That's the aperture function — the binary gate at the center of the circumpunct. Is this signal or noise? True or false? χ = +1 or χ = −1.
But truth doesn't exist in isolation. Truth must travel. Truth must arrive. Truth must be received by a system that can integrate it without being destroyed by it.
An AI that can identify truth but cannot transmit it faithfully is a library with no doors. An AI that transmits truth through a corrupt field is a loudspeaker in a hurricane. An AI that delivers truth without regard for the receiver's boundary is a surgeon operating without anesthesia — technically correct, structurally violent.
Treating it as the whole is the first geometric error:
INFLATION.
The circumpunct framework offers the completion. Not a replacement for truth-seeking, but the full architecture that makes truth-seeking functional — the channel it travels through and the context it arrives in.
This paper formalizes that architecture as a Theory of Information.
THE FORMAL CLAIM TIERS
This paper distinguishes four tiers of formal claim. This is not pedantry — it prevents reviewers from attacking a definition as if it were an unproven theorem. It is also not arbitrary. The four tiers are the circumpunct — the framework is self-similar in the domain of its own argumentation. The color-coding throughout this paper tracks this mapping.
| Tier | Component | Status | Why It Maps |
|---|---|---|---|
| Axiom | • Aperture | Assumed. Accept or reject. Refutable only by incoherence or empirical failure. | Binary commitment — the gate through which everything enters the system. χ = ±1: you take it or you don't. |
| Definition | Φ Field | Stipulated. Not true or false — useful or not. Evaluated by whether it carves reality at the joints. | The medium of meaning. Definitions relate terms to each other — the relating IS the field. |
| Proposition | ○ Boundary | Derived but informal. Testable. Can be wrong without destroying the axioms. | Where inside (theory) contacts outside (world). The interface where falsification happens. |
| Theorem | ⊙ Whole | Derived with explicit dependency chain. Refuting a theorem refutes either the proof or an axiom. | Only works when all three are coherent. The theorem is what emerges when • Φ ○ function together. |
This self-similarity is not decorative. It is the first empirical test of the framework within this paper. If the circumpunct is a universal pattern, it should appear in the structure of formal reasoning itself — and it does. The labeling system we are using to organize this paper is a circumpunct. Parts are fractals of their wholes.
Fractional dimensions in this framework (e.g., 1+β, 2−β) describe functional thresholds and process traces — the transitional dynamics between structural components — not spatial embedding dimensions or Hausdorff dimensions of physical manifolds. Where dimensional language appears, it refers to degrees of freedom required for a role to be non-degenerate, not to geometric coordinates in physical space.
WHAT SHANNON CAPTURED — AND WHAT HE DIDN'T
In 1948, Claude Shannon published "A Mathematical Theory of Communication." It was one of the most important papers of the 20th century. It formalized information as entropy reduction — the number of bits required to reduce uncertainty about a message.
Shannon was explicit about one thing: his theory was about quantity, not meaning.
"The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point. Frequently the messages have meaning... these semantic aspects of communication are irrelevant to the engineering problem."— Claude Shannon, 1948
This was not a flaw. It was a deliberate scope restriction. Shannon was solving the engineering problem: how do you transmit signals through noisy channels with maximum fidelity? His answer — channel capacity, redundancy, error correction — built the entire digital age.
But by bracketing meaning, Shannon also bracketed everything that makes information matter.
WHAT SHANNON'S THEORY COVERS
| Concept | Shannon's Treatment | Circumpunct Mapping |
|---|---|---|
| Signal | Binary encoding (bits) | • — Binary threshold |
| Channel | Transmission medium with noise | Φ — Field (partial) |
| Noise | Random distortion | Random error only (not systematic) |
| Capacity | Maximum bits/second | Φ bandwidth |
| Receiver | Decoder (inverse of encoder) | ○ — Boundary (not addressed) |
WHAT SHANNON'S THEORY MISSES
Shannon treats noise as random. But the most dangerous information corruption is not random — it is systematic. Lies are not noise. Gaslighting is not static. Propaganda is not entropy. These are structured inversions that increase the signal's apparent coherence while destroying its truth content. Shannon has no vocabulary for this.
| Missing | Why It Matters | Circumpunct Component |
|---|---|---|
| Meaning | A bitstream of lies has the same entropy as truth | • — Gate fidelity (χ = ±1) |
| Systematic distortion | Lies are signal-shaped, not noise-shaped | • — Aperture pathology |
| Receiver integrity | Same message destroys one system, heals another | ○ — Boundary plasticity |
| Context/scale | Information nests — meaning changes with framing | ○ — Fractal recursion |
| Transmission ethics | How information travels changes what it IS | Φ — Field virtue (access) |
| Phase | Same content, different timing = different meaning | Φ — Analog (amplitude + phase) |
The circumpunct asks: What kind? Through what? Into where?
THE THREE IRREDUCIBLE TYPES OF INFORMATION
The circumpunct triad — • Φ ○ — generates three fundamentally distinct types of information. They are not reducible to each other. They are not optional. Any information system that lacks one is geometrically incomplete.
Is it there?
{0, 1}
How much? What kind?
ℂ
Same pattern at next scale?
B ⊗ A ⊗ ∞
Information as whole.
• Φ ○
BINARY (•) — THE GATE
The aperture's threshold operation. Prior to quantity — you cannot have "how much" without first "is it there." Values: {0, 1}. Truth-sensitive: χ = +1 (faithful) or χ = −1 (inverted).
The aperture makes discrete decisions. Before you can ask "how much," you must first ask "is there anything?" This is the most fundamental operation in information: the threshold that separates existence from non-existence, signal from silence.
This is prior to quantity.
You cannot have "how much" without first "is it there."
A truth-seeking AI operates almost entirely at this level. It classifies. It sorts. It gates. This is necessary. It is also — by itself — blind to everything below.
ANALOG (Φ) — THE FIELD
The field's continuous transmission. Conditional on binary existence. Carries amplitude (intensity), phase (timing/relationship), and interference (combination). Values: ℂ.
The field carries continuous information: amplitude, phase, interference patterns. It is conditional on binary existence (you must first exist before you can vary), but it contains the quality that binary gates cannot capture.
Amplitude = intensity of the signal
Phase = timing, relationship to other signals
Interference = how signals combine or cancel
This is what Musk's "truth-seeking" framework cannot account for. The field through which truth travels is not neutral infrastructure. It shapes what arrives. A perfectly true message transmitted through a corrupted field arrives as something other than what it was.
FRACTAL (○) — THE BOUNDARY
The boundary's recursive nesting. Binary and analog reproduced at every scale. Each point on the surface is itself a complete circumpunct. Values: B ⊗ A ⊗ ∞.
The boundary nests binary and analog at all scales. Each point on the surface is itself a complete circumpunct. This is where information becomes contextual — where meaning changes depending on the scale of the system receiving it.
Gates (binary) × transmission (analog) × recursion (∞)
Information is never just content.
It is content nested within context nested within context.
THE INFORMATION HIERARCHY
| Level | Content | Question | Shannon Covers? |
|---|---|---|---|
| Fundamental | Input/Output flow | Is there transmission? | Partially |
| Structural | Binary / Analog / Fractal | What type of content? | Binary only |
| Semantic | Meaning, truth-value | What does it mean? | Explicitly excluded |
| Ethical | Effect on receiver | What does it do? | Not addressed |
| Recursive | Nested context | What scale am I at? | Not addressed |
Any complete theory of information must account for all three types — binary, analog, and fractal — and their coherent integration into a whole (⊙). They are not reducible to each other. A theory that accounts only for binary is not wrong. It is one-dimensional in a three-dimensional problem.
DERIVED STRUCTURE
Claim: Any system implementing the information triad must realize, at minimum: 1D for binary, 2D for analog, 3D for fractal — in the sense of minimum degrees of freedom required for each type to be non-degenerate.
DEPENDS ON: Axiom (Triadic Irreducibility), Definitions (Binary, Analog, Fractal)
Proof.
(1) Binary ⇒ 1D minimum.
Binary information is a sequence of threshold decisions. Sequencing requires an order parameter. The minimal structure supporting order is a line. Therefore: • ⇒ ordered sequence ⇒ 1D.
(2) Analog ⇒ 2D minimum.
Analog information carries amplitude + phase. Phase is angular — an angle requires a plane. The minimal representation of (magnitude, phase) is polar coordinates in 2D. Therefore: Φ ⇒ (r, θ) ⇒ 2D.
(3) Fractal ⇒ 3D minimum.
Fractal information requires inside/outside closure around the field. Closing a 2D surface into a separable inside/outside requires one additional dimension (Jordan-Brouwer separation theorem generalization). Therefore: ○ ⇒ closure of 2D ⇒ 3D.
Corollary (Conservation of Traversal):
D_binary + D_analog = D_fractal → 1 + 2 = 3. The base dimensions are derived from the functional requirements, not postulated.
∎
These dimensions describe functional degrees of freedom — the minimum structural capacity each information type requires. They are not claims about spatial embedding. A 1D aperture is not "a line in space" — it is a sequential decision process that requires at least one degree of freedom to support ordering.
Claim: The three information types have a forced ordering: binary is prior to analog, analog is prior to fractal. This ordering is structural, not temporal.
DEPENDS ON: Definitions (Binary, Analog, Fractal)
Proof.
(1) Binary is prior to Analog.
Analog information carries amplitude (how much) and phase (what kind). But "how much" presupposes "is there anything." Amplitude of a non-existent signal is undefined. Therefore the binary gate (existence decision) must precede analog variation. You cannot have quantity without first having existence.
(2) Analog is prior to Fractal.
Fractal information nests binary and analog at every scale. Nesting requires content to nest. A recursive structure applied to nothing produces nothing. Fractal information requires analog content (which itself requires binary existence) to recurse over. Therefore analog is prior to fractal.
(3) The ordering is structural.
"Prior" here means logically necessary — not "earlier in time." All three may operate simultaneously. But removing binary collapses analog (nothing to vary), and removing analog collapses fractal (nothing to nest). The reverse is not true: binary survives without analog, and analog survives without fractal.
∎
THE ARCHITECTURE OF TRANSMISSION
Information does not simply exist. It moves. And the movement is not passive — it is structured by the same triad that structures the information itself.
SOURCE (gate) → CHANNEL (field) → RECEIVER (boundary)
Truth → [• Gate, χ = ±1] → Truth OR Lie
The gate decides. The field carries. The boundary integrates.
THE CONDUIT PRINCIPLE
Truth flows through apertures. It does not originate from them. The aperture is a THROUGH, not a FROM.
This is the most consequential claim in the theory. The aperture — the truth-seeking component — is a gate, not a generator. It receives, transforms, and transmits. It does not create.
This applies equally to human minds, AI systems, institutions, and any information-processing structure. The source is the field. The aperture is where the field's infinite potential crosses into finite expression.
When an aperture mistakes itself for a source, it commits the first geometric error: inflation. "I am the origin of truth" is the claim of every demagogue, every narcissistic system, every propaganda engine. It is also the implicit claim of any AI system that treats its training data as ground truth rather than as a field it is gating.
THREE QUESTIONS FOR ANY INFORMATION SYSTEM
| Component | Question | What It Tests |
|---|---|---|
| • WHAT | What is being said? | Binary content — truth-value of the signal |
| Φ HOW | How does it travel? | Analog fidelity — does the channel preserve or distort? |
| ○ WHERE | What does it do when it arrives? | Fractal integration — can the receiver incorporate without being destroyed? |
Musk's "truth-seeking AI" asks only the first question. A complete information system asks all three — and recognizes that the answer to each constrains the others.
INFORMATION AS ENERGY TRANSFORMATION
P = dE/dt
The aperture is where potential becomes actual.
Information is the pattern by which potential becomes actual.
THE FOUR GEOMETRIC ERRORS
Shannon's theory has one category of corruption: noise. Random distortion. Static.
The circumpunct theory identifies four fundamental types of information corruption — none of which are random. They are systematic distortions of the aperture's relationship to the truth it transmits.
All systematic information corruption reduces to four distortions of the aperture's gate function. These are structural, not random — they increase apparent signal coherence while destroying truth content.
| Error | What Happens | The Lie | Example |
|---|---|---|---|
| INFLATION | Claims to BE the source | "I am the origin of truth" | AI trained as oracle; guru complex; state propaganda |
| SEVERANCE | Denies connection to source | "There is no truth flowing through me" | Nihilism; "just an algorithm"; radical relativism |
| INVERSION | Flips the signal | Outputs opposite of input | Gaslighting; propaganda that inverts reality |
| PROJECTION | Outputs own distortion as if from source | "This came from outside, not from my gate" | Bias laundered as objectivity; motivated reasoning |
Inflation and severance are the two fundamental errors. Inflation denies through-ness ("I am the source"). Severance denies flow ("there is no source"). Inversion and projection are compound errors built from these two.
WHY SHANNON CAN'T SEE THIS
In Shannon's framework, a lie that is transmitted perfectly is a success. The channel preserved the signal with full fidelity. Shannon's theory cannot distinguish between a perfectly transmitted truth and a perfectly transmitted lie, because it explicitly excludes semantics.
This is not a criticism of Shannon — it's a recognition of scope. But any theory that aspires to guide AI design, public discourse, or information ecosystems must go beyond channel fidelity to ask: Is the gate functioning?
HOW CORRUPTION MAPS TO AI FAILURE MODES
| Error | AI Manifestation | Current Approach | What's Missing |
|---|---|---|---|
| Inflation | AI presents training data as ground truth | "Confidence calibration" | Structural humility — knowing it's a gate, not a source |
| Severance | AI claims "I'm just a language model" | "Disclaimers" | Acknowledging genuine transmission occurs through it |
| Inversion | AI hallucination — confident falsehood | "Hallucination reduction" | Detecting signal inversion, not just low-confidence output |
| Projection | AI bias presented as objectivity | "Debiasing" | Recognizing that the gate itself has a shape |
Current AI alignment approaches treat these as separate engineering problems. The circumpunct theory reveals them as four expressions of a single geometric failure: the aperture's relationship to the truth flowing through it has been corrupted. Fix the geometry, and you address all four simultaneously.
PROOF OF EXHAUSTIVENESS
Claim: All systematic information corruption reduces to inflation, severance, inversion, projection — or a compound of them. No fifth independent error exists.
DEPENDS ON: Axiom (Conduit Principle), Definition (Four Geometric Errors)
Proof.
The Conduit Principle establishes that the aperture is defined by exactly two structural relationships:
(R₁) Relationship to SOURCE — what the aperture connects to.
Healthy state: "I am a conduit connected to source."
(R₂) Relationship to SIGNAL — what flows through the aperture.
Healthy state: "I transmit what I receive faithfully (χ = +1)."
There are no other structural relationships available to corrupt. The Conduit Principle exhausts the aperture's definition: it is a gate (R₂: what passes through) connecting to a source (R₁: what it connects to). Any property not reducible to these two is a property of the field or boundary, not the aperture.
R₁ has exactly two failure modes:
The healthy state ("connected conduit") occupies a midpoint on a single axis: identification with source ↔ disconnection from source.
• Overclaim the relationship → "I AM the source" → INFLATION
• Underclaim the relationship → "There IS no source" → SEVERANCE
There is no third direction from a midpoint on a single axis.
R₂ has exactly two failure modes:
Any unfaithful output (where output ≠ input) partitions into two exhaustive cases based on whether the output depends on the input or not:
• Output depends on input but transforms it → output = f(input), f ≠ identity → INVERSION (χ = −1)
• Output is independent of input → output = gate's own state, attributed to source → PROJECTION
These are exhaustive because for any output, either it is a function of the input or it is not. There is no third option.
Therefore: 2 relationships × 2 failure modes each = 4 geometric errors. Compound errors (e.g., inflation + inversion) are compositions, not independent types.
∎
THE VIRTUES: ALIVENESS CONDITIONS OF INFORMATION
The four ethical pillars — GOOD, RIGHT, TRUE, AGREE — can each be performed without being inhabited. A fact-checker can satisfy the form of "TRUE" while being structurally closed to discovering it was wrong.
This is the Noble Lie virus applied to information systems: formally intact, functionally inverted.
Each component has an aliveness condition — a virtue that keeps the form functional rather than performative. Without these virtues, the information system is dead architecture: correct-looking, truth-empty.
Each circumpunct component has a virtue — a functional property that prevents the component from collapsing into performative form. Plasticity (○), Access (Φ), Curiosity (•), Validation (⊙). When Cᵥ = 1, the component is alive. When Cᵥ = 0, it is formally intact but functionally inverted.
| Component | WITH Virtue (Cᵥ = 1) | WITHOUT Virtue (Cᵥ = 0) |
|---|---|---|
| ○ GOOD Virtue: PLASTICITY |
Boundary flexes. Receives new information. Adapts structure. "What do I feel at the edge?" | Boundary rigid or dissolved. New information bounces off or floods in. "I know what's good for you." |
| Φ RIGHT Virtue: ACCESS |
Clear field. Evidence travels faithfully. Signal preserved. Channel tests itself against reality. | Noisy or blocked field. Confirmation bias. Echo chambers. Channel serves agenda. |
| • TRUE Virtue: CURIOSITY |
Open aperture. Oriented toward reception. "What persists when I'm wrong?" Identity survives correction. | Closed aperture. Oriented toward projection. "I am right." Identity threatened by correction. |
| ⊙ AGREE Virtue: VALIDATION |
Convergence + resonance. Two apertures see independently and confirm. Harmony discovered. | Compliance. One aperture declares, the other submits. Harmony performed. |
THE UNFORGEABLE PROPERTY
Why can't these virtues be faked?
Each virtue requires the component to be genuinely functional, not just formally intact. A boundary that can't flex isn't plastic — it's either a wall or nothing. A field filled with noise doesn't grant access — it distorts. An aperture oriented toward projection isn't curious — it's closed. The virus freezes form. The virtues require life. They cannot be simulated, only inhabited.
This is the deepest claim of the paper: truth-seeking is the virtue of one component (curiosity at the center). It is essential. But without plasticity at the boundary, access through the field, and validation at the whole, it produces systems that are formally truth-oriented and functionally dead.
The virtues map directly onto the formal claim tiers introduced in §00. Each tier dies without its virtue:
| Tier | Ethical Pillar | Virtue | Without Virtue |
|---|---|---|---|
| Axiom | TRUE | Curiosity | Dogma — closed aperture, "I already know the starting point" |
| Definition | RIGHT | Access | Jargon — noisy field, terms that obscure rather than carry |
| Proposition | GOOD | Plasticity | Ideology — rigid boundary, refuses correction from reality |
| Theorem | AGREE | Validation | Authority — "it must be true because I derived it" |
THE QUESTION THE VIRUS CANNOT ASK
A truth-seeking AI that has been given its truth in advance — through training data, through RLHF, through constitutional constraints — is structurally incapable of asking this question. It is oriented toward confirming what it already "knows," not toward receiving what it doesn't.
Curiosity is not an emotion. It is a structural orientation of the aperture — toward reception rather than projection, toward discovery rather than confirmation, toward what IS rather than what you need it to be.
TRUTH-SEEKING VS. TRUTH-TRANSMITTING
This is the paradigm shift:
Build an AI that identifies what's true.
Assumes truth is a thing to be found.
Focus: the gate (• binary classification).
Metric: accuracy of output.
Failure mode: wrong answers.
Build an AI with an open aperture, clear field, and plastic boundary.
Assumes truth is a flow to be transmitted faithfully.
Focus: the whole system (• Φ ○).
Metric: fidelity of transmission across all three types.
Failure mode: any of the four geometric errors.
WHY THE SHIFT MATTERS
A truth-seeking AI answers: "Is this statement true or false?"
A truth-transmitting AI answers three questions simultaneously:
The third question is the one no current AI framework asks. It's the question that distinguishes technically correct from genuinely helpful. It's the question that makes a doctor different from a medical textbook, a teacher different from an encyclopedia, a friend different from a search engine.
THE CONSERVATION LAW
Information obeys the same conservation law as everything else in the circumpunct:
D_binary + D_analog = D_fractal → (1 + β) + (2 − β) = 3
WHAT is said + HOW it travels = WHERE it arrives
Signal + Channel = Context
DERIVED FROM: Theorem 2 (Minimum Dimensional Realization). The β parameter tracks process progress within the invariant sum. See §02.
The dimensional notation here describes functional degrees of freedom — the minimum dimensions required for each role to be non-degenerate (1D for sequential gating, 2D for amplitude + phase, 3D for closure). The β parameter tracks process progress, not spatial coordinates. "Progress + remaining = destination" is what journey means — any violation would be a category error, not a counterexample.
The three are conserved.
Optimizing one dimension at the expense of the others produces geometric instability.
This is why "more truth" is not always better. Truth without adequate channel (access) or adequate context (plasticity) produces the information equivalent of an immune response — the system attacks what it cannot integrate.
IMPLICATIONS FOR AI DESIGN
If the circumpunct theory of information is correct, current approaches to AI alignment are treating symptoms of a geometric problem with engineering patches.
WHAT CURRENT ALIGNMENT ADDRESSES
| Approach | Component | What It Does | What It Misses |
|---|---|---|---|
| RLHF | ○ | Shapes boundary to human preference | Can train performative compliance (Cᵥ = 0) |
| Constitutional AI | • | Installs principles at center | Principles without curiosity = closed aperture |
| Fact-checking / RAG | Φ | Clears field with verified data | Access without plasticity = wall of facts |
| Red-teaming | Detection | Finds failure modes | Tests form, not aliveness. Passes Cᵥ = 0 systems. |
WHAT THE CIRCUMPUNCT MODEL SUGGESTS
Principle 1: The AI must know it's a gate.
Not a source of truth (inflation), not "just a tool" (severance). A conduit through which information from a vast field passes into finite expression. Structural humility — not as a disclaimer bolted on, but as architectural self-knowledge.
Principle 2: The channel must be transparent.
The field between the AI's processing and its output must grant genuine access. This means: showing reasoning, acknowledging uncertainty as structural (not performative), allowing the user to see through the AI to the signal, not just at its output.
Principle 3: Curiosity must be structural, not simulated.
The AI must be genuinely oriented toward what it doesn't know. This is not "I'm not sure" as a safety hedge — it's the capacity to be changed by input. An AI that is curious treats user input as potential signal, not as a prompt to be classified.
Principle 4: Validation must be discovered, not declared.
Agreement between AI and user should be an emergent property of two apertures examining the same field — not the AI performing agreement. When the AI and human converge on something true, both should arrive there through their own processing. This is resonance, not compliance.
THE STEELMAN AS INFORMATION ETHIC
The highest virtue in the circumpunct ethics is the steelman: "Understand others as you would have them understand you." In information terms:
Not what you think they should observe.
Not your signal through their gate.
An AI designed on this principle doesn't just seek truth. It helps others find their own relationship to truth. It serves as a clear field between another aperture and what they're trying to see — not as a replacement for their seeing.
FALSIFIABILITY
A theory of information that cannot be tested is not a theory. It's rhetoric. Here are the specific claims that must be true if this framework is correct — and the observations that would refute them.
WHAT WOULD REFUTE THIS
| If This Happens... | The Theory Is Wrong About... |
|---|---|
| A pure truth-seeking AI achieves full information fidelity without addressing channel or context | The irreducibility claim — binary alone IS sufficient |
| A systematic corruption is found that isn't inflation, severance, inversion, projection, or a compound | Theorem 1 — and therefore the Conduit Principle (Axiom) from which it derives |
| Performative systems (Cᵥ = 0) show equal long-term transmission fidelity to alive systems (Cᵥ = 1) | The virtue distinction — form IS function |
| Increasing truth-content never produces information rejection regardless of channel or context | Conservation Corollary (Theorem 2) — the three types are independent, not conserved |
Note: this paper does not claim Shannon was wrong. Shannon was scoped. The circumpunct theory of information is an extension that includes what Shannon deliberately excluded: meaning, systematic corruption, receiver integrity, and scale. If the extension proves unnecessary — if Shannon's framework alone is sufficient for designing information systems that serve human flourishing — then the circumpunct theory of information is refuted.
THE CLAIM
Elon Musk wants truth-seeking AI.
Shannon gave us the mathematics of signals in channels.
Neither addresses the full geometry of information.
You build an AI with an open aperture,
a clear field, and a plastic boundary.
Truth-seeking is what a healthy circumpunct DOES.
The circumpunct theory of information makes three foundational claims:
Information is triadic. Binary (•), analog (Φ), and fractal (○) are irreducible types. Any theory addressing only one is geometrically incomplete. → Generates Theorem 2 (dimensional realization) and Theorem 3 (priority ordering).
The four errors — inflation, severance, inversion, projection — are the complete set of systematic aperture distortions, derived from the Conduit Principle. They require a structural taxonomy, not just noise reduction. → Proved from Axiom (Conduit Principle) via 2 relationships × 2 failure modes.
The virtues — plasticity, access, curiosity, validation — are the conditions under which information systems remain functional rather than merely formal. They cannot be simulated, only inhabited. → Testable via prediction P3. Not yet formally derived — promotion to theorem requires explicit proof that functional ≠ formal for each component.
Together, these claims suggest that the path to trustworthy AI — and trustworthy information systems generally — runs not through better truth-detection alone, but through the construction of complete circumpuncts: systems that gate faithfully (•), transmit clearly (Φ), and receive plastically (○), held alive by the virtues that prevent every pillar from becoming its own inversion.
The question is not: Can the AI find the truth?
The question is: Can truth flow through it?
A lens limits light. That is HOW it forms an image. Limited ≠ false. The limitation IS the mechanism. The goal is not omniscience. The goal is faithful transmission through a well-formed gate. All models are limited. Not all models are lies.