SYMBOL DICTIONARY

Exposure Theory (ET) and Signal Resolution Theory (SRT)

Core Flow

Dₜ → Aₜ → Jₜ → Wₜ → ◇ₜ → Yₜ → xₜ

Signal domain → Exposed signal set → Admissible configuration family → Engaged configuration → Resolution → Resolution output space → Operative input

I. EXPOSURE THEORY (ET)

Dₜ

Pronounced: “D sub t”
Name: Signal domain

Definition:
The total set of signals present at time t prior to exposure.

Ψₜ

Pronounced: “psi sub t”
Name: Exposure function

Definition:
Maps the signal domain to the exposed signal set.

Form:
Ψₜ : Dₜ → Aₜ

Aₜ

Pronounced: “A sub t”
Name: Exposed signal set

Definition:
The set of signals accessible to the system after exposure filtering.

Form:
Aₜ = Ψₜ(Dₜ)

Jₜ

Pronounced: “J sub t”
Name: Admissible signal configuration family

Definition:
The set of all exposed signal configurations admissible under the operative structural and interaction constraints at time t.

Form:
Jₜ = { j ⊆ Aₜ | j is admissible under Hₜ and Iₜ }

Thus:

Jₜ ⊆ PowerSet(Aₜ)

j

Pronounced: “j”
Name: Signal configuration

Definition:
An individual admissible signal configuration such that j ∈ Jₜ.

Hₜ

Pronounced: “H sub t”
Name: Structural constraint field

Definition:
The field of structural constraints governing admissibility of signal configurations, including capacity, compatibility, and co-presence relations.

Iₜ

Pronounced: “I sub t”
Name: Interaction regime state

Definition:
The operative interaction conditions under which configurations are admissible.

II. SIGNAL RESOLUTION THEORY (SRT)

Wₜ

Pronounced: “W sub t”
Name: Engaged signal configuration

Definition:
A single admissible configuration selected from Jₜ for engagement.

Form:
Wₜ ∈ Jₜ

In the paper this is also written structurally as:

Jₜ → Wₜ with Wₜ ∈ Jₜ

◇ₜ

Pronounced: “diamond sub t”
Name: Resolution operator

Definition:
Maps an engaged signal configuration to a non-empty set of admissible effective signal representations.

Form:
◇ₜ : Wₜ → Yₜ

with

xₜ ∈ ◇ₜ(Wₜ)

Yₜ

Pronounced: “Y sub t”
Name: Resolution output space

Definition:
The set of all admissible resolved representations produced from Wₜ.

xₜ

Pronounced: “x sub t”
Name: Effective signal representation

Definition:
The operative input passed downstream into the Algebra of Becoming.

System operation occurs on xₜ, not on Wₜ.

III. RESOLUTION AXIOMS

Non-emptiness

Pronounced: “non-emptiness”

Form:
Wₜ ≠ ∅ ⇒ ◇ₜ(Wₜ) ≠ ∅

Meaning:
If an engaged configuration exists, resolution yields a non-empty output.

Dependence

Pronounced: “dependence”

Form:
◇ₜ(Wₜ) depends only on Wₜ

Meaning:
Resolution is defined over the engaged configuration itself.

Non-identity (refined)

Pronounced: “non-identity”

Form:
◇ₜ(Wₜ) ≠ Wₜ

except in degenerate or identity-preserving systems.

Meaning:
Resolution is not generally identical to engagement.

Transformation

Pronounced: “transformation”

Form:
∃ xₜ ∈ ◇ₜ(Wₜ) such that xₜ ∉ Wₜ

(non-degenerate systems)

Meaning:
Resolution may produce an operative representation not identical to the engaged configuration.

IV. ENGAGEMENT REGIMES

W^(△)

Pronounced: “W triangle”
Name: Stochastic regime

Definition:
Engagement variation governed primarily by stochastic conditions.

W^(▽)

Pronounced: “W nabla” or “W down-triangle”
Name: Dynamic regime

Definition:
Engagement variation governed primarily by dynamic conditions.

W^(□)

Pronounced: “W square”
Name: Capacity regime

Definition:
Engagement variation governed primarily by capacity constraints.

W^(◇)

Pronounced: “W diamond”
Name: Meaning-modulated regime

Definition:
Engagement variation modulated upstream by meaning without evaluating candidate meanings.

ωᵣ

Pronounced: “omega sub r”
Name: Regime weight

Definition:
Weight assigned to regime r in a non-universal engagement representation.

Scoreᵣ(j)

Pronounced: “score sub r of j”
Name: Regime score

Definition:
The score assigned to configuration j under regime r in a non-universal engagement representation.

V. ENVIRONMENT

E

Pronounced: “E”
Name: Environment

Definition:
Shapes signal formation, exposure, and configuration admissibility upstream.

Upstream role:
E → Dₜ, Ψₜ, Hₜ, Iₜ

Downstream AoB role:
xₜ, σₜ, E → Qₜ

Boundary condition:
E does not directly select engagement, define resolution, or determine continuation admissibility Ωₜ.

VI. ALGEBRA OF BECOMING INTERFACE

σₜ

Pronounced: “sigma sub t”
Name: Realized system state

Definition:
The current realized state used downstream in candidate generation and continuation.

Qₜ

Pronounced: “Q sub t”
Name: Candidate meanings

Definition:
Generated candidate meanings in the Algebra of Becoming.

Form:
Qₜ = Gen(xₜ, σₜ ; E)

Qₜᴿ

Pronounced: “Q sub t R”
Name: Reference-compatible candidate meanings

Definition:
The subset of candidate meanings admissible under AoB reference conditions.

ADLₜ

Pronounced: “A D L sub t”
Name: Action Determinacy Loss

Definition:
The condition marking transition from determined to undetermined continuation.

Nₜ

Pronounced: “N sub t”
Name: Distinct candidate trajectory count

Definition:
The number of distinct candidate trajectories after collapsing equivalence under AoB ordering relations.

Ωₜ

Pronounced: “Omega sub t”
Name: Continuation space

Definition:
The set of admissible successor states defined in PoB/AoB.

Form:
Ωₜ = Ω(σₜ ; K)

K

Pronounced: “K”
Name: Constraint structure

Definition:
The structure governing continuation admissibility in PoB/AoB.

VII. NOTATIONAL CONVENTIONS

Subscript t

Pronounced: “sub t”

Indicates time index.

Set inclusion

⊆
Pronounced: “is a subset of”

Used to indicate admissible family inclusion, as in:

Jₜ ⊆ PowerSet(Aₜ)

Set membership

∈
Pronounced: “is an element of”

Used to indicate membership, as in:

j ∈ Jₜ
xₜ ∈ ◇ₜ(Wₜ)

PowerSet(Aₜ)

Pronounced: “power set of A sub t”

The set of all subsets of Aₜ.

VIII. CLOSURE

All ET and SRT processes terminate at:

xₜ

Candidate generation begins downstream in the Algebra of Becoming.

Interpretation becomes required only when the AoB activation condition holds:

ADLₜ = 1 AND |Qₜᴿ| ≥ 2 AND Nₜ ≥ 2