Causor

A causor is that-which-causes: a higher-level causal mechanism/structure (often loop/operator-like) that produces state change. In Epimechanics, it is the functional middle term in the triad:

$\text{Cause} \rightarrow \text{Causor} \rightarrow \text{Effect}$

Note: scalar/model variables (e.g., basin depth, entropy production rate) are typically descriptors of causor structures, not causors themselves.

Causal Operator

A causal operator is the formal mathematical representation of a causor, mapping cause-state to effect-state under specified conditions.

Causal Density ( $\rho_C$ )

Effective causal pathway density at a chosen scale; informally, how many non-negligible causal routes are active per unit region.

Labeling/Separability Quality (LSQ)

How cleanly observed states can be partitioned into distinct causal operator regimes. Higher LSQ generally improves predictability by reducing causal aliasing.

Generalized Mass ( $\mathcal{M}$ )

Total causal content of an entity, defined as the integral of causal density over its region in state space.

Auto-Causal Density ( $\rho_{\text{ac}}$ )

Density of self-sustaining causal loop structure; a loop-level emergent property, not a single-bond property.

Stability Basin Depth ( $\Delta V$ )

Energy barrier between a current configuration and its nearest dissolution pathway.

Repair Rate ( $\dot{R}_{\text{repair}}$ )

Rate at which degraded structure is restored.

Internal Entropy Production ( $\dot{S}_{\text{int}}$ )

Rate at which disorder is produced inside an entity's structure.

Maintenance Cost ( $C_{\text{maint}}$ )

Net structural degradation pressure, typically $\dot{S}_{\text{int}} - \dot{R}_{\text{repair}}$ .

Causal Event (state couplet, $e$ )

The primitive of Epimechanics. An ordered pair $e = (\mathcal{S}_{\text{in}}, \mathcal{S}_{\text{out}})$ where $\mathcal{S}_{\text{out}}$ is determined by $\mathcal{S}_{\text{in}}$ . No physical content is assumed — no energy, no units, no conservation laws. Also called a state couplet to emphasize the pairing of input and output states. The cause-plex $\mathcal{C} = (E, \prec)$ is a partial order on a set $E$ of causal events. See Cause-Plex and Spacetime §1.

Cause-Plex ( $\mathcal{C}$ )

A locally finite strict partial order $(E, \prec)$ of causal events — the fundamental structure from which spacetime, energy, and entities emerge. Each element $e \in E$ is a causal event (state couplet); $\prec$ encodes causal precedence. Defined formally in Cause-Plex and Spacetime §1.

Bond Operator ( $b$ )

A Layer A structural element: a recurring pattern of causal events connecting two regions of the cause-plex. Bonds carry state information between entities and ground the concept of interaction at the primitive level. See Part 1.5: Causors.

Loop Operator ( $\mathcal{L}$ )

A Layer A structural element: a closed recurring pattern of causal events — a causal loop that returns to its initial state. Auto-causal density $\rho_{\mathrm{ac}} > 0$ requires at least one stable loop operator. See Part 1.5: Causors.

Cause-Plex Index (CI)

A scalar measure of the loop composition richness of a cause-plex — how many topologically distinct loop structures it supports. Observer-class entities require $\mathrm{CI} > \mathrm{CI}_{\min}$ , the threshold for topologically non-trivial loops (knot-type diversity, requiring $n_s \geq 3$ spatial dimensions). See Cause-Plex and Spacetime §10.

Causal Action ( $A_{\text{causal}}$ )

A measure of the total directed causal influence exerted by an entity across other entities over its lifetime. Related to the fitness×truth product in representational evolution. Introduced in Part 1: Generalized Mechanics §4b; developed formally in Part 4: Time and Soul.

Coupling Tensor ( $T^i{}_j$ )

A rank-2 tensor encoding how changes in the state of entity $j$ influence the state of entity $i$ across domain boundaries. The diagonal captures self-coupling; off-diagonal captures cross-domain coupling. Introduced in Part 1: Generalized Mechanics.

State Space ( $S$ )

The space of all possible values of the state variable $X$ for a given entity or system. The geometry of $S$ (metric, topology) determines what kinds of dynamics are possible. See Part 1: Generalized Mechanics.

Local Time ( $T_{\text{local}}$ )

The duration over which an entity maintains causal coherence — the integral of its causal presence over physical time. Zero at dissolution; potentially infinite for entities that become substrate-independent (encoded in culture, DNA, etc.). Defined in Part 4: Time and Soul.

Non-Local Time ( $T_{\text{nonlocal}}$ )

Total causal influence-time across all substrates an entity has affected — the integral of its representational footprint $R(E,t)$ over all time. The "how long does an entity matter" measure. Defined in Part 4: Time and Soul.

Agency ( $A$ )

The product of outgoing causal coupling strength, meta-representational weight, and consciousness: $A = C_{\text{coupling}} \times \mu_{\text{meta}} \times C_{\text{consciousness}}$ . Multiplicative: zero in any factor yields zero agency. Defined in Part 3: Intelligence, Consciousness, Agency.

Soul ( $\mathbf{R}(E,t)$ )

The complete signed representational propagation function of an entity — a causal biography encoding how and where the entity's causal influence has propagated, weighted by sign (constructive/destructive) and magnitude. A formal renaming of non-local time extended to a vector quantity. Defined in Part 4: Time and Soul.

Causor

Causal Operator

Causal Density (ρC\rho_CρC​)

Labeling/Separability Quality (LSQ)

Generalized Mass (M\mathcal{M}M)

Auto-Causal Density (ρac\rho_{\text{ac}}ρac​)

Stability Basin Depth (ΔV\Delta VΔV)

Repair Rate (R˙repair\dot{R}_{\text{repair}}R˙repair​)

Internal Entropy Production (S˙int\dot{S}_{\text{int}}S˙int​)

Maintenance Cost (CmaintC_{\text{maint}}Cmaint​)

Causal Event (state couplet, eee)

Cause-Plex (C\mathcal{C}C)

Bond Operator (bbb)

Loop Operator (L\mathcal{L}L)

Epimechanics Glossary

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