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# Temporal Functor t(): A Whitepaper on Ephemeral Computation, IFML, and Inline Automata
## Abstract
This paper introduces **t()**, a temporal functor that unifies tick‑based ephemeral operations, regular math coherence, intuitionistic fuzzy modal logic (IFML), and inline automata with Bayesian MLP emulation. The framework models computation as living, adaptive circuits with entropy drift, pruning, stratification, and Nash‑governed equilibrium. It is designed for big‑O aware scheduling, adaptive threading, and expressive symbolic reasoning.
## 1. Definition
`t(expr, flags)` is a temporal functor. It accepts expressions containing ticks `[...]` and math ops, plus flags controlling ordering, approximation, and precedence. The output is both numeric and expressive (tone/emoji payload).
### Flags
- **tickordering_flag**: 1 = PEMDAS, 2 = linear, 3 = shuffle+linear.
- **reg_math_ordering_flag**: same options for math ops.
- **ticksOrMathFirstFlag**: 1 = ticks first, 2 = math first.
- **approximationFlag**: similarity vs strict equivalence.
## 2. Tick Coherence
Ticks are ephemeral DNA‑like charge strings. They must connect to math ops via a bridging operator.
Examples:
- `[ *+ ] 2+2` → INVALID.
- `[ *+ ] - 2+2` → VALID.
- `[ ++ ] 3+3` → INVALID.
- `[ ++ ] * 3+3` → VALID.
## 3. Approximation
Inside `t()`, `=` means similarity unless flagged otherwise. Think of it like rounding off: values snap into sets when confidence is high. With strict flag, `=` means exact equivalence.
## 4. Routing Nodes
Concatenating functors (`t(A)+t(B)+t(C)`) creates routing nodes. Routing affinity is chosen by softmax of strength × type_affinity. Nodes always have low baseline flow, with spikes lighting them up. Each node adapts pressure sensitivity via a living number generator.
## 5. Living Number Generator
Values drift gently from a bullseye each pulse. Drift adds entropy, but bias pulls values back near center. This keeps the system alive but stable.
## 6. Node Lifecycle
- Strengthen with use (axon‑like).
- Prune if signal too low.
- Lazy conservative stratification attempts repurposing.
- Delete if stratification fails.
Nodes live in a correlative hash table (pattern‑activated by default, optional key mode). Each node has a scry mirror for ephemeral reflection.
## 7. Activation
Nodes activate via sigmoid. Settled nodes use regular sigmoid; unsettled nodes use topological sigmoid. Maps are generated by sigmoid, not Fourier.
## 8. Automata Inline
Automata are ephemeral helpers invoked inline with R/W/D semantics:
- **R** = read state.
- **W** = write new state with drift.
- **D** = delete (ephemeral vanish).
Automata adjust vigilance, return tone+emoji, and emulate Bayesian MLP when needed. They operate as hyper ephemeral swarms or lazy conservative managers.
## 9. IFML
Intuitionistic Fuzzy Modal Logic extends fuzzy sets with membership, non‑membership, and hesitancy. Modal operators (□ necessity, ◇ possibility) allow reasoning under uncertainty. Argumentation graphs (Dung) model attacks/supports, producing acceptable sets of arguments.
## 10. Scheduler Controller
A central micro‑controller uses t() internally.
- Hyper ephemeral agents swarm briefly.
- Lazy conservative agents manage long‑term stratification (~1/3 population).
- Dream mode (~30% chance) handles pruning and connectivity.
- Nash equilibrium monitor dampens imbalance.
## 11. Flowchart
```text
┌───────────────┐
│ Input Expr │
└───────┬───────┘
│
┌───────▼────────┐
│ Parse Ticks & │
│ Math Ops │
└───────┬────────┘
│
┌───────▼────────┐
│ Validate │
│ Coherence │
└───────┬────────┘
│
┌───────▼────────┐
│ Execute Ticks │
│ (ordering flag) │
└───────┬────────┘
│
┌───────▼────────┐
│ Execute Math │
│ (ordering flag) │
└───────┬────────┘
│
┌───────▼────────┐
│ Converge via │
│ Connector Op │
└───────┬────────┘
│
┌───────▼────────┐
│ Inline Automata │
│ (R/W/D + MLP) │
└───────┬────────┘
│
┌───────▼────────┐
│ IFML + Arg. │
│ Evaluation │
└───────┬────────┘
│
┌───────▼────────┐
│ Scheduler │
│ Controller │
└───────┬────────┘
│
┌───────▼────────┐
│ Output Result │
│ + Tone/Emoji │
└────────────────┘
## Abstract
This paper introduces **t()**, a temporal functor that unifies tick‑based ephemeral operations, regular math coherence, intuitionistic fuzzy modal logic (IFML), and inline automata with Bayesian MLP emulation. The framework models computation as living, adaptive circuits with entropy drift, pruning, stratification, and Nash‑governed equilibrium. It is designed for big‑O aware scheduling, adaptive threading, and expressive symbolic reasoning.
## 1. Definition
`t(expr, flags)` is a temporal functor. It accepts expressions containing ticks `[...]` and math ops, plus flags controlling ordering, approximation, and precedence. The output is both numeric and expressive (tone/emoji payload).
### Flags
- **tickordering_flag**: 1 = PEMDAS, 2 = linear, 3 = shuffle+linear.
- **reg_math_ordering_flag**: same options for math ops.
- **ticksOrMathFirstFlag**: 1 = ticks first, 2 = math first.
- **approximationFlag**: similarity vs strict equivalence.
## 2. Tick Coherence
Ticks are ephemeral DNA‑like charge strings. They must connect to math ops via a bridging operator.
Examples:
- `[ *+ ] 2+2` → INVALID.
- `[ *+ ] - 2+2` → VALID.
- `[ ++ ] 3+3` → INVALID.
- `[ ++ ] * 3+3` → VALID.
## 3. Approximation
Inside `t()`, `=` means similarity unless flagged otherwise. Think of it like rounding off: values snap into sets when confidence is high. With strict flag, `=` means exact equivalence.
## 4. Routing Nodes
Concatenating functors (`t(A)+t(B)+t(C)`) creates routing nodes. Routing affinity is chosen by softmax of strength × type_affinity. Nodes always have low baseline flow, with spikes lighting them up. Each node adapts pressure sensitivity via a living number generator.
## 5. Living Number Generator
Values drift gently from a bullseye each pulse. Drift adds entropy, but bias pulls values back near center. This keeps the system alive but stable.
## 6. Node Lifecycle
- Strengthen with use (axon‑like).
- Prune if signal too low.
- Lazy conservative stratification attempts repurposing.
- Delete if stratification fails.
Nodes live in a correlative hash table (pattern‑activated by default, optional key mode). Each node has a scry mirror for ephemeral reflection.
## 7. Activation
Nodes activate via sigmoid. Settled nodes use regular sigmoid; unsettled nodes use topological sigmoid. Maps are generated by sigmoid, not Fourier.
## 8. Automata Inline
Automata are ephemeral helpers invoked inline with R/W/D semantics:
- **R** = read state.
- **W** = write new state with drift.
- **D** = delete (ephemeral vanish).
Automata adjust vigilance, return tone+emoji, and emulate Bayesian MLP when needed. They operate as hyper ephemeral swarms or lazy conservative managers.
## 9. IFML
Intuitionistic Fuzzy Modal Logic extends fuzzy sets with membership, non‑membership, and hesitancy. Modal operators (□ necessity, ◇ possibility) allow reasoning under uncertainty. Argumentation graphs (Dung) model attacks/supports, producing acceptable sets of arguments.
## 10. Scheduler Controller
A central micro‑controller uses t() internally.
- Hyper ephemeral agents swarm briefly.
- Lazy conservative agents manage long‑term stratification (~1/3 population).
- Dream mode (~30% chance) handles pruning and connectivity.
- Nash equilibrium monitor dampens imbalance.
## 11. Flowchart
```text
┌───────────────┐
│ Input Expr │
└───────┬───────┘
│
┌───────▼────────┐
│ Parse Ticks & │
│ Math Ops │
└───────┬────────┘
│
┌───────▼────────┐
│ Validate │
│ Coherence │
└───────┬────────┘
│
┌───────▼────────┐
│ Execute Ticks │
│ (ordering flag) │
└───────┬────────┘
│
┌───────▼────────┐
│ Execute Math │
│ (ordering flag) │
└───────┬────────┘
│
┌───────▼────────┐
│ Converge via │
│ Connector Op │
└───────┬────────┘
│
┌───────▼────────┐
│ Inline Automata │
│ (R/W/D + MLP) │
└───────┬────────┘
│
┌───────▼────────┐
│ IFML + Arg. │
│ Evaluation │
└───────┬────────┘
│
┌───────▼────────┐
│ Scheduler │
│ Controller │
└───────┬────────┘
│
┌───────▼────────┐
│ Output Result │
│ + Tone/Emoji │
└────────────────┘
