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PCAM-24: A Phase-Centric Action Model for Deterministic Interactive Simulation

Abstract

This paper introduces PCAM-24 (Phase-Centric Action Model), a simulation model in which discrete phase—rather than continuous time—is the authoritative coordinate for action progression, interaction adjudication, and cross-system synchronization. PCAM-24 defines actions as cyclic phase processes within a fixed modular phase space and expresses all gameplay-relevant semantics (e.g., hit windows, invulnerability, cancels, transitions) as phase membership.

By elevating phase to a first-class primitive, PCAM-24 eliminates timing inference between subsystems, simplifies deterministic networking, and provides a shared semantic language for animation, combat, AI, and tooling. The model is particularly suited to real-time interactive simulations where perceived fairness, explainability, and determinism are critical.

1. Introduction

Modern interactive simulations—especially games—coordinate multiple subsystems that each operate on their own notion of time. Animation systems advance clip time, combat systems evaluate frame-based windows, AI systems reason in ticks, and networking layers reconcile wall-clock deltas. While effective in practice, this fragmentation produces systemic problems:

  • Desynchronization between animation and gameplay outcomes.
  • Brittle timing logic expressed in floats or frame counts.
  • Ambiguous interaction adjudication under latency.
  • Difficulty explaining or debugging why a given outcome occurred.

PCAM-24 proposes a different foundation: replace time as the primary semantic coordinate with discrete phase. Rather than asking "when did something happen?", PCAM-24 asks "what stage of the action is occurring?"

2. Core Concept

2.1 Phase Space

PCAM-24 defines a fixed, cyclic phase space:

\[\text{Phase} \in \mathbb{Z}_{24} = \{0, 1, \dots, 23\}\]

Phase advances discretely and wraps modulo 24. Phase progression is monotonic and integer-valued; partial phases and fractional authority are disallowed.

The choice of 24 phases reflects a balance between expressive resolution and cognitive tractability. It provides sufficient granularity to model nuanced action stages while remaining small enough to reason about as a complete cycle.

2.2 Actions

An action is the atomic unit of interactive intent (e.g., attack, dodge, parry, block). Each action owns:

  • A current phase value.
  • A phase progression rule.
  • A set of named phase windows.
  • Deterministic transition rules.

An action is not measured in seconds. It progresses through semantic stages defined by phase.

3. Phase Windows and Semantics

A phase window is a named subset of the phase space. Formally, each window is a set:

\[W \subseteq \mathbb{Z}_{24}\]

Examples include:

  • ACTIVE: Phases during which an attack can deal damage.
  • INVULN: Phases during which damage is negated.
  • PARRY_PERFECT: Phases during which a parry fully succeeds.
  • RECOVERY: Phases during which vulnerability or restrictions apply.

All authoritative gameplay decisions are reduced to window membership tests. Time, frame count, or animation normalized time are never authoritative inputs.

4. Phase Authority

PCAM-24 enforces several non-negotiable axioms:

  • Phase is authoritative: Phase is the sole coordinate for ordering, gating, and adjudication of actions and interactions.
  • Discrete semantics: All gameplay-relevant logic must be expressible as phase membership or phase-gated transitions.
  • Monotonic progression: Phase advances monotonically on the cyclic ring. Rewinds are prohibited; corrections occur by snapping phase or restarting actions.
  • Subsystem subscription: Subsystems (animation, combat, AI, VFX, audio, UI) observe phase and windows but do not advance or reinterpret them.
  • Interaction resolution by phase: Cross-entity interactions are resolved exclusively through phase-defined rules and explicit precedence.

5. Action Lifecycles

PCAM-24 categorizes actions by lifecycle semantics:

  • Impulse actions (e.g., melee attack): Progress once through the phase cycle and terminate.
  • Sustained actions (e.g., block hold): Loop through phases while input is maintained.
  • Reactive actions (e.g., parry): Feature narrow success windows and defined failure recovery.
  • Evasive actions (e.g., dodge roll): Include invulnerability or mitigation windows and phase-driven movement.

Each action must explicitly define what phase wrap means (termination, loop, or clamp), preventing ambiguous lifecycle behavior.

6. Cancels, Transitions, and Buffering

Action transitions—such as cancels, combos, or state changes—are phase-gated:

  1. Cancels are allowed only within defined windows.
  2. Inputs may be buffered and consumed deterministically when entering valid windows.
  3. If multiple transitions are eligible simultaneously, a deterministic priority rule resolves the outcome.

This replaces ad-hoc frame windows and timing constants with inspectable, authorable phase logic.

7. Interaction Adjudication

PCAM-24 requires explicit precedence for contested interactions. A canonical ordering is:

  1. Evasion (e.g., invulnerability windows)
  2. Perfect defense (e.g., parry)
  3. Mitigating defense (e.g., block)
  4. Hit (full effect)

When an attack intersects a defender, the outcome is determined by the defender’s current action and phase windows—not by animation timing, render order, or wall-clock arrival.

This makes outcomes deterministic, explainable, and consistent under network conditions.

8. Networking and Determinism

PCAM-24 is inherently network-friendly because it replicates phase, not time.

  • Network replication transmits action identifiers, phase values, and any start-captured parameters.
  • Clients may predict locally by advancing phase using the same rules.
  • Reconciliation is performed by snapping phase to authoritative values, optionally with bounded grace policies expressed in phase units.

No reconstruction of exact elapsed time is required.

9. Tooling and Explainability

A PCAM-24 system is only viable if its semantics are visible. Tooling must allow inspection of:

  • Current action and phase.
  • Active phase windows.
  • Eligible transitions and their conditions.
  • Recent interaction outcomes.

By making phase explicit, PCAM-24 transforms timing bugs from opaque artifacts into inspectable state.

10. Benefits and Implications

PCAM-24 offers several advantages over time-centric models:

  • Consistency: Animation, combat, AI, and networking share a single semantic clock.
  • Determinism: Discrete phase eliminates floating-point drift and ambiguous comparisons.
  • Explainability: Outcomes can be justified directly by phase membership.
  • Authorability: Designers reason in semantic stages rather than frames or milliseconds.
  • Extensibility: New systems subscribe to phase without redefining timing logic.

11. Non-Goals

PCAM-24 does not attempt to:

  • Replace continuous physics solvers.
  • Reform civil or real-world timekeeping.
  • Mandate a specific engine or update loop.
  • Eliminate all uses of real time in rendering or presentation.

It defines only what is authoritative for interaction semantics.

12. Conclusion

PCAM-24 reframes interactive simulation timing from a question of when to a question of what stage. By elevating discrete phase to a first-class primitive, it provides a unifying semantic substrate across subsystems that are traditionally decoupled and inference-driven. The result is a model that is deterministic, inspectable, and aligned with how players perceive actions—not as durations, but as stages of intent.

PCAM-24 is not an optimization of existing timing systems. It is a replacement of their underlying assumption.