Kalpana: Resonant Interference Memory for O(1) Long-Context Sequence Modeling via Phase-Coded Holographic Dynamics

The fundamental bottleneck in scaling autoregressive Transformer sequence models is the memory wall imposed by the Key-Value (KV) cache, which scales linearly O(N) with sequence length. In this work, we present Kalpana, a constant-memory neural architecture centered on the Resonant Interference Field (RIF)—a bounded memory substrate that encodes sequence context through continuous Fourier phase-coded superposition in complex Hilbert space. Unlike token-indexed architectures that allocate linear physical memory registers, Kalpana maintains a strictly fixed-size state S in C^B x D, enabling exact O(1) memory scaling invariant to context depth. We formulate and evaluate Kalpana across two complementary paradigms: (1) Paradigm A (Native Attention Replacement), which replaces in-layer KV-cache buffers in RoPE-equipped models with continuous Fourier phase accumulators, flatlining cross-layer persistent memory at 48.00 MB (FP16) across sequences exceeding 3,000,000 tokens while preserving 100% multi-query associative recall (7.2 ms query latency); and (2) Paradigm B (Decoupled Memory Substrate), which equips unmodified pre-trained LLMs with an external holographic memory layer for long-document reasoning up to 100K+ tokens within a constant 6 MiB state. We derive the Spectral Packing Law, proving that retrieval capacity is bounded by spectral phase crowding (Gamma ≈ 12.21) rather than memory exhaustion, and prove that unitary phase conservation avoids the dissipative decay (rho(A) < 1) observed in State Space Models. Hardware profiling demonstrates 892,000 tokens/sec ingestion throughput, a 300x increase in concurrent GPU serving density, and local multi-million token execution via WebGPU on consumer edge devices.