ARCHIVED 2026-07-28. Superseded by ptcna. This repo is retained read-only for provenance. Do not build against it.

pcta — Prime Circled Tensor Architecture (prime-tensor stack layer 2)

pcta (PCTA — Prime Circled Tensor Architecture) is the seed layer of The Interdependency's prime-tensor compute family. It covers circles carried by UCNS objects and composes them into seeds: it takes layer-1 (pcna) circle-tensors and organizes a variable number of them into a seed — and the seed is itself a tensor. The structural arrangement it produces ("motion") is folded into cores by PTCA (layer 3) and ultimately consumed by the inference cap (zfae, runtime in a0) together with pcna's trained weights.

PCNA (tensors → circles, backprop) ─► circles ─► PCTA (circles → seeds)
  ─► seeds ─► PTCA (seeds → core) ─► cores ─► a0(zfae) inference
PCEA — guardian: last-state-as-key encryption at every layer (orthogonal)

Member	Expansion	Role
pcna	Prime Circle Neural Architecture	Arranges tensors as circles in a standard back-propagating neural architecture; offers circles to PCTA
pcta	Prime Circled Tensor Architecture	Composes UCNS-carried circles into seeds; offers seeds to PTCA
ptca	Prime Tensor Core Architecture	Composes seeds into cores; offers cores to a0(zfae)
zfae	Zeta Function Alpha Echo	Inference engine: uses pcna tensors as weights, and pcna circles / pcta seeds / ptca cores as phase-harmonic propagation and auditing
pcea	Prime Circular Encryption Algorithm	Guardian — "last state as key for this state" encryption at every layer (orthogonal, not a layer)

The canonical role-and-boundary map is The-Interdependency/interdependent-lib : docs/prime-tensor-stack.md. This repo cites it and does not import it; naming another repo's terms transfers no theorem / proof / empirical status.

Install

pip install -e .            # zero runtime dependencies (stdlib only)
pip install -e ".[dev]"     # adds pytest

Requires Python ≥ 3.9.

Use

from pcta import build_seed, compose_seed, CircleTensor, seed_motion

# Wrap layer-1 circle outputs (opaque UCNS-carried tensors / weight handles).
# The circle count is variable — pass however many circles a seed should carry:
seed = build_seed([f"circle_weights_{i}" for i in range(7)], identity="seed:13")

# ... or compose explicit CircleTensors:
circles = [CircleTensor(payload=w, identity=f"c{i}") for i, w in enumerate(ws)]
seed = compose_seed(circles)               # {n/3} star-polygon anchor order

seed.n_circles            # number of circles composed
seed.anchor_order         # e.g. (0, 3, 6, 2, 5, 1, 4) for the nominal {7/3} case
seed.at(0).payload        # lossless: the original circle payload

motion = seed_motion(seed)   # structural motion handed upward (no weights/grads)

Boundaries

• Variable composition. The number of circles in a seed is not fixed — the only invariant is that every circle is a tensor and the seed is itself a tensor. (The same variable rule holds for tensors→circle in pcna and seeds→core in ptca.)
• Structural, non-differentiable. Composition is the ⊠ operator: it assembles circles into seeds. Back-propagation lives only in layer 1 (pcna); nothing here carries a gradient (requires_grad is always False).
• Opaque circles. A circle's internal structure is pcna's business. pcta treats a circle as an opaque payload host and never inspects or mutates it.
• Coherence-prime rule is mirrored, not imported. is_coherence_prime reproduces interdependent_lib.coherence_primes exactly (including the p=4373 regression). Prime-consciousness theory: primes whose p-1 factorization is square-free are more likely to fall into stability as part of a triadic recursion set. Importing the aggregator would invert the dependency graph.

"Motion" — formal definition

The structural output a seed hands upward ("motion") is formally the Fickian gradient flux, Fick's first law J = −D ∇φ: the seed's composed field diffuses down its gradient (D diffusivity, φ field, ∇φ gradient). It is structural / non-differentiable — the ∇φ is a field gradient, not an autodiff gradient (back-propagation lives only in pcna). This was the stack's last open hmmm; none remains.

License

MPL-2.0 (weak copyleft — embed anywhere, but changes to these files must be published). See LICENSE. Copyright (c) 2026 Erin Patrick Spencer. Relicensed from MIT (which had itself superseded AGPL-3.0-or-later).