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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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The Phase–Scalar Spiral: Why Systems Fail When They Scale — and What Restores Coherence

Restoring Coherence in Systems of Infinite Scale (Applications of Phase–Scalar Reconstruction and Spiral Coordinates)
Authors: Tang, Lit Meng (Robert);

The Phase–Scalar Spiral: Why Systems Fail When They Scale — and What Restores Coherence

Abstract

This paper constitutes Stage X of an independent Phase–Scalar research program developed between 2025–2026. It introduces the Phase–Scalar Spiral as a universal diagnostic for identifying why complex systems fracture as they scale. Across mathematics, physics, distributed computing, artificial intelligence, biological systems, and organizational systems, recurring failure modes appear when systems scale: paradoxes in infinite constructions, divergences and "ghosts" in certain quantization programs, coordination breakdowns in distributed systems, hallucinations in large language models, dysregulated growth in biological systems, and metric-induced breakdowns in human institutions. These phenomena are typically treated as domain-specific anomalies. This paper proposes a unifying diagnostic explanation: many scale-failures are representational mismatches generated when global measurement and abstraction (Scalar) outrun local relational coordination (Phase). Building on Phase–Scalar Reconstruction (PSR) and the Spiral Coordinate System (SCS), we formalize a general principle: coherence is preserved when Phase precedes Scalar at each recursive level of growth. We present the Phase–Scalar Spiral as an applied synthesis: a cross-domain lens that explains why locality-preserving methods (e.g., renormalization, neighborhood-based computation, context-grounded inference) stabilize systems, while scalar-first expansions often produce artifacts (divergence, paradox, hallucination, institutional dysfunction). The contribution is methodological and diagnostic: it proposes no new physical laws and does not modify established domain formalisms. Instead, it offers a disciplined way to classify when a problem is ill-posed due to category collapse, and how to restore coherence by re-establishing local coordination before re-scaling.

Keywords

coordination, quadratic gravity, ghosts, PSR-B, representational mismatch, Phase and Scalar Time, infinite sets, renormalization, Spiral Coordinate System, boundary enforcement, cross-domain synthesis, temporal representation, systems theory, cancer biology, distributed systems, locality preservation, PSR, CAP theorem, diagnostic methods, organizational coherence, Phase–Scalar Reconstruction, scaling failure, AI hallucination, Phase–Scalar Spiral, coherence, biological coherence, measurable graphs, system coordination, SCS

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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