Dynamical Evolution of the Informational Stiffness Field: Wave Propagation in Curved Spacetime

Dynamical Evolution of the Informational Stiffness Field: Wave Propagation in Curved Spacetime develops the time-dependent structure of the informational stiffness field introduced in the Unified Recursion Theory (URT) framework. Building on the static formulation established in Informational Field Theory in Strong Curvature (IFT-SC), this paper derives the linear dynamics of small perturbations of the stiffness field and shows that these disturbances propagate as informational scalar waves (ISWs) on a fixed spacetime background.

The analysis introduces a decomposition of the stiffness field into a stationary background sigma_0(x) and a small perturbation delta_sigma(x,t). Consistency with the URT Core Framework and general covariance restricts the propagation operator to the covariant d'Alembertian. The resulting wave equation describes massless scalar propagation with no geometric backreaction: ISWs evolve on the spacetime metric but do not modify it.

Thermodynamic damping arises from the URT recursion-efficiency law, which links the local magnitude of the stiffness field to irreversible update cost. This produces a damping coefficient Gamma(x) that suppresses wave amplitude in regions of high stiffness. In low-curvature environments, waves propagate freely; near horizons, redshift dominates but damping remains weak; deep inside compact objects, stiffening leads to overdamping and the extinction of informational disturbances. This confirms dynamically the finite informational depth previously identified in IFT-SC.

The paper also identifies observational signatures of ISWs, including fractional modulations of recursion efficiency (delta_lambda / lambda), curvature-dependent damping patterns, and geometric scattering effects. These signatures provide a clear, falsifiable path for empirical testing across astrophysical and high-coherence laboratory systems.

This work completes the dynamical sector of the stiffness field and establishes the foundational wave mechanics required for subsequent analyses of informational flow, black hole evaporation, and measurement processes within the URT framework.

URT PAPER FAMILY

This work forms part of the Unified Recursion Theory (URT) research program, which develops a cross-domain framework for physical evolution based on constrained informational recursion and an energy–entropy proportionality law. Each paper in the series is self-contained, while collectively establishing the theoretical structure across quantum, geometric, biological, cosmological, and particle-level domains.

Related URT works available on Zenodo:

FOUNDATIONAL PAPERS

1. Unified Recursion Theory — Core Framework (URT Core)

DOI: 10.5281/zenodo.17642761
Record: https://zenodo.org/records/17642761

2. Discrete Admissible Regimes in Unified Recursion Theory: Operator Closure, Constraint Topology, and the Necessity of Five Operators

DOI: 10.5281/zenodo.18148192
Record: https://zenodo.org/records/18148193

3. Informational Field Theory in Strong Curvature (IFT-SC)

DOI: 10.5281/zenodo.17850379
Record: https://zenodo.org/records/17850379

4. Dynamical Evolution of the Informational Stiffness Field (ISW Theory)

DOI: 10.5281/zenodo.17860533
Record: https://zenodo.org/records/17860533

RESOLUTION PAPERS (PHYSICAL PARADOXES)

5. Informational Recursion and the Dissolution of the Black Hole Information Paradox

DOI: 10.5281/zenodo.17868662
Record: https://zenodo.org/records/17868662

6. ORM and the Quantum Measurement Problem (ORM)

DOI: 10.5281/zenodo.17881944
Record: https://zenodo.org/records/17881944

BRIDGING / CONSTRAINT PAPER

7. Distinguishability Geometry in Informational State Space

DOI: 10.5281/zenodo.17957062
Record: https://zenodo.org/records/17957062

Provides the geometric foundation for informational state space.
Underpins the emergence of spacetime, efficiency universality, and landscape geometry.

THEORETICAL EXPANSION PAPERS

8. Emergent Spacetime from Informational Recursion

DOI: 10.5281/zenodo.17885555
Record: https://zenodo.org/records/17885555

9. λ-Universality Across Scales (λ-UAS)

DOI: 10.5281/zenodo.17934065
Record: https://zenodo.org/records/17934065

10. Free-Energy Landscape Geometry in Unified Recursion Theory

DOI: 10.5281/zenodo.17940995
Record: https://zenodo.org/records/17940995

BIOLOGY / COMPLEXITY PAPER

11. URT in Biology: Efficiency, Folding Funnels, Replication Fidelity, and Molecular Motor Dynamics

DOI: 10.5281/zenodo.17945209
Record: https://zenodo.org/records/17945209

COSMOLOGICAL EXTENSIONS

12. Cyclic Cosmology from Informational Recursion

DOI: 10.5281/zenodo.17955043
Record: https://zenodo.org/records/17955043

13. Antimatter as Inverse Recursion: Temporal Operator Asymmetry and Matter–Antimatter Imbalance in Unified Recursion Theory

DOI: 10.5281/zenodo.17955043
Record: https://zenodo.org/records/17955625