Technical Foundations of Synkyria
This page collects the more technical notes and preprints that underpin the Synkyrian trilogy and the network framework. It is not exhaustive, but it gives readers a map of the core mathematical and physical constructions.
Where possible, links will point to Zenodo DOIs or public PDFs.
See also: the full Library ledger with PDF links.
1 · Open-system viability and the Holding Equation
These works define and refine the Holding Equation as a gauge for open-system viability, consistent with the Second Law.
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The Holding Equation: A Second-Law–Consistent Gauge for Open-System Viability
Introduces the viability gauge
[ H = \kappa\,\frac{\Phi_S - \sigma}{R(1 + \hat\rho)} ] linking free-energy surplus, entropy production, relaxation and congestion into a single open-system holding index. -
ΜΕΡΡ and MEPP-consistent Channels
Explores how maximum entropy production principles (MEPP) can be reconciled with explicit holding constraints, leading to MEPP-consistent channels that respect finite viability.
2 · Kernel Stability and canonical indices
These works extend holding to networks of states and define canonical Synkyrian indices.
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The Kernel Stability Principle (KSP)
Extends single-node viability to kernel-level dynamics and shows how sustained overload on a kernel degrades both short-term viability growth and long-run attractors.
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From Variability to Holding: Canonical Synkyrian Indices and a Unified View of HE · KSP · MEPP
Clarifies the role of indices such as CRQ, SCP and T as downside- and tail-aware functionals built on the Holding Equation and Kernel Stability; unifies earlier “legacy” forms under a single Synkyrian architecture.
3 · Holding as a Viability Functional (series)
The Holding as a Viability Functional series makes the notion of holding as a functional on paths and environments mathematically precise.
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Holding as a Viability Functional V – Synkyrian Surrogates and a Representation Theorem
Studies surrogate holding indices (H_{\mathrm{syn}}) and proves that, under a conservative viability bound and a calibration axiom against failure probabilities, (H_{\mathrm{syn}}) must be a monotone transform of the rigorous log-hazard functional (H_{\mathrm{rig}}).
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Holding as a Viability Functional – Environmental Left Tails and Long-Time Survival of Open Systems
Treats holding as a functional of the left tail of environmental decay rates and classifies long-time survival in terms of the behaviour of that distribution near zero.
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Holding as a Viability Functional X – A Variational Principle for Flow under Viability Constraints
Formulates a variational problem for flows (and entropy production) subject to a hard holding constraint (H_{\mathrm{rig}} \ge H_{\min}). Shows that optimal operation sits on the critical surface (H = H_{\min}).
More entries in this series (VII, XI, …) refine the connection between holding, flows, and effective dynamics.
4 · Holding and Morphogenesis
These works connect holding with collapse, transition and form.
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Holding and Morphogenesis: Collapse–Transition Regimes and Synkyrian Companions
Splits exits into destructive collapse versus morphogenetic transitions, defines distinct holding exponents for each regime, and sketches how a two-layer Companion (safety vs. morphogenesis) can act inside these dynamics. -
Holding as a Viability Functional – Bridging to Geometric Morphogenesis
Technical bridges that support the “Synkyrian Geometric Morphogenesis” paper: how CRQ, SCP and transformation windows arise from hazard-weighted path integrals of the holding functional.
(More detailed links to be added.)
5 · Networks, Cheeger bounds and composition
These works underpin the Synkyrian Networked Fields note and the network layer of the programme.
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XI – Cheeger-type Bounds for Synkyrian Network Holding
Establishes Cheeger-type inequalities for the long-horizon holding exponent of killed Markov networks, linking asymptotic holding (H_{\infty}) to a Synkyrian Cheeger constant built from hazards and coupling weights.
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Network Composition, Coupling and Kernel Stability
Analyses how network-level holding can be represented as a coupling factor times a sum of node-wise contributions, disentangling topology, interaction strength and local holding dynamics.
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Bridge Notes on Networked Fields
Additional notes (e.g. on hazard-weighted cuts, shared-capacity measures and coupling operators) that connect the abstract Cheeger picture with concrete Synkyrian network applications.
(Links to be added.)
6 · Work in progress and additional notes
There are further technical pieces – including Tropic Physics (Vol.30), extended TEE systems, and bridges to open-system thermodynamics and cosmology – which are being consolidated.
As these stabilise and are released on Zenodo or similar platforms, they will be added here with links and short descriptions.
For now, this page should be read as a map, not as a complete catalogue.
Core papers
- P0 — Synkyrian Stability (canonical spine) — Page · PDF
- P1 — Tropic Information Theory — Page · PDF
- P2 — Synkyrian Geometric Morphogenesis — Page · PDF
- P3 — Thermodynamic Right to Refusal — Page · PDF
- P4 — Invariant-Preserving Morphogenetic Filtering — Page · PDF
- P5 — Synkyrian Networked Fields — Page · PDF
- P6 — Synkyrian Network Policies — Page · PDF