Project index and reading guide

Scale Space / CNRS Research Programme

A modular research programme connecting logarithmic scale geometry, complex positional representation, and cross-scale physical and biological modelling.

Donald G. Palmer — Independent Researcher — Little River, South Carolina — updated 2026-07-04 from Concept DOI workbook

Start Here Zenodo Community Scale Space Records CNRS Records Code Record

Start Here

This page is the public index for the Scale Space / CNRS programme. It connects the live project website, the Zenodo Community archive, the book, technical papers, code repository, open problems, and Zenodo concept DOIs.

How to read this project: the book is the synthesis and research-programme statement; the papers are the technical record; the GitHub repository is the executable-code entry point; the CNRS records are the mathematical and documentation entry points. Concept DOIs resolve to the latest Zenodo version of each record. Each card also shows the current default/latest DOI from the uploaded workbook. The archival record set is collected in the Zenodo Community.

Book-level synthesis

Across Scale: A Geometry of Size and Representation provides the reader-facing architecture: motivation, scale geometry, quantum/biology extensions, CNRS, bridge questions, tests, and failure modes.

Technical derivations

The Scale Space papers provide the formal physics, geometry, dynamical-closure, cosmology, matter-source, and prediction record. Use these records when citing specific technical claims.

Mathematics and code

The CNRS records provide the mathematical background. The GitHub-linked Zenodo record provides the citable software release for the CNRS Scientific Toolkit.

Zenodo records indexed

from the Concept DOI workbook; most archived in the community

Scale Space records

Framework and numbered papers

CNRS records

mathematics, guides, bridges

Code/software record

CNRS Scientific Toolkit

Zenodo Community Archive

The Zenodo Community is the archival collection for the programme records. Use it when browsing the full record set; use this page when choosing a reading path or locating the current concept/default DOI for a specific item.

Scale Space / CNRS Research Programme Community

The community gathers the Scale Space framework and paper sequence, CNRS mathematical records, bridge documents, and software/code records under one archival umbrella.

Open Zenodo Community

Public architecture

www.nul1.com is the readable front door. The Zenodo Community is the archival collection. GitHub is the working code and issue-tracking layer. The book is the synthesis; the papers are the technical record.

Suggested record wording: This record is part of the Scale Space / CNRS Research Programme. The current project index, reading guide, papers, code, and open-problem map are maintained at www.nul1.com. The archival record set is collected in the Zenodo Community “Scale Space / CNRS Research Programme.”

Book and Programme Architecture

Recommended Zenodo structure: one project landing record, one book record, individual paper records, and separate code/software records. This page is suitable for the project landing record.

Across Scale

Role: reader-facing synthesis and research-programme statement. The book should cite this project landing record and the relevant technical-paper concept DOIs. Technical claims should be traced to the paper records below.

Citation logic

Cite the book for programme-level synthesis; cite individual Scale Space papers for physics derivations; cite CNRS papers and software records for arithmetic, branch-index, and implementation claims.

Book arc	Technical source family	Status of connection
Chs. 1–8: scale coordinate, metric, gravity, predictions	Framework; Scale Space Papers 1–12	Core Scale Space development; observational translation remains open for several predictions.
Chs. 9–12: quantum and biology extensions	Scale Space Papers 3–5, 18, 23	Model-level and exploratory extensions; empirical calibration required.
Chs. 13–15: dynamical closure and complex scale	Scale Space Papers 13–17, 20, 23, 25; CNRS bridge records	Technical frontier; several results are ansatz-dependent or await independent review.
Chs. 16–19: CNRS	CNRS roadmap, architecture, problem papers, software guide	Constructed mathematical programme with implemented components and open formal questions.
Chs. 20–24: convergence, tests, status, invitation	All records; especially triangulation, tetrad, physics-connection, and code records	Programme synthesis; bridge remains conditional rather than proved.

Recent Workbook Defaults

The newest default/latest records in the uploaded Concept DOI workbook.

Date	ID	Title	Version
2026-07-01	Framework	Four-Dimensional Scale Space: A Theoretical Framework	v13
2026-06-30	CNRS-Sum	The Complex Numeric Representational System Programme A Comprehensive Summary: Origins, Architecture, Results, and Status	v8
2026-06-30	CNRS-Rdmp	Complex Numeric Representational System Programme Full Programme Scope: All Four Problems	v8
2026-06-30	CNRS-MN	Complex Numeric Representational System (CNRS) Programme Master Summary	v8
2026-06-27	CNRS-MS	Complex Numeric Representational System (CNRS) Programme Master Summary	v3
2026-06-24	Paper 25	Scale-Extended Matter Sources and the 4D Poisson Equation	v2
2026-06-24	CNRS-Git	CNRS Scientific Toolkit	v0.10.0
2026-06-21	Paper 20	Dynamical Closure of the Scale-Space Framework: Complex Scale Potential, Newtonian Recovery, and the Hidden Configurational Sector	v6

Code Repository and Software DOI

The CNRS Scientific Toolkit is the open research-code implementation layer for CNRS.

CNRS-Git GitHub v0.10.0 2026-06-24

Start Here

Book-level synthesis

Technical derivations

Mathematics and code

Zenodo Community Archive

Scale Space / CNRS Research Programme Community

Public architecture

Book and Programme Architecture

Across Scale

Citation logic

Recent Workbook Defaults

Code Repository and Software DOI

CNRS Scientific Toolkit

How the layers fit together

Scale Space Framework — 24 Records

Four-Dimensional Scale Space: A Theoretical Framework

A Geometric Model of Logarithmic Scale as an Extra Dimension: Anti-de Sitter Geometry, Emergent Gravity, and RG Flow

Candidate Gravitational Signatures of the Four-Dimensional Scale Space Framework: Asymmetric Force, Wave Polarisations, and Scale Dragging

Scale Uncertainty Principle, Effective Mass, and the Geometric Quantum-to-Classical Transition

Cross-Scale Geodesics in Biological Systems: Signalling, Quantum-Classical Boundary, and Morphogenesis

Four-Dimensional Extended Objects: Scale Pressure, Boundary Conditions, and Fractal Biological Architecture

A Linearised Rotating Exterior Perturbation of the Four-Dimensional Scale Space Framework: Scale-Kerr to First Order in Angular Momentum

Vector-Mode Gravitational Wave Amplitude from a Rotating Binary in the Four-Dimensional Scale Space Framework

Interior Matching for the Linearised Rotating Exterior Perturbation of the Four-Dimensional Scale Space Framework: Mode Selection, Amplitude Normalisation, and the Scale Separation of Binary Pulsars

Time, Proper Duration, and the Five-Dimensional Parent Theory of the Scale Space Framework

Resolving the Gravitational Time Dilation Discrepancy in the Five-Dimensional Scale Space Framework: The Corrected gtt and Its Consequences

The Five-Dimensional Einstein Tensor of the Corrected Scale-Space Metric: Vacuum Structure, Required Stress-Energy, and the Non-Vacuum Nature of the Framework

The Geometric Status of c in the Scale-Space Framework: Manifold Radius, Null Propagation, and the Nat as a Unit of Length

The Complex Structure of Scale: From Configurational Deficit to the Conjecture that the Scale Coordinate is a Single Complex Value

Dynamical Origin of the Scale-Space Poisson Equation: Newton's Law from Linearised 5D Field Equations

The Scale-Integration Reduction: Effective Four-Dimensional Einstein Equations from the Five-Dimensional Scale-Space Field Theory

Near-Term Tests of the Complex Scale Coordinate Conjecture: Sub-leading Structure, Native vs Projected Treatment, and the Phase-Shift Prediction

The 5D Field Equations with Complex Scale Coordinate: Classical Neutrality, Quantum Phase, and the Level Structure of the Complex zs Conjecture

Multi-Scale Turing Pattern Formation via CNRS-H Digit Strings: Cross-Scale Coupling in the Gierer-Meinhardt System

The Representational Requirement: The CNRS Programme as Paper 13 Step 5

Dynamical Closure of the Scale-Space Framework: Complex Scale Potential, Newtonian Recovery, and the Hidden Configurational Sector

Complex-Scale Quantum Mechanics: Native Action, Geometric Neutrality, and Hydrogenic Phase Shifts in a Weak Gravitational Field

Scale-Space Signatures in FLRW Consistency Diagnostics: A Third Class of Cosmological Model

Scale-Extended Matter Sources and the 4D Poisson Equation

CNRS Mathematical Programme — 19 Records

The Complex Numeric Representational System Programme A Comprehensive Summary: Origins, Architecture, Results, and Status

Complex Numeric Representational System Programme Full Programme Scope: All Four Problems

Complex Numeric Representational System (CNRS) Programme Master Summary

Complex Numeric Representational System (CNRS) Programme Master Summary

A Combined Architecture for Complex Numeric Representation Systems: Arithmetic, Analytic Continuation, Operator Calculus, and Physical Structure

Toward a Definition of Base−b for All b∈R+: Extending the Ito–Sadahiro (−β)-Expansion Framework

Problem 1 Extension: The β = (3 + √5)/2 Test Case and the Invariance Gap Supplement to the CNRS Problem 1 Working Paper

Complex Numbers as Single Values: A Three-Layer Architecture for the Complex Numeric Representational System

Incorporating the Branch Index into the CNRS Digit String

A Single-Value Complex Numeral System via Canonical Number Systems and the Riemann Surface of the Logarithm

Arithmetic Closure for the Complex Numeric Representational System: Working Paper - Problem 3 of the CNRS Programme

The Explicit One-Argument Multiplication Transducer for CNRS-A: Carry Sets, State Graphs, and Verified Examples

The CNRS Programme and Schmidt's Symbolic Cover Framework: A Complete Mathematical Mapping

Complex Numbers as Single Values: A Working Demonstration of the Complex Numeric Representational System

Partial Operational Completeness of the Complex Numeric Representational System Working Paper — Problem 4 (Sub-question Q3) of the CNRS Programme

The CNRS Programme and the Scale-Space Framework: How Papers 1–13 Connect to the Mathematical Programme

The Metric Correction from the Vierbein Formalism: Tetrad Re-derivation, Sub-leading Structure, and the Complex Geodesic Connection

The Triangulation Function: Conditional Derivation within the Static Diagonal Ansatz and Unification of Metric Correction, Clock Rate, and Einstein Tensor Deficit

Scale-Derivative Exactness and Structural Cross-Scale Coupling in Multi-Scale Diffusion: A Progressive Place-Value Framework

Open Problems and Collaboration Entry Points

Scale Space physics

CNRS mathematics

Experimental/calibration work

Earlier Published Precursors

Toward a Unified Multidisciplinary Model of Reality

New Directions for Tying Physics and Biologic Systems