Project index and reading guide

The Forgotten Coordinate: The Missing Geometry of Size, from Atoms to Galaxies

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 — SS-GEO v4 release baseline recorded 2026-09-11

Start HereZenodo CommunityScale Space RecordsCNRS RecordsCode Record
Zenodo Community: The archival collection for Scale Space / CNRS Research Programme records is now available.
Open Zenodo Community

Start Here

This page is the public index for the Scale Space / CNRS programme. It connects the technical paper corpus, stable Framework, Book 1, Technical Companion, Zenodo Community, code, references, and open problems.

How to read this project: the technical papers are the claim-bearing foundation. They drive the stable Framework synthesis and the exposition in Book 1 and the Technical Companion. Journal publication is important, but follows construction and verification of the technical corpus. The GitHub repository is the executable-code entry point; the CNRS records are the mathematical and documentation entry points. Begin with the stable Framework synthesis and SS-GEO, the current Scale Space geometry foundation. Continue to current successor papers as they are approved and deposited, then use the CNRS mathematics, applications, Book 1, and Technical Companion. Retired and transition-stage records remain available for provenance. Every record card retains its Concept DOI as the stable pointer and refreshes its live Zenodo metadata when the page opens.
Live Zenodo metadata: waiting to refresh.

Technical foundations

The Scale Space and CNRS papers carry the detailed claims, derivations, algorithms, evidence boundaries, corrections, and prior-art engagement. Accepted papers drive all later exposition.

Stable synthesis

The Scale Space–CNRS Programme: A Theoretical Framework, Version 19, is the stable programme-level synthesis deposited on Zenodo. It deliberately excludes fast-moving paper, audit, reference-ingestion, and formalization status.

Book 1 and Technical Companion

The Forgotten Coordinate: The Missing Geometry of Size, from Atoms to Galaxies provides the reader-facing exposition. The Forgotten Coordinate: Technical Companion preserves full technical detail. Both are built from the accepted paper corpus.

46
Zenodo concept records
Live Zenodo metadata loads when the page opens
25
Scale Space records
Framework, SS-GEO, and numbered records
20
CNRS records
mathematics, guides, bridges
1
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.

46

Concept records indexed

represented by landing-page cards

145

Version records

including the Framework v19 release

2026-09-11

Snapshot through

SS-GEO v4 publication date

How the archive is used here: The Concept DOI is the stable latest-version pointer; the version DOI is the immutable citation for a specific release. The supplied community export provides the static snapshot, while the page also checks Zenodo live. New community concepts not yet classified on the page are surfaced automatically in the “Additional Community Records” area.

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 technical papers are the claim-bearing foundation; they drive the Framework, Book 1, and Technical Companion.

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.”

Publication Architecture

The revised programme is paper-driven: the technical corpus establishes the detailed claims; the Framework stabilizes the architecture; Book 1 and the Technical Companion turn the accepted corpus into complementary expositions.

Technical papers

Role: primary technical foundation. Each successor paper should be claim-bounded, versioned, referenced, independently checked where appropriate, and explicit about corrections or supersession of earlier work.

Framework v19

Role: stable programme-level synthesis. Published 6 September 2026 under version DOI 10.5281/zenodo.22552998; the concept DOI remains 10.5281/zenodo.19136376.

Book 1

The Forgotten Coordinate: The Missing Geometry of Size, from Atoms to Galaxies is the reader-facing exposition. Its substantive technical claims should be traceable to the accepted papers.

Technical Companion

The Forgotten Coordinate: Technical Companion carries fuller derivations, methods, evidence boundaries, references, and verification detail inherited from the accepted papers.

LayerFunctionChange discipline
Technical paper corpusClaim-bearing foundation for Scale Space and CNRSRevised as claims, calculations, references, and verification mature
Framework v19Stable architecture and programme-level synthesisNot updated for routine implementation or status changes
Book 1Accessible narrative built from accepted technical resultsRevised after the supporting paper corpus stabilizes
Technical CompanionDetailed technical exposition and evidence trailRevised from the accepted paper corpus and its governed references

Latest Zenodo Records

The eight newest programme records in the supplied community/version export, rebuilt again from live Zenodo metadata when available.

DateIDTitleVersion
2026-09-11SS-GEOLogarithmic Scale as a Geometric Coordinate: Hyperbolic Structure and Finite-Profile Projectionv4
2026-09-06FrameworkThe Scale Space–CNRS Programme: A Theoretical Frameworkv19
2026-07-31CNRS-KeyDifferentiation, the Divided-Power Basis, and the Transcendental-Radix Obstructionsv7
2026-07-09CNRS-GitCNRS Scientific Toolkitv0.11.1
2026-07-02Paper 9Time, Proper Duration, and the Five-Dimensional Parent Theory of the Scale Space Frameworkv7
2026-06-30CNRS-MNThe Complex Number Representation System (CNRS): Foundations, Arithmetic, and Calculusv8
2026-06-30CNRS-RdmpComplex Numeric Representational System Programme Full Programme Scope: All Four Problemsv8
2026-06-30CNRS-SumThe Complex Numeric Representational System Programme A Comprehensive Summary: Origins, Architecture, Results, and Statusv8

Code Repository and Software DOI

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

CNRS-Git GitHub v0.11.1 2026-07-09

CNRS Scientific Toolkit

Concept DOI Latest version DOI Open Zenodo record

Zenodo metadata: checking…

Zenodo Community snapshot: current version indexed.

Concept: 10.5281/zenodo.20574852
Latest: 10.5281/zenodo.21271997

Files: DonGPalmer/CNRS_Scientific_Toolkit-v0.11.1.zip

How the layers fit together

GitHub is the working development layer. Zenodo is the archival and citation layer for versioned releases and research records. The Zenodo Community gathers the archival record set. This landing page connects code, book-level synthesis, paper records, and CNRS mathematics.

GitHub Repository Zenodo Community

Current Scale Space Corpus

The Framework provides the stable programme synthesis. SS-GEO is the current claim-bearing geometry foundation. Additional successor papers will enter this section only after approval and deposit.

Recommended reading path: Read the Framework for programme architecture, then SS-GEO for the current geometry. Numbered papers undergoing retirement remain available below for provenance and transition review.
Framework Current synthesis v19 2026-09-06

The Scale Space–CNRS Programme: A Theoretical Framework

Concept DOI Latest version DOI Open Zenodo record

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Zenodo Community snapshot: current version indexed.

Concept: 10.5281/zenodo.19136376
Latest: 10.5281/zenodo.22552998

Files: Scale_Space_Framework_v19_Zenodo.pdf, Scale_Space_Framework_v19_Zenodo.tex

Role: Stable programme-level synthesis; current and citation-authoritative.

SS-GEOCurrentPreprintv42026-09-11

Logarithmic Scale as a Geometric Coordinate: Hyperbolic Structure and Finite-Profile Projection

Concept DOIVersion DOIOpen Zenodo record

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Concept: 10.5281/zenodo.22700740
Version: 10.5281/zenodo.22700741

Files: SS-GEO_scale_coordinate_geometry_v4_Zenodo.pdf, SS-GEO_scale_coordinate_geometry_v4_Zenodo.tex, SS-GEO_v4_verify.py

Role: Current Scale Space geometry foundation; independently audited, approved, and citation-authoritative. Obsoletes Paper 1 as a claim-level source.

CNRS and Multi-Scale Applications

Current application work that remains independent of the numbered Scale Space retirement.

Paper 18 Independent current v3 2026-05-18

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.20089231
Latest: 10.5281/zenodo.20317237

Files: cnrs_reaction_diffusion.py, paper18_reaction_diffusion_v3_Zenodo.pdf

Role: Active CNRS / multi-scale application paper; excluded from the numbered Scale Space retirement.

Scale Space Retirement Transition

These numbered papers are not current citation-authoritative sources, but have not yet completed formal retirement. Their precise status is taken from the authoritative DOI index.

Show 21 retirement-pending and retirement-hold records
Paper 2 Retirement pending v12 2026-05-25

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19169397
Latest: 10.5281/zenodo.20399341

Files: paper2_gravity_predictions_v12.pdf

Status: Planned for retirement but not yet through the formal closeout gates.

Paper 3 Retirement hold v9 2026-05-12

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19192004
Latest: 10.5281/zenodo.20159380

Files: paper3_quantum_v9.pdf

Status: Formal retirement is on hold pending the governing review.

Paper 4 Retirement pending v4 2026-05-12

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19194148
Latest: 10.5281/zenodo.20159672

Files: paper4_biology1_v4.pdf

Status: Planned for retirement but not yet through the formal closeout gates.

Paper 5 Retirement pending v5 2026-05-12

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19194284
Latest: 10.5281/zenodo.20159786

Files: paper5_biology2_v5.pdf

Status: Planned for retirement but not yet through the formal closeout gates.

Paper 6 Retirement pending v9 2026-05-12

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19208248
Latest: 10.5281/zenodo.20169874

Files: scale_kerr_sympy_verification.py, paper6_scale_kerr_v9.pdf, scale_kerr_poincare_exact.py

Status: Planned for retirement but not yet through the formal closeout gates.

Paper 7 Retirement pending v8 2026-05-12

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19209675
Latest: 10.5281/zenodo.20171516

Files: paper7_amplitude_computation_v1.py, paper7_vector_modes_v8.pdf

Status: Planned for retirement but not yet through the formal closeout gates.

Paper 8 Retirement pending v6 2026-05-12

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19222639
Latest: 10.5281/zenodo.20171206

Files: paper8_interior_matching_v6.pdf, paper8_sympy_verification_v2.py

Status: Planned for retirement but not yet through the formal closeout gates.

Paper 9 Retirement hold v7 2026-07-02

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19222717
Latest: 10.5281/zenodo.21197789

Files: paper9_lorentzian_v7.pdf

Status: Formal retirement is on hold pending the governing review.

Paper 10 Retirement pending v7 2026-05-12

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19244886
Latest: 10.5281/zenodo.20170409

Files: paper10_corrected_metric_v7.pdf, verify_corrected_metric.py

Status: Planned for retirement but not yet through the formal closeout gates.

Paper 11 Retirement pending v5 2026-05-12

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

Concept DOI Latest version DOI Open Zenodo record

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Zenodo Community snapshot: current version indexed.

Concept: 10.5281/zenodo.19270349
Latest: 10.5281/zenodo.20182691

Files: compute_5d_einstein.py, paper11_einstein_tensor_v5.pdf

Status: Planned for retirement but not yet through the formal closeout gates.

Paper 12 Retirement pending v8 2026-05-25

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19270528
Latest: 10.5281/zenodo.20399438

Files: paper12_c_geometric_v8.pdf

Status: Planned for retirement but not yet through the formal closeout gates.

Paper 13 Retirement pending v6 2026-05-12

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19270737
Latest: 10.5281/zenodo.20171842

Files: paper13_complex_s_v6.pdf

Status: Planned for retirement but not yet through the formal closeout gates.

Paper 14 Retirement pending v3 2026-05-25

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.20088695
Latest: 10.5281/zenodo.20399487

Files: paper14_sympy_verification_v1.py, paper14_dynamical_poisson_v3.pdf

Status: Planned for retirement but not yet through the formal closeout gates.

Paper 15 Retirement pending v3 2026-05-25

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

Concept DOI Latest version DOI Open Zenodo record

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Zenodo Community snapshot: current version indexed.

Concept: 10.5281/zenodo.20088926
Latest: 10.5281/zenodo.20399399

Files: paper15_reduction_v3.pdf

Status: Planned for retirement but not yet through the formal closeout gates.

Paper 16 Retirement pending v2 2026-05-12

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.20089020
Latest: 10.5281/zenodo.20172200

Files: paper16_zs_conjecture_nearterm_v2.pdf

Status: Planned for retirement but not yet through the formal closeout gates.

Paper 17 Retirement pending v2 2026-05-12

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.20089132
Latest: 10.5281/zenodo.20172304

Files: paper17_5d_field_eqs_complex_zs_v2.pdf

Status: Planned for retirement but not yet through the formal closeout gates.

Paper 19 Retirement pending v2 2026-05-12

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.20089285
Latest: 10.5281/zenodo.20171947

Files: paper19_representational_v2.pdf

Status: Planned for retirement but not yet through the formal closeout gates.

Paper 20 Retirement pending v10 2026-07-29

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.20201178
Latest: 10.5281/zenodo.21684395

Files: audit_Tconf_divergence_v2.py; audit_VL_v2.py; provenance_manifest.txt; SS_Paper20_dynamical_closure_v10.pdf; SS_Paper20_dynamical_closure_v10_Zenodo.tex

Status: Planned for retirement but not yet through the formal closeout gates.

Paper 23 Retirement pending v4 2026-05-28

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.20208060
Latest: 10.5281/zenodo.20445807

Files: paper23_EPJD_v1_Zenodo.pdf

Status: Planned for retirement but not yet through the formal closeout gates.

Paper 24 Retirement hold v1 2026-05-26

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.20416152
Latest: 10.5281/zenodo.20416389

Files: step c results.csv, step_b_final_diagnostics.pdf, step_b_computation.py, step_b_final_results.csv, paper24_flrw_diagnostics_v1.pdf

Status: Formal retirement is on hold pending the governing review.

Paper 25 Retirement pending v2 2026-06-24

Scale-Extended Matter Sources and the 4D Poisson Equation

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.21108449
Latest: 10.5281/zenodo.21108450

Files: paper25_earth_prem.py, paper25_analytic.py, paper25_calc.py, paper25 extended source v2.pdf, paper25_eos.py

Status: Planned for retirement but not yet through the formal closeout gates.

Retired Scale Space Papers — Historical Development Record

Retired records are preserved for provenance. They are not current claim-level citation authorities.

Show 1 formally retired record
Paper 1 Retired v14 2026-05-08

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19137149
Latest: 10.5281/zenodo.20098622

Files: paper1_scale_geometry_v14_preprint.tex, paper1_scale_geometry_v14_preprint.pdf

Retirement: Historical development record; not citation-authoritative. Superseded by SS-GEO.

CNRS Mathematical Programme — 20 Records

CNRS mathematics, architecture, guides, and Scale Space bridge documents. Concept DOI is the stable latest-version pointer; latest/default DOI is the workbook-selected version record.

Executable CNRS code: for the current CNRS Scientific Toolkit, including tests and examples, see the code section above and the GitHub repository.
Historical bridges: CNRS-Phy, CNRS-Tri, and CNRS-Tet depended on the retired Scale Space architecture and are retained for provenance, not as current CNRS or Scale Space claims.
CNRS-KeyReportv72026-07-31

Differentiation, the Divided-Power Basis, and the Transcendental-Radix Obstructions

Concept DOILatest version DOIOpen Zenodo record

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Concept: 10.5281/zenodo.21722741
Latest: 10.5281/zenodo.21722742

Files: CNRS_ebase_differentiation_keystone_jul_31_2026_v7_Zenodo.tex, CNRS_ebase_differentiation_keystone_jul_31_2026_v7_Zenodo.pdf

CNRS-Sum Working v8 2026-06-30

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19338814
Latest: 10.5281/zenodo.21105442

Files: CNRS comprehensive summary v8.pdf

CNRS-Rdmp Working v8 2026-06-30

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19325069
Latest: 10.5281/zenodo.21105781

Files: CNRS programme roadmap v8.pdf

CNRS-MS Working v3 2026-06-27

Complex Numeric Representational System (CNRS) Programme Master Summary

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.20185553
Latest: 10.5281/zenodo.21105324

Files: CNRS_master_summary_v3.pdf

CNRS-MN Preprint v8 2026-06-30

The Complex Number Representation System (CNRS): Foundations, Arithmetic, and Calculus

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.21108838
Latest: 10.5281/zenodo.21108839

Files: CNRS main paper v8 draft.pdf

CNRS Arch Working v4 2026-05-11

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19394226
Latest: 10.5281/zenodo.20158574

Files: CNRS_combined_architecture_v4.pdf

CNRS-Pr1 Working v6 2026-05-14

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19554909
Latest: 10.5281/zenodo.20185318

Files: CNRS_problem1_base_definition_v6.pdf

CNRS-P1-Ext Working v3 2026-05-14

Problem 1 Extension: The β = (3 + √5)/2 Test Case; Supplement to the CNRS Problem 1 Working Paper (v6)

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19691829
Latest: 10.5281/zenodo.20185217

Files: CNRS_problem1_beta_golden_v3.pdf

CNRS-Pr2 Working v8 2026-05-11

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19555139
Latest: 10.5281/zenodo.20172556

Files: CNRS_problem2_capstone_v8.pdf

CNRS Pr2-2 Working v3 2026-06-11

Incorporating the Branch Index into the CNRS Digit String

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.20179101
Latest: 10.5281/zenodo.21109659

Files: CNRS_branch_index_incorporation_v3.pdf

CNRS-Pr1-2 Preprint v4 2026-05-11

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19563061
Latest: 10.5281/zenodo.20172649

Files: CNRS_layers12_standalone_v4.pdf

CNRS-Pr3-1 Working v5 2026-06-16

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19555323
Latest: 10.5281/zenodo.20709942

Files: CNRS_problem3_arithmetic_closure_v5.pdf

CNRS-Pr3-2 Working v2 2026-05-11

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.20173246
Latest: 10.5281/zenodo.20173247

Files: CNRS_multiplication_transducer_v2.pdf

CNRS Schmidt Working v2 2026-05-14

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.20201367
Latest: 10.5281/zenodo.20201368

Files: CNRS_schmidt_framework_mapping_v2.pdf

CNRS UG Software Doc v1 2026-05-13

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

Concept DOI Latest version DOI Open Zenodo record

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Zenodo Community snapshot: concept indexed, but the supplied export lists an earlier version.

Concept: 10.5281/zenodo.19797882
Default: 10.5281/zenodo.20048874

Files: CNRS_user_guide_v1.pdf, cnrs_demo.py

CNRS-Pr4 Working v2 2026-05-11

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19794152
Latest: 10.5281/zenodo.20173050

Files: CNRS_problem4_partial_completeness_v2.pdf

CNRS Phy Historical v2 2026-05-11

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

Concept DOI Latest version DOI Open Zenodo record

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Concept: 10.5281/zenodo.19332621
Latest: 10.5281/zenodo.20172848

Files: CNRS_physics_connection_v2.pdf

CNRS-Tet Historical v2 2026-05-11

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

Concept DOI Latest version DOI Open Zenodo record

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Zenodo Community snapshot: current version indexed.

Concept: 10.5281/zenodo.19794533
Latest: 10.5281/zenodo.20200572

Files: CNRS_tetrad_subleading_v2.pdf

CNRS-Tri Historical v2 2026-05-11

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

Concept DOI Latest version DOI Open Zenodo record

Zenodo metadata: checking…

Zenodo Community snapshot: current version indexed.

Concept: 10.5281/zenodo.20200867
Latest: 10.5281/zenodo.20200868

Files: CNRS_triangulation_unification_v2.pdf

CNRS-Multi Preprint v1 2026-05-08

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

Concept DOI Latest version DOI Open Zenodo record

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Zenodo Community snapshot: current version indexed.

Concept: 10.5281/zenodo.20089340
Latest: 10.5281/zenodo.20173005

Files: CNRS_multiscale_diffusion_v1.pdf, cnrs_reaction_diffusion.py

Open Problems and Collaboration Entry Points

The project is designed to be engaged modularly. These are the specialist entry points most likely to advance the programme.

Scale Space physics

GR/dynamical-closure review, strong-field dynamics, rotating-body treatment, compact-object observable models, cosmological diagnostics, matter-source modelling, and Bianchi consistency checks.

CNRS mathematics

e-base theorem, block classification, metric completeness, Layer 2 algebra, complex-base number systems, and independent proof review.

Experimental/calibration work

Compact-object spectroscopy, optical-clock residual modelling, SANS/SAXS calibration of g(s), cosmology-data diagnostics, and biological signal-reach test design.

Earlier Published Precursors

These peer-reviewed papers are listed for historical provenance. The current technical record is the Zenodo Community and the indexed paper/code set above.

Toward a Unified Multidisciplinary Model of Reality

Palmer, D. G. (2025). Advances in Theoretical and Computational Physics, 8(4), 01–09.

DOI: 10.33140/ATCP.08.04.04

New Directions for Tying Physics and Biologic Systems

Palmer, D. G. (2025). Space Science Journal, 2(4), 01–05.

DOI: 10.33140/SSJ.02.04.02