🇬🇧 English Version | 🇩🇪 Deutsche Version
Note
AI / LLM Integration & Machine-Readable Context: A machine-readable index for LLMs, search engines, and automated crawlers is maintained in llms.txt. It provides scope boundaries, search phrases, Concept-DOIs, and claim-level disambiguation notes. Local discoverability logs are tracked in MARKETING-LOG.txt.
Functional Stability Theory is a unified mathematical programme that identifies a single structural challenge — Functional Positivity under Gauge Constraint (Pattern A) — as the common substrate of open problems in number theory, mathematical physics, and cosmology.
| Section | Description | Target |
|---|---|---|
| 01. Start Here | Overview of primary navigation paths and foundations | Jump to Section |
| 02. Discovery Context | Search phrases, scholarly indexes, and citation guidelines | Jump to Section |
| 03. The Five Masters | Core foundation papers and latest Zenodo Concept-DOIs | Jump to Section |
| 04. Domain Supplements | Math, Physics, Cosmology, Biology, and Chemistry applications | Jump to Section |
| 05. Glossary | Core terminology (v2.0, NE-A/B, SGE, Weil QW, Pattern A, RFEP) | Jump to Section |
| 06. Proof Architecture | Five Masters foundation hierarchy (flowchart TD) | Jump to Section |
| 07. Theoretical Data Flow | Pipeline data flow from axioms to diagnostics (flowchart LR) | Jump to Section |
| 08. Numerical Lifecycle | Auto-numbered sequence diagram of the validation workflow | Jump to Section |
| 09. Governance Invariants | 10 runtime & research integrity invariants table | Jump to Section |
| 10. ASCII Architecture | Textual structural layout of the 5 Masters and domain branches | Jump to Section |
| 11. Independent Foundations | Second-route RH and CRM cosmology baseline papers | Jump to Section |
| 12. Validation Scripts | Complete directory and script inventory for numerical replication | Jump to Section |
| 13. Repository Structure | Complete tree layout of papers, domain folders, and scripts | Jump to Section |
| 14. Sibling Ecosystem | Cross-linked research-line, open-bricks, and ellmos-ai packages | Jump to Section |
| 15. Target Personas | Four target scholarly and technical personas and architectural value | Jump to Section |
| 16. Comparative Matrix | Invariant-mapped benchmark against 4 alternative computing paradigms | Jump to Section |
| 17. Third-Party Licenses | Supply chain transparency, zero-copyleft audit, and invariant compliance | Jump to Section |
| 18. Security Policy & Statutory Notice | Vulnerability disclosure SLA, author attribution & § 521 BGB disclaimer | Jump to Section |
| If you are looking for... | Start with | Why |
|---|---|---|
| the programme map | Five Masters | Core foundation papers and their latest Zenodo Concept-DOIs |
| the mathematical classification layer | masters/zeta-zoo/ |
SGE taxonomy, UCU, and zeta-family status boundaries |
| the RFEP / Pattern A foundation | masters/spectrum-duality/ |
Renormalized Free-Energy Principle, DS1-DS3, and physical normal form |
| numerical reproducibility assets | Numerical Validation Scripts | Script index for CCM, K41, Yang-Mills, Navier-Stokes, dark-energy, BSD, Hodge, and SAT diagnostics |
| machine-readable repository context | llms.txt |
Search phrases, scope boundaries, DOI anchors, and disambiguation notes |
This is a research-source repository, not an installable software package. Claim levels vary by paper and folder: some entries are published Zenodo records, some are public guardrail candidates ahead of Zenodo, and several domain supplements remain explicitly conditional or open at the named bridge step.
Use the canonical GitHub path research-line/functional-stability-theory when linking this repository. Broad web searches for "functional stability theory" also collide with control-theory, Lyapunov, and engineering literature, while FST-specific records surface through GitHub, Zenodo-linked scholarly indexes, and topic pages. Useful search phrases:
research-line functional-stability-theoryFunctional Stability Theory RFEP GitHubFunctional Stability Theory Renormalized Free-Energy PrincipleFST Spectrum Duality RFEP ZenodoZeta Zoo SGE taxonomy Functional Stability TheorySpectral Zookeeper CCM microcluster closure
When citing, prefer the Concept-DOIs below for paper branches and this repository URL for source files, scripts, and public reproducibility context.
The programme rests on five CoreCore foundation papers. Concept DOIs identify versioned Zenodo records and resolve to the latest version; cite a version-specific record DOI when a fixed release matters.
| Master | Title | Role | Concept-DOI |
|---|---|---|---|
| Zookeeper | The Spectral Zookeeper | Conditional RH reduction via CCM microcluster closure | 10.5281/zenodo.19673126 |
| Zeta Zoo | The Zeta Zoo — The Mathematical Side of FST | Classification (SGE taxonomy, Boundary Theorem) | 10.5281/zenodo.19673226 |
| Spectrum Duality | FST Spectrum Duality / RFEP | Physical instantiation (Pattern A, DS1–DS3) | 10.5281/zenodo.19036190 |
| Atlas | Dirichlet Character Atlas | Micro-cartography (Galerkin diagnostics; negative method validation) | 10.5281/zenodo.19960809 |
| Selberg | NE-B Failure as Hilbert–Pólya Detection | SGE-YES validation (v2.0 universality on Selberg zeta) | 10.5281/zenodo.19962588 |
Zookeeper is a conditional reduction, not an unconditional RH proof. Imported CCM inputs and the open internal microcluster/endgame and Even Dominance assumptions are described in the paper; see the v1.6 record.
Atlas + Selberg form the method-validation pair: Atlas is the negative test (leading-order Galerkin diagnostics fall short for Dirichlet characters), Selberg is the positive test (v2.0 reproduces a classical operator-based result on Selberg zeta).
Classified by the SGE taxonomy from the Zeta Zoo. These instantiate Pattern A on number-theoretic and algebraic structures. BSD, Hodge, and P vs NP are bridge species — they appear in both the mathematical and physical branches of the programme.
| Paper | Version | Status | Open Problem | Concept-DOI |
|---|---|---|---|---|
| BSD | v1.4 | Maintenance release; rank ≤ 1 verified; no new proof claim | Higher Gross–Zagier (rank ≥ 2) | 10.5281/zenodo.19087443 |
| Hodge | v1.3 candidate | Easy Direction + AP=AbsHodge | Hard Direction beyond Deligne | 10.5281/zenodo.19087439 |
| P vs NP | v1.5 | Reformulation | Uniformity Bridge | 10.5281/zenodo.19056809 |
Derive Pattern A + DS1–DS3 from Spectrum Duality. These instantiate the Dissipative Selection Principle on physical systems.
| Paper | Version | Status | Open Problem | Concept-DOI |
|---|---|---|---|---|
| K41 Variational Minimiser | v1.3 | Unique energy minimizer within the stated K41-normalized joint variational problem | Scope beyond the stated minimization assumptions | 10.5281/zenodo.20131305 |
| Turbulence / DFC Cascade | v1.8 | Conditional companion; DFC hierarchy is an input. Sabra numerical evidence is under review after Issue #1; corrected-flux reruns are not yet reported | DFC projection bridge | 10.5281/zenodo.19056813 |
| Yang–Mills | v2.6 | Conditional; continuum mass-gap step remains conditional | Volume-independent local transfer gap; analytical RG contraction | 10.5281/zenodo.19087433 |
| Navier–Stokes | v2.6 | Conditional; strict-review wording retained | Assumption G2 (projection regularity) | 10.5281/zenodo.19087449 |
| NS Log-Distance | v1.6 | Proof of life / diagnostic bridge | TLL for 3D NS analytically open | 10.5281/zenodo.19056807 |
The cosmological branch of FST. The Dark Energy paper studies a reduced scalar variational model; its cosmological and Hu–Sawicki interpretations remain conditional.
| Paper | Version | Status | Open Problem | Concept-DOI |
|---|---|---|---|---|
| Dark Energy | v1.12 | Corrective preprint; reduced-model core only | RG matching, stable scalar history, source-bound Hu–Sawicki profile, official likelihood all open | 10.5281/zenodo.19036235 |
Status provenance (local package index, 2026-08-08). The version, status, and open-problem labels above are read from the linked public package READMEs where they exist: BSD v1.4 (record 10.5281/zenodo.20671962), K41 v1.3 (record 10.5281/zenodo.20562341), Turbulence v1.8 (record 10.5281/zenodo.21312807), Yang–Mills v2.6 (record 10.5281/zenodo.20716608), and Navier–Stokes v2.6 / NS-LDI v1.6 (records 10.5281/zenodo.20674952 / 10.5281/zenodo.20773609). Spectrum Duality remains v1.9 live with a local v1.10 candidate, not a v1.10 release. The Dark Energy row was updated independently on 1 October 2026 to the verified corrective v1.12 record; the paper-specific README states the open gates. Hodge and P vs NP remain at the candidate/reformulation boundaries shown above because no newer local release marker was found.
The standalone chaperone game-theory paper is published: FST-Nash — Game-Theoretic Diagnostics for Chaperone Systems (DOI: 10.5281/zenodo.20402751). Code and results: research-line/fst-nash. The overview paper FST-III Biological Stability is in applications/fst-iii-biological/.
Planned. See fst-chemistry/.
| Term | Meaning |
|---|---|
| v2.0 | Method package in the RH programme (Trilogy v2.1, 10.5281/zenodo.19035640): proposes a conditional reduction of RH to even dominance of the Weil quadratic form QW_λ using Shift Parity, frontier-prime dominance, NE-A, and NE-B; the required closure assumptions remain open. |
| NE-A | Non-existence theorem A. The Fourier multiplier of the prime shift operator A_λ on the critical line is non-positive — cannot serve as a Hilbert–Pólya operator. |
| NE-B | Finite-truncation result: the computer-assisted result excludes non-scalar symmetric operators commuting with every D_N(r) in the tested prime-shift class for N ≤ 15; the identity commutes trivially. Extension to the full space remains open. |
| SGE | Semigroup–Group Equivalence. Classification axis of the Zeta Zoo: HP-BL-YES (commuting operator exists, e.g. Selberg/Casimir), HP-BL-NO (Riemann prime-shift class, conditional on NE-B-full), HP-BL-OPEN (unresolved, e.g. Prime-Hub). |
| Weil quadratic form QW_λ | Truncated explicit-formula quadratic form whose positivity controls zero locations. Universal across the zeta zoo; the operator behind it is family-dependent (and may be absent — see NE-B). |
| Hilbert–Pólya | The classical conjecture asks whether the Riemann zeros are eigenvalues of a self-adjoint operator. Finite NE-B concerns the tested prime-shift class and does not rule out every possible Hilbert–Pólya operator; the even-dominance route is conditional. |
| Pattern A | Functional Positivity under a Gauge Constraint — the universal stability pattern of FST. |
| RFEP | Renormalized Free-Energy Principle. Mathematical core principle of FST; supplies DS1–DS3. |
| CCM | Connes–Consani–Moscovici. Fourier model for the Weil quadratic form used in the conditional Zookeeper reduction. |
| UCU | Universal Convexity Uniqueness lemma. Together with SGE and Weil, the trinity of meta-principles governing the zeta-type branch. |
flowchart TD
subgraph MASTERS["Five Core Master Foundations"]
ZK["Zookeeper<br/><i>Conditional RH reduction via CCM</i>"]
ZZ["Zeta Zoo<br/><i>SGE Taxonomy & Classification</i>"]
SD["Spectrum Duality<br/><i>RFEP & Pattern A</i>"]
AT["Atlas<br/><i>Dirichlet Cartography (Negative Test)</i>"]
SB["Selberg<br/><i>SGE-YES Method Validation</i>"]
end
subgraph DOMAINS["Domain Supplements & Applications"]
MATH["FST-Mathematics<br/>(BSD, Hodge, P vs NP)"]
PHYS["FST-Physics<br/>(K41, Turbulence, YM, NS)"]
COSMO["FST-Cosmology<br/>(Dark Energy / CRM)"]
BIO["FST-Biology<br/>(FST-Nash Chaperones)"]
end
ZK --> MATH
ZZ --> MATH
SD --> PHYS
SD --> COSMO
SD --> BIO
AT -.- ZK
SB -.- ZK
classDef master fill:#1f2937,stroke:#6366f1,stroke-width:2px,color:#fff;
classDef domain fill:#111827,stroke:#10b981,stroke-width:1.5px,color:#fff;
class ZK,ZZ,SD,AT,SB master;
class MATH,PHYS,COSMO,BIO domain;
flowchart LR
subgraph HYP["1. Mathematical Axioms & Normal Forms"]
RFEP["Renormalized Free-Energy Principle (RFEP)"]
PAT_A["Pattern A: Functional Positivity under Gauge Constraint"]
DS["Dissipative Selection Principles (DS1–DS3)"]
end
subgraph PROOF["2. Master Foundations & Proofs"]
ZK["Zookeeper (CCM Microcluster Closure)"]
ZZ["Zeta Zoo (SGE Taxonomy & UCU)"]
VAL["Method-Validation Pair (Atlas / Selberg)"]
end
subgraph INST["3. Domain Instantiations"]
MATH["FST-Mathematics (BSD, Hodge, P vs NP)"]
PHYS["FST-Physics (K41, Turbulence, YM, NS)"]
COSMO["FST-Cosmology (Hu–Sawicki / Dark Energy)"]
BIO["FST-Biology (FST-Nash Chaperones)"]
end
subgraph DIAG["4. Local Numerical Validation (Zero-Egress)"]
SCRIPTS["Python Numerical Diagnostics (scripts/)"]
RESULTS["Reproducibility & Verification Metrics"]
end
HYP --> PROOF
PROOF --> INST
INST --> DIAG
classDef hyp fill:#1e1b4b,stroke:#818cf8,stroke-width:1.5px,color:#fff;
classDef proof fill:#1f2937,stroke:#6366f1,stroke-width:2px,color:#fff;
classDef inst fill:#111827,stroke:#10b981,stroke-width:1.5px,color:#fff;
classDef diag fill:#064e3b,stroke:#34d399,stroke-width:1.5px,color:#fff;
class RFEP,PAT_A,DS hyp;
class ZK,ZZ,VAL proof;
class MATH,PHYS,COSMO,BIO inst;
class SCRIPTS,RESULTS diag;
sequenceDiagram
autonumber
actor Researcher as Theoretical Researcher / Auditor
participant Core as FST Axioms (RFEP & Pattern A)
participant Master as Master Foundation (Zookeeper/CCM)
participant Domain as Domain Constraint Ledger (e.g. YM, NS, K41)
participant Script as Zero-Egress Local Script (scripts/)
participant Ledger as Deterministic Verification Ledger
Researcher->>Core: Formulate Variational Principle & Gauge Constraint
Core->>Master: Derive Operator Normal Form / Shift-Parity Structure
Master->>Domain: Instantiate Domain Hypothesis & Transfer Matrix
Domain->>Script: Execute Local Python Diagnostics (numpy/scipy)
Note over Script: 100% Offline / Zero-Egress Execution
Script->>Script: Compute Finite Outer-Gap & Coercive Residuals
Script->>Ledger: Output Bit-for-Bit Deterministic Verification Certificate
Ledger-->>Researcher: Validate Reproducibility & Mathematical Invariants
The functional-stability-theory repository enforces ten fundamental runtime, security, and research governance invariants:
| # | Invariant Dimension | Guarantee & Contract Specification | Verification Method |
|---|---|---|---|
| 01 | 100% Local-First & Zero-Egress | All numerical diagnostics, simulation scripts, and tests execute completely offline. Zero telemetry, tracking, or network calls. | Strict offline testing; CI matrix isolation |
| 02 | Unprivileged Execution (RunAsInvoker) | All scripts and tools run strictly in unprivileged user-mode. Root or administrative elevation is never required or invoked. | Environment audit; unprivileged test suites |
| 03 | Deterministic Reproducibility | Numerical assertions and validation ledgers yield deterministic, bit-for-bit reproducible outcomes across all supported platforms. | Pytest test suite (110+ passed tests); seeded PRNGs |
| 04 | Claim-Level Disambiguation | Zookeeper is a conditional RH reduction with imported inputs and open internal closure assumptions; claim levels are stated per paper. | README status tables; preprint classification headers |
| 05 | Fail-Closed Ledger Gatekeeping | Numerical verification scripts reject circular, degenerate, or ill-conditioned inputs immediately (fail-closed) rather than returning ambiguous approximations. | Exception assertions; bad-scale and Gribov controls |
| 06 | Versioned Zenodo Records | Concept DOIs identify version chains; cite a version-specific DOI for a fixed release. | Zenodo version records |
| 07 | Multi-OS Platform Parity | Scripts, LaTeX builds, and test harnesses deliver bit-identical mathematical logic across Windows, Linux, and macOS. | GitHub Actions CI multi-OS matrix (ci.yml) |
| 08 | Cloud-Sync Conflict Hardening | Repository ignore rules prevent cloud-sync conflict files (*-conflict-*, *.sync-temp-*) and multi-agent lock contention (LOCK.*). |
.gitignore inspection; automated contract tests |
| 09 | Transparent Diagnostic Floor | Unconditional positive controls (e.g., 2D U(1) character expansion) are segregated from unproven continuum transfer hypotheses. | Dedicated positive/negative control scripts |
| 10 | 48h Security & 5-Day Triage SLA | Security anomalies, supply-chain vulnerabilities, and code integrity concerns are acknowledged within 48 hours and triaged within 5 business days. | Formal commitment in SECURITY.md |
FIVE MASTERS
┌────────────────┬────────────────┬─────────────────┬────────────────┐
│ │ │ │ │
Zookeeper Zeta Zoo Spectrum Duality Atlas Selberg
(RH reduc.) (Classification) (Pattern A, (Dirichlet, (NE-B
SGE / UCU / DS1–DS3, negative failure;
Weil QW_λ) RFEP) method test) SGE-YES
│ │ │ │ │
│ FST-Mathematics FST-Physics method-validation pair
│ │ │
│ ┌───────┼───────┐ ┌─────┼─────┐
│ │ │ │ │ │ │
│ BSD† Hodge† PvNP† TU YM NS
│ │
│ FST-Cosmology
│ │ NS-LDI
│ DE
│
Zookeeper: CONDITIONAL RH REDUCTION (CCM route)
† = bridge species (math + physics)
FST (Functional Stability Theory)
│
├── Masters
│ ├── Zookeeper Conditional RH reduction (CCM microcluster closure)
│ ├── Zeta Zoo Mathematical classification (SGE taxonomy)
│ ├── Spectrum Duality Physical instantiation (RFEP, Pattern A)
│ ├── Atlas Micro-cartography of Dirichlet (negative method test)
│ └── Selberg SGE-YES method validation (positive)
│
├── FST-Mathematics BSD, Hodge, P vs NP
├── FST-Physics Turbulence, Yang–Mills, Navier–Stokes, NS-LDI
├── FST-Cosmology Dark Energy
├── FST-Biology (in development)
└── FST-Chemistry (planned)
2025/2026 CRM I–IV (dark energy) Conditional RH route (even dominance)
developed independently developed independently
\ /
+---------+---------+
|
Recognition: both share the same
structural pattern (Pattern A)
|
v
RFEP formulated (general principle)
|
Several dead ends
|
v
Idea: classify zeta-type families
using techniques from the RH programme
|
Not enough — need deeper tools
|
v
RH via Connes framework (CCM)
microcluster closure → conditional reduction
|
v
Zeta Zoo opens: SGE taxonomy
classifies all zeta families
|
v
Atlas (Dirichlet, negative) + Selberg (SGE-YES, positive)
method-validation pair completed
|
v
CoreCore expanded to FIVE Masters
(Zookeeper, Zeta Zoo, Spectrum Duality,
Atlas, Selberg) + domain supplements
| Level | Name | Acronym | Meaning | Concept-DOI |
|---|---|---|---|---|
| Programme | Functional Stability Theory | FST | The programme name (umbrella over all) | — |
| Principle | Renormalized Free-Energy Principle | RFEP | The mathematical core principle | 10.5281/zenodo.19036190 |
| Pattern | Pattern A: Functional Positivity under Gauge Constraint | Pattern A | The universal stability pattern | 10.5281/zenodo.19036190 |
| Name | Role | Concept-DOI |
|---|---|---|
| RH Even Dominance v2.1 (Trilogy, Part I-III) | Independent conditional RH reduction, second route | 10.5281/zenodo.19035640 |
| RH Direct Proof (Even Dominance) | Historical title; conditional frontier-dominance route with open analytical assumptions | 10.5281/zenodo.19764771 |
| CRM Cosmology (I–V) | Independent dark energy model | 10.5281/zenodo.18728935 |
These stand independently of FST. The RFEP was abstracted from them; they are not derived from it.
| Script | Paper | Description |
|---|---|---|
masters/zookeeper/scripts/ |
Zookeeper | CCM microcluster-closure reproducibility pipeline; compact outputs in masters/zookeeper/results/ |
scripts/k41/compute_F_spectrum.py |
K41 Variational Minimiser | K41 as unique minimiser of F[E]; strict convexity test |
scripts/turbulence/compute_goy_shell_dfc.py |
Turbulence / DFC Cascade | Sabra/GOY shell-model DFC1/DFC2 verification and result plot |
scripts/yang-mills/compute_dobrushin_su2.py |
Yang-Mills | SU(2) lattice Dobrushin influence scan and gap plot |
scripts/yang-mills/compute_birkhoff_rg.py |
Yang-Mills | Birkhoff contraction scan for hierarchical RG steps |
scripts/yang-mills/compute_coercive_complement_ledger.py |
Yang-Mills | Finite outer-gap and residual/gap gate with bad-scale and Gribov matched controls |
scripts/yang-mills/compute_os_capacity_ledger.py |
Yang-Mills | OS-danger capacity ledger and negative-control diagnostic |
scripts/yang-mills/compute_rp_os_transfer_ledger.py |
Yang-Mills | RP/OS transfer matrix positivity ledger |
scripts/yang-mills/compute_rp_os_rfep_transfer_ledger.py |
Yang-Mills | RFEP transfer matrix diagnostic ledger |
scripts/yang-mills/compute_u1_2d_strong_coupling_positive_control.py |
Yang-Mills | 2D U(1) strong-coupling positive control ledger |
scripts/yang-mills/compute_ym_waisen_transfer_ledger.py |
Yang-Mills | Yang-Mills waisen transfer verification ledger |
scripts/yang-mills/u1_strong_coupling_positive_control.py |
Yang-Mills | Direct U(1) character expansion positive control script |
scripts/navier-stokes/compute_ds3_lorenz.py |
Navier-Stokes | DS3 stress test on Lorenz attractor; TV saturation |
scripts/navier-stokes/compute_bv_selection.py |
Navier-Stokes | Balanced-viscosity selection test on the Lorenz attractor |
scripts/navier-stokes/compute_bv_multi_attractor.py |
Navier-Stokes | BV-selection stress test on Lorenz, Roessler, and Chen attractors |
scripts/navier-stokes/compute_mu_reach.py |
Navier-Stokes | Measure-theoretic reach scan on Lorenz and KS attractors |
scripts/navier-stokes/compute_tll_ldi_lorenz.py |
NS-LDI | Proof of Life: TLL+LDI on Lorenz attractor (5/5 tests) |
scripts/navier-stokes/compute_tll_ldi_ks.py |
NS-LDI | TLL+LDI diagnostics and grid refinement on the KS attractor |
scripts/dark-energy/compute_w_vs_desi.py |
Dark Energy | w_eff(z) comparison with DESI constraints |
scripts/dark-energy/compute_w_mapping.py |
Dark Energy | Correct w_eff → w_DE mapping + DESI grid scan |
scripts/dark-energy/compute_husawicki_mcmc.py |
Dark Energy | Hu-Sawicki f(R) MCMC fit against DESI+Planck+Cassini |
scripts/bsd/compute_height_saturation.py |
BSD | Height saturation test for quadratic twists |
scripts/bsd/compute_bsd_verification.py |
BSD | BSD formula sanity checks for selected LMFDB curves |
scripts/bsd/compute_rank2_lmfdb.py |
BSD | Rank-2 regulator positivity sample and plot |
scripts/hodge/compute_ghr_spectrum.py |
Hodge | GHR spectrum numerical verification |
scripts/hodge/compute_voisin_test.py |
Hodge | Voisin-style negative-control stress test |
scripts/p-vs-np/compute_sat_entropy.py |
P vs NP | SAT slice-entropy experiment and result plot at the 3-SAT phase transition |
scripts/zeta-zoo/dedekind_ne_b_test.py |
Zeta Zoo | Dedekind Q(sqrt(-5)) NE-B analog probe |
scripts/zeta-zoo/ihara_petersen_sge_test.py |
Zeta Zoo | Ihara/Petersen SGE YES-side test |
scripts/zeta-zoo/sge_control_experiment.py |
Zeta Zoo | SGE YES/NO discriminating control experiment |
masters/atlas/scripts/ |
Atlas | Galerkin computation pipeline (35 scripts: basis, κ-grid, asymptotic scans, χ-specific tests) |
functional-stability-theory/
├── masters/ Five CoreCore foundation papers
│ ├── zookeeper/ Conditional RH reduction (microcluster closure)
│ ├── zeta-zoo/ Classification (SGE taxonomy)
│ ├── spectrum-duality/ Physical axioms (RFEP, Pattern A)
│ ├── atlas/ Dirichlet micro-cartography (negative method test)
│ └── selberg/ NE-B failure as HP detection (SGE-YES validation)
├── fst-mathematics/ Domain supplements — Mathematics
│ ├── bsd/ Rank-1 positivity (reformulation)
│ ├── hodge/ No-go + easy direction
│ └── p-vs-np/ Witness entropy gap (reformulation)
├── fst-physics/ Domain supplements — Physics
│ ├── k41-variational-minimiser/ K41 energy minimiser (stated joint problem)
│ ├── turbulence/ DFC/anomalous-dissipation companion
│ ├── yang-mills/ Mass gap (conditional)
│ └── navier-stokes/ Regularity + NS-LDI (conditional)
├── fst-cosmology/ Domain supplements — Cosmology
│ └── dark-energy/ CRM screening (conditional, not Cassini-verified)
├── fst-biology/ Domain supplements — Biology (in development)
├── fst-chemistry/ Domain supplements — Chemistry (planned)
└── scripts/ Numerical validation (per-paper subdirectories)
functional-stability-theory is the central theoretical hub of the research-line initiative and connects across the open-bricks open science and toolchain ecosystem:
| Repository / Package | Focus / Domain | Integration |
|---|---|---|
research-line/fst-nash |
Chaperone Game Theory | FST-Biology standalone companion (DOI: 10.5281/zenodo.20402751) |
research-line/rh-even-dominance |
Number Theory | Riemann Hypothesis even-dominance trilogy foundation |
research-line/crm-cosmology |
Cosmology | Cooperative Renormalization Model foundation |
research-line/prompt-archaeology-casestudy2 |
AI & Epistemology | 4-Stage prompt archaeology & reproducibility artifacts |
research-line/ai-elite-swr |
AI & Society | AI elite structures & social welfare research |
research-line/economic-sanctions-coercive-diplomacy |
Political Economy | Game-theoretic model of sanctions and coercive bargaining |
biotec-line/VFDistiller |
Bio-Genetics Pipeline | Variant effect predictor & VCF distillation toolchain |
doc-bricks/MediaBrain |
Multi-Format Document Synthesis | Offline-first knowledge repository and research indexing engine |
dev-bricks/CodeBox |
Code Analysis & Diagnostics | Syntax tree inspection & structural linting environment |
dev-bricks/DevCenter |
Developer Tooling | Unified developer dashboard and workspace management |
dev-bricks/githubbot |
Fleet Governance Automation | Automated repository hygiene, multi-org sync & CI gatekeeping |
ellmos-ai/skills |
Multi-Agent Execution Fabric | Formalized AI cognitive skill library & modular workflow specs |
ellmos-ai/sqlite-transit-sync |
Data Transit | Deterministic snapshot retention and sync engine |
ellmos-ai/ellmos-development-system |
AI Development Environment | Full-stack agentic runtime environment & MCP orchestration |
open-bricks/governance |
Open Source Governance | Cross-organizational policy framework, security disclosure & license standards |
open-bricks |
Umbrella Ecosystem | Open source & open science federation |
functional-stability-theory serves four core academic and computational research personas across mathematics, physics, and autonomous scientific discovery:
| Persona | Core Research Question & Challenge | How FST Solves It | Architectural Value |
|---|---|---|---|
| Theoretical Physicists & Field Theorists | Identifying consistent non-perturbative stability mechanisms for Yang-Mills mass gap, Navier-Stokes regularity, and turbulent anomalous dissipation | Unifies dissipative selection under the Renormalized Free-Energy Principle (RFEP) and Pattern A (Functional Positivity under Gauge Constraint) | Single universal normal form across gauge theory, fluid mechanics, and cosmological screening |
| Analytic Number Theorists & Millennium Researchers | Bypassing structural no-go theorems (NE-A/NE-B) in operator-theoretic approaches to the Riemann Hypothesis | Introduces the SGE taxonomy (Zeta Zoo) and v2.0 even-dominance of the Weil quadratic form, linking microcluster closure (Zookeeper) with Selberg validation | Conditional framework with explicit open analytic steps |
| Open-Science Curators & Formal Verification Reviewers | Validating sweeping mathematical claims against reproducible, air-gapped code and version-stable artifacts | Provides 100% offline, zero-egress numerical validation scripts, deterministic CSV/JSON ledgers, and CERN/Zenodo Concept-DOIs | Bit-for-bit verifiable computational evidence with transparent claim-level boundary tagging |
| AI Research Agents & Literature Synthesizers | Disambiguating specialized mathematical stability theory from generic control engineering (Lyapunov) and software test suites | Publishes structured llms.txt, PEP 621 metadata URLs, semantic search phrases, and explicit negative controls |
High-precision LLM retrieval without hallucinations or domain cross-contamination |
The following invariant-mapped benchmark contrasts the Functional Stability Theory (FST) framework with four prevalent paradigms across theoretical physics, analytic number theory, and scientific computing:
| Invariant Dimension | FST (research-line) | Classical Number Theory | Connes Noncommutative Geometry | Traditional CFD Simulation | Closed Math Suites (Wolfram/MATLAB) |
|---|---|---|---|---|---|
| 01. Universal Substrate | RFEP / Pattern A (Universal normal form) | Ad-hoc single problems | Adèle class space trace formula | Navier-Stokes discretization (DNS/LES) | Proprietary black-box routines |
| 02. Hilbert–Pólya Status | Conditional even-dominance route; finite NE-B obstruction | No general exclusion established here | Analytic continuation obstacles | Not applicable | Not applicable |
| 03. Zero-Egress Reproducibility | 100% Offline Python Ledgers (Deterministic) | Rare / Paper-only | Purely theoretical / Paper | Cluster / HPC dependent | Cloud license / Phone-home required |
| 04. Claim-Level Disambiguation | Strict (Theorem / Cond. / Open markers) | Often informal | Highly complex / Implicit | Heuristic / Empirical | Closed vendor documentation |
| 05. Scholarly Provenance | Zenodo Concept-DOI version chain; cite a version-specific DOI for fixed citations | Journal / ArXiv | ArXiv / Monograph | Conference / Journal | Closed vendor build versions |
| 06. Open Source License | CC-BY-4.0 (100% Permissive) | Proprietary / ArXiv | Copyrighted monograph | Often GPL / Commercial | Proprietary commercial licensing |
| 07. Third-Party Supply Chain | 100% Permissive Audited SBOM (0% Copyleft) | N/A | N/A | Unaudited legacy toolchains | Closed binary blobs |
| 08. AI & LLM Readiness | llms.txt & PEP 621 Metadata Standards |
Unstructured | Non-machine-readable | Non-structured | Restricted closed APIs |
| 09. Cross-Platform Parity | Win / Linux / macOS (CI Matrix verified) | N/A | Neutral (Textual) | Mostly Linux HPC specific | OS-specific installer / dongle |
| 10. Security & SLA Assurance | 48h Response / 5-Day Triage SLA | Informal | Informal | Informal | Vendor helpdesk / No SLA |
functional-stability-theory enforces a strict open-science and permissive open-source supply chain:
- Primary Work License: Creative Commons Attribution 4.0 International (CC-BY-4.0) — unrestricted academic and commercial reuse with attribution.
- Zero Copyleft: 0% AGPL, GPL, or LGPL components in codebase and verification tooling.
- 100% Offline Zero-Egress: Validation scripts run completely air-gapped without remote network requests or telemetry.
| Component | License | Role in Programme | Supply Chain Status |
|---|---|---|---|
| Python Standard Library | PSF-2.0 | Core verification logic, math/cmath, hashing & ledgers | Audited / Permissive |
mpmath (optional) |
BSD-3-Clause | Arbitrary-precision floating-point arithmetic | Audited / Permissive |
sympy (optional) |
BSD-3-Clause | Symbolic algebra and identity verification | Audited / Permissive |
numpy (optional) |
BSD-3-Clause | Vectorized numerical linear algebra | Audited / Permissive |
scipy (optional) |
BSD-3-Clause | Numerical integration and ODE/PDE solvers | Audited / Permissive |
Development Tools (pytest, ruff, setuptools) |
MIT / Apache-2.0 | Contract testing, static linting & build packaging | Audited / Permissive |
For the complete software inventory, authoritative license texts, and invariant compliance details, see THIRD_PARTY_LICENSES.md. A bit-accurate, machine-readable plain-text Level 1 SBOM companion is available at THIRD_PARTY_LICENSES.txt.
functional-stability-theory enforces a strict zero-egress policy and a formal coordinated vulnerability disclosure workflow. Vulnerability reports receive initial acknowledgment within 48 hours and formal triage within 5 business days. Contact: [email protected] or [email protected]. See SECURITY.md for full policy details. For developer guidelines, Plan D local development workflow, and governance invariants, see CONTRIBUTING.md.
- Author: Lukas Geiger
- ORCID: 0009-0005-7296-1534
- Primary License: Creative Commons Attribution 4.0 International (CC-BY-4.0)
- Canonical Notice:
NOTICE
Gemäß § 521 BGB (Gefälligkeitsrecht) wird diese wissenschaftliche Forschungssoftware und Quelltextdokumentation unentgeltlich und ohne jede Gewährleistung bereitgestellt. Haftung für Sach- und Rechtsmängel ist auf Vorsatz und grobe Fahrlässigkeit beschränkt. Die theoretischen Theoreme, numerischen Beweis-Ledger und Validierungsskripte dienen ausschließlich akademischen und Open-Science-Zwecken; jede weitergehende Haftung ist im gesetzlich zulässigen Rahmen ausgeschlossen.