Intismeran Autogene and k = 3 Correspondence in QCD etc.: GOLDEN-ANGLE HELIX COORDINATES AND FIBONACCI–LUCAS NEOANTIGEN ARCHITECTURE by Stefan Geier et al.

 

Intismeran Autogene and k = 3 Correspondence in QCD etc.: GOLDEN-ANGLE HELIX COORDINATES AND
FIBONACCI–LUCAS NEOANTIGEN ARCHITECTURE

A refined short hypothesis paper clarifying the descriptive putative unifying 3.62 ± 0.02 (± 0.55%) core window

Stefan A. Geier*, Caroline Geier, Stephanie Geier, Constantin Geier, Katharina Geier,
Nora Blättermann-Goldstein, and Michèle Geier-Noehl

Institute for Structuralistic Theory of Sciences Simssee (ISTS), Gerhart-Hauptmann-Straße 6, 83071 Haidholzen, Germany; Ludwig-Maximilians-Universität Munich, Germany
*Correspondence: wissenschaftstheorie.simssee.1@gmail.com

Epistemic status This note proposes a typed and falsifiable bridge between two author manuscripts. The decimal windows are explanatory summaries, not measured uncertainties. The note does not claim intentional golden-ratio design, Fibonacci anyons in biomolecules, or a cellular realization of QCD/F-theory geometry.

Abstract

Part III defines the exact golden-algebraic benchmark Φ+2=Φ²+1=3.61803398875…, the golden-angle contraction xΦ=40 exp(−2π/Φ²)=3.62885156298…, and the rational helical coordinate 40/11=3.636363636…. For transparent communication, Φ+2 and xΦ form a descriptive core window 3.62±0.01=[3.61,3.63]; an extended context window 3.62±0.02=[3.60,3.64] also contains the rounded canonical α-helical repeat and 40/11. Neither window is a confidence interval, and prospective tests should retain the exact xΦ target. The intismeran manuscript independently identifies the patent-defined Fibonacci–Lucas coordinates 34=F₉, 29=L₇, 5=F₅, 21=F₈ and L₇+F₅=F₉ across a pathway containing A-form RNA, possible precursor helices, proteolytic resetting, and extended or polyproline-II-like peptide–HLA states. We propose a cautious bridge in which documentary recurrence counts and a preregistered local helix-state descriptor jointly predict cleavage, peptide–HLA abundance and T-cell response beyond conventional sequence, RNA-folding and HLA models. Present evidence supports a testable mediation programme, not a causal, anyonic or dimensional interpretation.

Keywords: intismeran autogene; V940; golden angle; 3.62 ± 0.01;0.02; α-helix; Fibonacci–Lucas coordinates; helix-state transduction; peptide–HLA; Fibonacci anyons; falsifiability

1. A transparent decimal-window notation

The four nearby values should be displayed in a way that distinguishes an exact mathematical target from a rounded explanatory band. Let c₀=3.62. The core expression c₀±0.01 means the closed decimal interval [3.61,3.63]. It contains Φ+2=3.61803398875… and xΦ=3.62885156298…, but it does not contain the rounded α-helical repeat 3.600000 or 40/11=3.636363636…. A wider context interval c₀±0.02=[3.60,3.64] contains all four values. The ± signs therefore communicate numerical clustering; they do not report experimental error, biological variability or statistical coverage.

Figure 1. Nested decimal windows around 3.62. The core band is a transparent shorthand for the two Part III mathematical coordinates; the extended band provides helical context. Neither band is an uncertainty interval.

 

1.1 Numerical ledger and prospective-use rule

Coordinate	Value	Deviation from 3.62	Inside 3.62±0.01?	Scientific use
Canonical α-helix	≈3.600000	−0.020000	No	Rounded structural context; inside ±0.02
Φ+2=Φ²+1	3.618034	−0.001966	Yes	Exact golden-algebraic benchmark
xΦ=40 exp(−2π/Φ²)	3.628852	+0.008852	Yes	Exact prospective Part III target
40/11	3.636364	+0.016364	No	Rational helical coordinate; inside ±0.02

For prospective analysis, the exact value xΦ—not the rounded 3.62 centre and not a movable tolerance band—should be frozen before data inspection. The decimal windows are retained only to make the hierarchy of nearby coordinates immediately visible and to prevent “approximately 3.62” from being mistaken for an exact equality.

2. Source-derived coordinates and the proposed interface

The intismeran manuscript supplies a different kind of exactness: source-defined design counts. Its central nested identity is 29+5=34, or L₇+F₅=F₉, together with 34=F₉ and a 21-day coordinate 21=F₈. It also distinguishes four non-equivalent conformational levels: local A-form-like RNA; a dynamic translated precursor that may contain α-, 3₁₀-, turn-, coil- or coiled-coil states; proteolytically generated fragments; and groove-constrained peptide–HLA complexes. Class-I ligands are generally extended or bulged, whereas many class-II ligands follow an extended, polyproline-II-like trajectory rather than a canonical α-helix [2,6–8]. Accordingly, any Part III connection should be sought upstream in RNA or precursor-state ensembles, not assumed at the final HLA-bound state.

Figure 2. Putative typed bridge between the Part III mathematical layer and the intismeran conformational pathway. The central map is a hypothesis to be tested, not an established physical identity.

3. A minimal, falsifiable bridge hypothesis

Let fα(s) denote the measured occupancy of α-like conformers for a precursor segment s, and let nα(s) denote the mean residues-per-turn value within those conformers. A Part III-derived local descriptor can be defined prospectively as

CΦ(s) = { fα(s), ΔΦ(s) },     ΔΦ(s) = | nα(s) − xΦ |,     xΦ = 3.62885156298…

The descriptive core window 3.62±0.01 may be reported alongside CΦ(s), but it should not replace xΦ in the primary analysis. The putative bridge is a mediation model rather than a numerical identification: documentary recurrence coordinates and CΦ(s) are tested as predictors of precursor accessibility, cleavage, peptide abundance, peptide–HLA presentation and T-cell response.

BΦ,Int :  (recurrence coordinate, CΦ)  →  cleavage  →  pHLA abundance  →  T-cell response

Support would require CΦ(s) to improve prediction after adjustment for amino-acid composition, ordinary helix propensity, linker and cleavage motifs, RNA structure, expression, HLA allele and binding affinity. A finding that only conventional variables predict function would falsify the proposed bridge while leaving the exact arithmetic intact.

 

Table 2. Typed correspondence and scientific boundary

Part III element	Intismeran element	Admissible link	Not established
Φ²+1=Φ+2; Fibonacci global dimension	34, 29, 5 and 21 as Fibonacci/Lucas coordinates	Shared recurrence algebra and a prespecified mathematical vocabulary	Fibonacci anyons or topological order in the biological product
xΦ and the 3.62±0.01 core window	Possible α/3₁₀/coiled-coil precursor states	A local, measured helix-state predictor with exact xΦ frozen	A fixed product-wide helix or a causal design principle
Typed correspondence and validation gates	Helix-state transduction across RNA, precursor, cleavage and pHLA	A mediation model with matched controls	Equality of topological, spacetime and biomolecular dimensions
Prospective prediction	Matched sequence and neighbouring-length interventions	Replication of structure-to-function mediation	Retrospective proximity as proof

4. Prospective test

A compact test can use patient-independent model concatemers with identical mutant epitope cores. Synonymous ORFs would vary the RNA ensemble while holding the amino-acid precursor fixed. Flanking or linker variants would generate α-promoting, α-breaking and PPII/coil-biased precursor contexts without changing the core epitope or its predicted HLA anchors. Neighbouring-length controls —13 versus 14 residues and 20, 21 and 22 residues—would separate Fibonacci membership from ordinary length and processing effects. Measurements should include SHAPE-MaP or DMS probing, translation and decay, circular dichroism plus residue-resolved structural methods, controlled proteolysis, immunopeptidomics, peptide–HLA abundance and T-cell activation [2,5–8].

The primary model, exact xΦ target, secondary 3.62±0.01 communication window, competing conventional predictors, multiplicity correction and failure criteria should all be preregistered. Support requires a reproducible chain CΦ → precursor state → cleavage/pHLA → T-cell response in held-out constructs. The bridge fails if neighbouring values perform equally well, if the signal is absorbed by ordinary sequence or folding models, or if the functional endpoint does not replicate.

5. Conclusion

The most defensible Part III–intismeran link is not a literal identity between QCD/F-theory, Fibonacci anyons and therapeutic biomolecules. It is a two-layer research hypothesis: exact Fibonacci–Lucas counts organize the documented intismeran architecture, while the exact Part III value xΦ supplies a prespecified descriptor for transient upstream helix states. The shorthand 3.62±0.01 makes the central mathematical cluster transparent, but it neither encompasses the full 3.60-to-3.636 helical context nor represents experimental uncertainty. A descriptive 3.62±0.02 window encompasses the full 3.60-to-3.636 helical context and thus needs further consideration and could show explanative power in future. At present no public product-specific helix map, intentional golden-ratio design, anyonic phase or causal mechanism has been established.

One-sentence conclusion Part III can be linked to intismeran most cautiously as a preregistered helix-state mediation hypothesis in which the exact target xΦ=3.62885156… is communicated by (but not replaced by) the descriptive 3.62±0.01 core window within an exact Fibonacci–Lucas documentary architecture. A descriptive 3.62±0.02(±0.55...%) window encompasses the full 3.60-to-3.636 helical context.

Source status

The two programme papers are author manuscripts and are used as primary sources for their own hypotheses and calculations. Peer-reviewed structural and topological literature supports the standard α-helix, RNA, peptide–HLA and Fibonacci-anyon statements. No new experimental data were analysed in this note.

References

1. Geier SA, et al. The k = 3 Correspondence in QCD and F-Theory—Part III: The Golden-Angle Exponential Between Eleven and Twelve. Submission manuscript, version 1.8; 2026.

2. Geier SA, Geier C, Geier S, et al. Intismeran autogene and the GEIER programme, Part 3: Helical, extended, and recursive structures from therapeutic mRNA to HLA presentation. Author manuscript, version 0.0.0.0; 2026.

3. Geier SA, Geier-Noehl M. Coiled Coil Helices Including Alpha-Keratin and Leucine Zippers are Related to the Golden Ratio Concept by the Omega Constant Ω and are Related to Tetrahedra Helices and to Quantum Physics. ResearchGate preprint. 2024. doi:10.13140/RG.2.2.11482.35525.

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6. Madden DR, Gorga JC, Strominger JL, Wiley DC. The structure of HLA-B27 reveals nonamer self-peptides bound in an extended conformation. Nature. 1991;353:321–325. doi:10.1038/353321a0.

7. Stern LJ, Brown JH, Jardetzky TS, et al. Crystal structure of the human class II MHC protein HLA-DR1 complexed with an influenza virus peptide. Nature. 1994;368:215–221. doi:10.1038/368215a0.

8. Jardetzky TS, Brown JH, Gorga JC, et al. Crystallographic analysis of endogenous peptides associated with HLA-DR1 suggests a common, polyproline II-like conformation for bound peptides. Proc Natl Acad Sci USA. 1996;93:734–738. doi:10.1073/pnas.93.2.734.

9. Nayak C, Simon SH, Stern A, Freedman M, Das Sarma S. Non-Abelian anyons and topological quantum computation. Rev Mod Phys. 2008;80:1083–1159. doi:10.1103/RevModPhys.80.1083.

The text is open for critique and discussion.
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