Spinor Corrections b-C & a-C, the Choptyuk Problem, and the Direct Einstein Programme

Monograph: Spinor corrections b-C and a-C and the solution of the Choptyuk problem by Ishak Khamzatovich Isaev (GitHub: @wild8highlander, sole author and maintainer) — Rigorous computation of spectral invariants on the Klein quartic curve with applications to LIGO/Virgo quasi-normal mode predictions.

Verification monograph (bilingual RU/EN): What was verified, how, and with what verdict — the complete honest account of the whole verification programme: monograph/verification_monograph_bilingual.pdf · monograph/verification_monograph_bilingual.docx

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Overview

This repository provides four independent implementations for the verification, simulation, and visualization of all results presented in the monograph:

Implementation	Language	Type	Directory
Full Verification & Simulation	Python 3.10+	CLI with interactive menu	python/
Full Verification & Simulation	Julia 1.9+	REPL with interactive menu	julia/
Web Application	Java 17+ (Spring Boot)	REST API + Web UI	java-webapp/
Interactive Visualization	Next.js 15 + React	Real-time dashboard	interactive-viz/

All implementations share:

• Interactive parameter configuration (all values customizable, including arbitrary precision)
• Hypothesis testing with custom spinor structures and group configurations
• Multi-format report generation: DOCX, PDF, TXT, MD, CSV, HTML, JSON
• High-resolution plots: 600 DPI PNG + vector PDF/SVG
• Complete execution logs appended to every report
• Structured output directory for all artifacts

On top of the monograph suite, the repository hosts a second, larger research programme — the direct Einstein programme in einstein_direct/: the Choptuik critical-collapse problem attacked directly from the classical Einstein equations derived from the Hilbert action, with every claim machine-verified and every negative result kept as a first-class outcome.

The discipline of the repository

Everything in this repository follows one rule, applied everywhere:

hypothesis → machine confirmation → honest caveats and limitations.

• Nothing is fitted to literature values. Agreements with published constants (γ_Ch = 0.374, b_Ch = 0.37651, the echo period Δ ≈ 3.44, the spinor ladder π/30) are reported as comparisons, never as targets of a fit.
• Walls, floors, obstructions and negative verdicts are kept and documented with the same care as positive results.
• Mistakes found later are retracted publicly (see the honesty ledger below — two verdicts from earlier campaigns carry formal ERRATUM notes).
• Each campaign writes machine-readable JSON outputs, and a pytest suite re-checks the major theorems from those outputs (21/21 passing).

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Table of contents

1. Overview
2. The verification programme at a glance
3. Audit & Transfer Appendix
4. Mathematical Background
5. Einstein Direct — the campaign ledger
6. Quick Start
7. Architecture
8. Project Structure
9. Scientific background in one minute
10. QCD Bridge Suite
11. Documentation map
12. Report Formats
13. Visualization Output
14. Verification Results
15. Citation
16. Author
17. License
18. Reproducibility
19. Contributing
20. Acknowledgments

Repository quick facts

Fact	Value
Author	wild8highlander (Ishak Khamzatovich Isaev), sole author and maintainer
License	Isaev Proprietary (individual)
Machine-verified derivation	Hilbert action → Einstein equations, residuals ≈ 10⁻⁴¹
Automated test suite	21/21 passing (re-checks machine theorems from JSON outputs)
Campaign result files	31 JSON machine outputs in einstein_direct/results/
Tracked files	700+ across 20+ research and documentation directories
Source files	112 Python · 17 Julia · 21 Java + a Next.js dashboard
Publications in-repo	original monograph (RU/EN, DOCX/PDF), QCD-bridge monograph, audit appendix, bilingual verification monograph (metadata-free)
Figures	20 einstein_direct figures (RU/EN) · 18 QCD-bridge 600-DPI figures · 19 4D animations · README charts from live JSONs
DSI laboratory	7 experiments (exp1–exp7) with pytest coverage
Runs on a phone	full pipeline under Termux (termux/)

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The verification programme at a glance

The two panels below summarize the growth of the verification machine: the number of machine theorems re-checked by the automated test suite after each campaign, and the honest log-scale zoom-depth record of the echo search across solver generations (from z ≈ 1.5 in the first characteristic solver to z = 9.35 in the stabilized annulus machine).

Verification highlights (all numbers are machine outputs)

Verification	Result
Hilbert action → Einstein equations (SymPy, 50 digits)	residuals ≈ 10⁻⁴¹ vs the exact Roberts–Oshiro solution
Solver validation	flat space 10⁻¹⁴; 5/5 regression tests
Critical amplitude (fixed grid, N = 1600)	A* = 0.0805333; honest mass-scaling floor documented
CSS echo period in the data	Δ ≈ 3.44 (Gundlach–Hodgson 3.44 ± 0.02)
Thorne hoop link in the data	M3/(R1·t0²) = 0.6687 vs exact 2/3 (0.3%)
Log-time tower books	τ_UV = 9/4 and τ_Mdef = 9/16, ratio exactly 4
Clock-pair theorem	exact on 12/12 bricks of the ladder, τ*(δ) = 27/(4−δ²), unique common clock
One-brick Berry screening (δ_C = π/7)	closes ln τ* from −2.57% to +0.062%
Global static census	zero non-degenerate static branches beyond the known families; the static structure is exhausted exactly
Nonlinear DAE march	the only solution manifold through the critical point is the flat line of equilibria
Verification suite	21/21 tests re-checking machine theorems

The clock-pair theorem on the brick ladder

The central exact result of the latest campaigns: on the ladder of independent-brick choices δ_k = π/k, the two clock equations of the tower (UV and Mdef branches) possess exactly one common positive root

τ*(δ) = 27 / (4 − δ²)

verified by SymPy factorization on 12/12 bricks (baseline included), with exact zero residual at the root. The naive incompatibility of the two clocks (9/4 vs 9/16) is dissolved by de-adiabatization: both branches close on ONE clock, and a single brick moves it to the observed value.

One brick closes the clock

With the additive Berry screening choice κ = 2 − π²/98 (the septinial sector, δ_C = π/7), the common clock moves from a −2.57% deviation to +0.062% of the observed clock scale — an observation, with the convention question openly stated, not a fit.

The tick does not select the brick

The finite-amplitude tick obstruction measured across the whole ladder is non-monotone in δ, is not a power law (log–log slope +0.65 with large residual), and its ladder minimum sits at k = 12 — not at the surviving septinial brick π/7. The independent-brick selection principle therefore remains an observation, not a derivation. This is exactly the kind of honest negative result the repository is built to preserve.

The static structure is exhausted

The global static census combines an exact factorization theorem with three independent numerical searches. The rest system on the chain reduces to TWO equations with the exact factorization

S ∩ chain = {R1h = 0} ∪ {T0h = 0} ∪ {T0h = T0h*}

(the half-tower is an exact degenerate family; the flat line is the only non-degenerate branch). A 2501-cell scan + 56-seed Gauss–Newton census and a 300-start off-chain free Newton find no new static branches — every landing belongs to the known families.

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Audit & Transfer Appendix (v1.0, September 2026)

A dedicated editorial-verification appendix audit_transfer/ now accompanies the monographs. Three results, fully machine-verified (Python + Julia, deterministic, zero fitted parameters):

#	Task	Result
1	Monograph audit	Corrections b-C and a-C reproduced at machine precision; catalog of seven typographical errors E1–E7 found and fixed in the sources
2	Closure of c_K3 = 0.04018	The last empirical input is derived at leading order from DSI with λ = 22 = b₂(K3): c_K3 = b_Ch(22) = 1 − cos(2π/22); braking-coupled RG → 0.04036; the 0.8% residual is the finite-window systematics, reproduced numerically
3	Stability lemma Ш.3	Uniform trace theorem F ≥ n/2 (proved); sharpness 5n/7 (exact construction + numerics to 10⁻¹⁴); the soficity bridge stated explicitly

Run it:

python3 audit_transfer/python/run_all.py     # Python (NumPy/SciPy/Matplotlib)
cd audit_transfer/julia && julia audit_transfer.jl   # Julia (stdlib only)

Full write-up: audit_transfer/README.md (Russian) · PDF appendix: audit_transfer/appendix/Audit_i_Perenos_Prilozhenie.pdf

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Mathematical Background

The monograph establishes the following chain of results on the Klein quartic curve (genus 3, automorphism group PSL(2,7) of order 168):

Core Constants

Constant	Formula	Value
Spinor phase δ_A	π/2	1.570796
Spinor phase δ_B	π/3	1.047198
Spinor phase δ_C	π/7	0.448799
First eigenvalue λ₁(Δ)	Bourque–Strohmaier 2024	3.838
Trivial Dirac λ₁(D²_σ₀)	λ₁(Δ) + R/4	3.338

The Choptyuk Formula

b-C correction (1st order, Berry phase):

Δ_bC = λ₁(D²_σ₀) + δ_C²/2 = 3.438710

a-C correction (2nd order, braking):

δ_eff = δ_C⁵/22 ≈ 1/1200 = 0.000828

Unified Choptyuk formula (base):

Δ_Ch = λ₁(D²_σ₀) + δ_C²/2 − δ_C⁵/22 = 3.437883

With higher orders:

Δ_Ch = Δ_Ch(base) + δ_C⁴/8 + δ_C⁶/2 = 3.447040

Choptyuk constant:

b_Ch = 1 − cos(2π/7) = 2·sin²(π/7) ≈ 0.377

Applications

• 64 spinor structures on the Klein curve — full enumeration and spectral analysis
• Bolza and Bring surfaces — comparative spectral invariants
• LIGO/Virgo QNM predictions — quasi-normal mode corrections for GW150914, GW170104, GW170814, GW190521
• Strong CP problem solution — the Choptuik–Strong CP operator framework, see docs/qcd_bridge/

Strong CP extension (v3.0)

The companion monograph docs/qcd_bridge/choptyuk_qcd_bridge.pdf extends the framework to the strong CP problem. The eight-step solution chain replaces QCD's free parameter $\bar\theta$ with a derived spectral quantity:

$$\bar\theta_{\mathrm{eff}} = \delta_C \cdot N\langle\lambda\rangle \cdot \mathcal{S}_{\mathrm{GUE}} = 0$$

because the Wigner semicircle is symmetric and forces $\langle\lambda\rangle = 0$ in the GUE regime (verified at framework BF ≥ 99 at the lattice-determined physical $\kappa_T > 2.62$, 95% CL). No new fields, scales, or symmetries are introduced. See docs/qcd_bridge/README.md for the full chain, the epistemic parity argument, and the falsification tests.

Result	Value	Status
Choptyuk critical exponent $\delta_C$	$\pi/7 \approx 0.4488$	derived
Spectrum size $N$	$22\ (K3) + 6\ (N_f) = 28$	structural
Lattice $\kappa_T$ (95% CL)	$> 2.62$	measured
Framework BF(GUE/Poi) at $\kappa_T > 2.62$	$\geq 99$ (strong)	interpolated
Framework BF(GUE/Poi) at best-fit $\hat\kappa_T = 8.45$	$510$ (decisive)	interpolated
Continuum $\bar\theta$	$0$ exactly	derived
Dynamic relaxation $\tau_{\mathrm{relax}}$	$\sim 5 \times 10^{-41}$ s	computed

Enhanced Verification (v2.0)

The enhanced monograph extends the theory to higher dimensions and broader applications:

Extension	Key Result	Status
4D spin manifold	δ_eff is conformally invariant; Seiberg-Witten compatible	✓ Verified
Kähler surfaces	Dolbeault correspondence; K3 hyperkähler (holonomy Sp(1)); I₇ elliptic fibration matches Klein	✓ Verified
Tyukovsky equations	δ_corr = δ₀ + δ_C²/2 − δ_C⁵/22; zero free parameters	✓ Verified
Einstein GR / QNM	ω^corr = ω·(1 − 1/(1200π²)) ≈ 0.999916·ω; shift ≈ 8.4×10⁻⁵	✓ Verified
Criticism response	b₂ = 22 unique (dev < 1%); non-coincidental (no better approx q < 1200); stable under deformation	✓ Verified

K3 Surface invariants:

• Betti numbers: b₀ = 1, b₁ = 0, b₂ = 22, b₃ = 0, b₄ = 1
• Hodge decomposition: b₂ = h^(1,1) + 2h^(2,0) = 20 + 2 = 22 ✓
• Dirac index: Â(K3) = 2; b₂/Â = 11
• Seiberg-Witten: b₂⁺ = 3 > 1 → SW-compatible ✓

QNM correction for LIGO events:

Event	f_QNM (Hz)	f^corr (Hz)	Δf (Hz)
GW150914	251.000	250.979	−0.0210
GW170104	293.000	292.975	−0.0246
GW170814	319.000	318.973	−0.0268
GW190521	110.000	109.991	−0.0092

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Einstein Direct — the campaign ledger (honest, from first principles to the clock)

The einstein_direct/ laboratory grew campaign by campaign. Every campaign below is documented in the repository history, in the per-campaign JSON outputs, and in the bilingual verification monograph. What follows is the compact honest ledger: what was attempted, what held, what was rejected, and what was retracted.

Foundation: Hilbert action → Einstein equations → critical collapse

The starting point solves the Choptuik problem directly: the field equations are derived from the Hilbert action with the Hilbert stress–energy tensor for a massless scalar field, reduced to a 1+1 double-null characteristic system, machine-verified with SymPy against the exact Roberts–Oshiro solution (residuals ~10⁻⁴¹), and integrated by a second-order solver (flat space to 10⁻¹⁴; Roberts convergence order 2.03–2.09). The critical amplitude A* = 0.0805333 is located by bisection; the honest fixed-grid mass-scaling measurement (γ = 0.11 ± 0.11) documents the resolution floor and the requirements for a percent-level verification of γ = 0.374 vs the framework constant b_Ch = 0.376510.

Reports: einstein_direct/report_ru.pdf, einstein_direct/report_en.pdf.

cd einstein_direct
python3 sympy_derivation.py && python3 roberts_test.py && python3 choptuik_scaling.py

Convergence and repulsion from first principles (v6-fundamentals)

einstein_direct/center_modes.py closes the fundamental level: it (i) machine-derives the Thorne/MTW mass identities from the Hilbert system — the null flux laws m_v = −2r²pt²/α², m_u = −2r²qs²/α² (residuals 0), the central mass–slope link M3 = 2R1·t0²/(3(1−χ)²) (exact at every y) and the center gauge (1−χ²)R1² = A0 from m(0) = 0; (ii) reduces the verified center hierarchy O1–O5 to a log-time tower with a CSS fixed point closed to ONE amplitude parameter τ by the Thorne link; (iii) linearizes and obtains the exact spectrum: {0, −1, −1, −2, −3} at τ→0 (integer convergence exponents of the stable modes), exactly one growing root λ⁺(τ) in the codim-1 window τ ≤ 27/80 (exact), the exact point λ⁺ = 2 at τ = 1/2, and the second growing mode beyond 27/80 (the "decays/assemblies" blow-up channel). The empirical anchors are not fitted: κ_obs = Δ_sp/γ ≈ 1.95–1.96 vs λ⁺(27/80) = 1.509 quantifies exactly what the deeper tower levels (O6+) must contribute for the percent-level γ. Results: results/center_modes.json, figures fig_ru/fig_modes.png, fig_en/fig_modes.png.

The PDE machine and the depth wall (v6 → v6.1)

Session v6.1 closed the death channels of the grid machine with seven principled fixes (t-aliasing wiring; d_edge feedback cap; horizon-trap filter; P2 early-accept; zone-rebuild and E0_free rate gates; cross mode t := mirror(s) — the exact CSS relation t(ξ) = s(−ξ); two-sided ring fit with an axis gate). Result: stages now end by v-exhaustion, not by death — z = 9.10/9.35 (record; the previous machine died at z = 3.83); 40–181 tau-rows per stable run; and the Thorne link is visible in discrete data for the first time: M3/(R1·t0²) = 0.6687 against the exact 2/3 = 0.6667 (0.3%). Honest: τ* is not yet measured (the W2 measurement is crushed: W2/t0² → 0 against the target 4/3), and the near-critical branch (eps ≤ 3e-3) still dies at zoom 1. The O6+ numerical analysis (sympy_center_o6_nsolve.py): the truncated tower has NO exact CSS point (the branches UV[ξ³] → τ = 2.25 and Mdef[ξ⁵] → τ = 0.5625 are incompatible) — the W2/R3/P4 sources are fundamentally dynamic. This is the quantitative form of the κ deficit +0.44.

The symbolic tower programme (v11–v14): corrections, ladders, annihilation

Three independent lines were pushed in these campaigns:

1. Repo corrections embedded in the towers (v11). The doors audit (SC, UV, Mdef are κ-free) and two machine theorems: ring consistency κ_C1 = κ_C2 plus branch consistency κ_C2 = κ_TH imply that the holonomy correction is admissible only as a uniform κ → κ_hol; the EXACT corrected family is τ*(κ) = 27/(2κ) with the holonomy-invariant station ladder (R3h = 3/2, W2h = 9, R5h = 183/40, M5h = −105/4, M3/R1 = 9/2, clock 1/3). The additive Berry screening κ = 2 − π²/98 closes ln τ* from −2.57% to +0.062% of κ_obs (observation; the convention question stays open). The monograph-sign multiplicative convention moves away (−7.43%). The π/30 phantom stays 2.6–3.5% from the ladder — no exact identity.
2. The baryon-asymmetry reading (v12). Sakharov mapping at the level of mechanisms, not numbers: equilibrium ↔ criticality/limit cycle, C/CP ↔ spinor phases (ONE survivor: bC = π²/98, phase π/7 — the septinial sector; asymmetric static insertion is lethal, 0.386), B-violation ↔ monodromy ≠ 1. Machine facts: the static monodromy is exactly 1 (log-sum 1.2e-125); the real sector annihilates exactly in all corrected points; the surviving residue is the imaginary sector near k·π/30. The one-brick run moves the phantom to Im λ = 0.107731 = +2.88% from π/30 (baseline +3.10%) — toward the ladder, but no closure.
3. The linear world annihilates exactly (v13–v14). The O6+ campaign ("second flows as limit-cycle variables") built the true quadratic pencil M(l) = Ja + l·Jv·P + l²·J2·P2 (18×9) and proved by EXACT characteristic polynomial (in Q(√3), degree 22, multiplicity(l=0)=4) that the only genuine mode is l = 0 marginal at both points: δ_mono = 0 at linear order — the tower's B-violation is NOT linear, and the phantom proximity is pseudospectral. The v14 march measured δ_mono per echo growth < 2.8e-14 (9.3e-14) by two independent marches; the closed evolution is the EXACT nilpotent Jordan-2 block B = [[0,−350/61],[0,0]]; the phantom gap 3.0e-3 is 1e4–1e5 times the march bound — NOT reproduced by linear dynamics. Verdict: the baryon-asymmetry residue is a finite-amplitude effect; the whole linear world annihilates exactly.

The nonlinear verdict (v15–v16): figures carry states, not motion

The nonlinear DAE march (v15) answered the assigned test: the march is impossible algebraically — and that is the result. The full nonlinear F(x) = 0 with exact prolongation closure, the compatibility r(x) = 0 (basis-invariant hidden constraints), and the joint Newton show: [T1] the flat line carries F = r = V = 0 EXACTLY to radius ~26 (a line of exact equilibria); [T2] the second zero direction b2 holds radius statically up to |x − x*| ~ 1.35; [T3] from b2 the flow leaves S immediately — the level-3 exit rate |Dr V| = (39.2 ± 0.2)·A at both points. The only solution manifold through the critical point is the flat line of equilibria; the linear M2 direction (Jordan-2) is a linearization artifact — the linearization of NO nonlinear flow. The baryon-asymmetry annihilation extends to the nonlinear level.

The HEXCYCLE-DAE campaign (v16) embedded the figure cycle (pyramid → cone → bowl) in the nonlinear DAE tower as a global predictor: the compensated book exists — minimal-correction static landings converge at ALL booked scales (12/12 collapse + 6/6 blowup), 32 states with F = 0 AND r = 0 — the first global static components of S away from x*. Verdict: the figures carry the STATES, not the MOTION — the compensated book is the static backbone of CSS-like equilibria; the echo dynamics remains with the PDE machine.

Clock closure through the one-brick form (v17): a pair book, not a static carrier

The T1c campaign closed the clocks through the one-brick source form:

• [C1] Clock-pair theorem (exact, SymPy). GCD(UV_xi3, Mdef_xi5) on the chain = T0h²(4T0h²−27)/4 at baseline (unique positive root τ* = 27/4 = 6.75) and T0h²(196−π²)((196−π²)T0h²−1323) one-brick (τ* = 1323/(196−π²) = 7.107920). The naive 9/4-vs-9/16 incompatibility is an adiabatic artifact dissolved by de-adiabatization: both branches close on ONE clock; one brick moves it to the observed value (ln τ* closure −2.57% → +0.062%).
• [C2] Books at x* EXACT at both points: W2/T0² = 2κ/3 (defect 0), the UV book 9R3/(2R1T0²) = κ/2 (defect 0), the ladder R3h = 3/2 exactly (the holonomy-invariant ladder in the data), s = 3P2/T0 = 1.
• [A0] ERRATUM (public retraction). The v16 "static landing" did NOT pin T0h: the v16 'compensated book' landings were trivial-branch captures (T0h 1.732 → 3.2e-6, chain deviation up to 1e6 missed by the R1h-only filter). Reproduced 0/36 book-like. The v16 "static backbone" verdict is retracted; the pin-independent v16 layers stand.
• [A1] Honest static map with HARD-pinned T0h: 0/18 non-degenerate static states at booked scales — all fall into the half-tower R1h → 0 (F 1e-14..1e-27). Clocks have no static carrier away from the critical scale; the linear tick freedom does not lift onto the joint manifold.
• Verdict: clock closure through one-brick T1c sources succeeded as a pair book and failed as a static carrier — living clocks remain with the PDE machine.

The brick ladder and the global census (v18): the static world is finished

The final campaign of the series ran two machines:

1. Intermediate bricks (δ_k = π/k, k = 2..14 + baseline). [B1] the flat line is brick-independent (F ≤ 1e-7, 12/12); [B2] the clock-pair theorem is EXACT on 12/12 bricks with the unique common root τ*(δ) = 27/(2−δ²)... in the κ convention τ*(κ) = 27/(2κ): 27/4 → 17.617 (k=2) → 7.108 (k=7) → 6.836 (k=14); [B3] the tick obstruction is non-monotone, not a power law (log–log slope +0.65, residual ln 2.1); the survivor brick π/7 is NOT the minimum (k = 12 is) — the tick does not select the brick; [B4] the phantom scan: best hit +1.139% at δ = π/3, nothing within 1%; [B5] the book defect F = 26.79 is κ-independent on all bricks (a κ-free sector). An ERRATUM to the v17 [C3] method was issued: r_max = max|W·res18| is basis-dependent via W_align mutation; the qualitative stall stands on the invariant ‖r‖, and the relative anchor one-brick < baseline survives (0.032 < 0.043 at kick 0.05).
2. Global static census. [G1a] FACTORIZATION THEOREM (exact): the rest system on the chain is TWO equations, UV_xi3 = 2·R1h·Mdef_xi5 EXACTLY, C1_xi1..3 vanish identically ⇒ S ∩ chain = {R1h=0} ∪ {T0h=0} ∪ {T0h=T0h*} EXACTLY (the half-tower is an exact degenerate family; the flat line the only non-degenerate branch; the clock pair is ONE clock equation in two branches — the machine reason for the v17 uniqueness). [G1] 2501-cell scan + 56-seed Gauss–Newton: all roots in the three families, 0 new. [G2] 300-start off-chain free Newton: 34 flat-line captures, ~165 trivial escapes, 0 new. [G3] the static kernel dF/da at x* is 1-dimensional (the flat-line tangent only); branching attempts along the line produce no off-line landings. Verdict: the static structure is exhausted exactly — no non-degenerate static branches away from the critical scale. The living clock with the echo physics belongs to the PDE machine (finite-amplitude echo on the three static families).

The honesty ledger (proven / confirmed / rejected / retracted)

Verdict	Statement	Where
Proven (exact)	Clock-pair theorem: unique common clock τ*(δ) = 27/(4−δ²) on 12/12 bricks	v17 [C1], v18 [B2]
Proven (exact)	Factorization: S ∩ chain = {R1h=0} ∪ {T0h=0} ∪ {T0h=T0h*}	v18 [G1a]
Proven (exact)	Weight rule for third-order tables; prolongation invariance; ±i phantoms	v14 (a)
Proven (exact)	Static monodromy = 1 (log-sum 1.2e-125)	v12
Proven (exact)	Closed evolution is nilpotent Jordan-2; δ_mono < 3e-14 per echo	v14 (c)
Confirmed	One-brick Berry screening closes ln τ* to +0.062%	v11, v17
Confirmed	Echo Δ ≈ 3.44 in the data; Thorne link 0.3%	v6.1, grid machine
Confirmed	Holonomy admissible only as uniform κ → κ_hol	v11
Rejected	The tick does NOT select the brick (minimum at k = 12)	v18 [B3]
Rejected	Non-degenerate static branches away from x* (0/300 starts; census exact)	v17 [A1], v18 [G]
Rejected	Naive O6+ closure: UV3 τ = 2.25 vs Mdef5 τ = 0.5625 incompatible	v6.1
Rejected	Linear dynamics reproduces the phantom gap (3.0e-3 ≫ march bound 1e-14)	v13–v14
Retracted	v16 "static backbone" verdict (unpinned T0h → trivial captures)	v17 [A0] ERRATUM
Retracted	v17 [C3] absolute r_max numbers (basis-dependent method; invariant ‖r‖ stands)	v18 [B3] ERRATUM

What remains open (the short list)

The full list with formulations is in the bilingual verification monograph; in brief: (1) the finite-amplitude echo carrier — PDE machine v6–v9 on the background of the three static families; (2) an independent selection principle for the septinial brick (outside the tick scan); (3) τ* measurement in the data (the W2 channel); (4) Puiseux branches at the soft pole τ = 45/8; (5) a selection principle for the static fan (Newton-path independence); (6) the percent-level γ on a resolved grid; (7) the convention question of the Berry screening (additive vs multiplicative); (8) global components of S off the chain beyond the census radius; (9) the π/30 phantom — real identity or persistent coincidence.

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Quick Start

The verification suite (fast, ~seconds)

cd einstein_direct
python3 -m pip install numpy scipy sympy matplotlib pytest
python3 -m pytest tests/ -q
# 21 passed

The symbolic derivation (machine-verified)

cd einstein_direct
python3 sympy_derivation.py     # Hilbert action → Einstein equations
python3 roberts_test.py         # exact-solution regression

Numerical campaigns

python3 choptuik_scaling.py --n-bisect 1200     # fixed grid: A*, scaling
python3 zoom_campaign_regular.py                # zoom campaign, ~5–8 min
python3 grid_machine_annulus.py                 # the PDE machine suite
python3 global_static_search.py                 # static census

Monograph verification suites

python3 -m pip install -r python/requirements.txt   # see python/README.md
(cd python && python3 run.py)                       # interactive CLI

julia --project=julia -e 'using Pkg; Pkg.instantiate()'
julia --project=julia run.jl                        # interactive REPL

Python (recommended for quick verification of the monograph)

cd python/
pip install -r requirements.txt
python run.py

Java Web Application

cd java-webapp/
mvn clean package
java -jar target/choptyuk-spinor-monograph-1.0.0.jar
# Open http://localhost:8080

Interactive Visualization

cd interactive-viz/
npm install
npm run dev
# Open http://localhost:3000

Online demo: https://wild8highlander.github.io/choptuik_ac_bc/

Using Makefile (one command)

make all          # Run verification + simulation + plots + reports
make verify       # Run verification only
make viz-dev      # Start interactive visualization
make setup        # Set up all environments
make docker-run   # Run via Docker

Using Docker

docker build -t choptyuk-verify -f docker/Dockerfile .
docker run --rm -v $(pwd)/output:/app/output choptyuk-verify

Using Dev Container

Open in VS Code with Dev Containers extension — all tools (Python, Julia, Java, Node.js) pre-installed.

On a phone (Termux)

bash termux/01_termux_install.sh      # once per device
bash termux/02_termux_run.sh          # full pipeline (~1 h)
bash termux/02_termux_run.sh --quick  # ~15 min, same protocol, coarser grids

All numerical machines pin the BLAS thread count to 1 on purpose: multithreaded LAPACK reshuffles near-critical bisection and horizon nucleation and breaks reproducibility.

---

Architecture

Mathematical pipeline

flowchart LR
    subgraph Geometry["Riemannian Geometry"]
        direction TB
        KC["Klein Quartic<br/><b>x³y + y³z + z³x = 0</b><br/>genus 3, PSL(2,7)"]
        LAP["Laplacian Δ<br/><b>λ₁(Δ) = 3.838</b><br/>Bourque–Strohmaier 2024"]
        SC["Scalar Curvature<br/><b>R = −2</b><br/>hyperbolic metric"]
    end

    subgraph Spinors["Spinor Analysis"]
        direction TB
        PH["Spinor Phases<br/><b>δ_A=π/2  δ_B=π/3  δ_C=π/7</b>"]
        DIR["Dirac Operator D<br/><b>λ₁(D²_σ₀) = 3.338</b><br/>Lichnerowicz: λ₁(Δ)+R/4"]
        S64["64 Spinor Structures<br/><b>2^(2g) = 2⁶ = 64</b><br/>trivial σ₀ → minimum"]
    end

    subgraph Choptyuk["Choptyuk Formula"]
        direction TB
        BC["b-C Correction<br/><b>Δ_bC = 3.438710</b><br/>Berry phase, 1st order"]
        AC["a-C Braking<br/><b>δ_eff ≈ 1/1200</b><br/>2nd order, δ_C⁵/22"]
        CH["Unified Formula<br/><b>Δ_Ch = 3.447040</b><br/>base + δ_C⁴/8 + δ_C⁶/2"]
    end

    subgraph Physics["Physical Predictions"]
        direction TB
        BCH["Choptyuk Constant<br/><b>b_Ch = 0.376510</b><br/>1 − cos(2π/7)"]
        QNM["QNM Frequencies<br/><b>LIGO/Virgo</b><br/>GW150914 GW170104<br/>GW170814 GW190521"]
    end

    KC --> LAP & SC
    LAP --> DIR
    SC --> DIR
    PH --> BC
    DIR --> BC & AC
    BC --> CH
    AC --> CH
    CH --> BCH --> QNM
    KC -.-> S64
    DIR -.-> S64

Loading

The direct Einstein verification pipeline

The second research line runs its own pipeline — from the Hilbert action to the closed clock theorems — with a machine check at every arrow:

flowchart LR
    subgraph Symbolic["Symbolic layer — SymPy, 50 digits"]
        direction TB
        HIL["Hilbert action<br/>massless scalar field"]
        EIN["1+1 double-null<br/>Einstein system"]
        ROB["Roberts–Oshiro regression<br/><b>residuals ~1e-41</b>"]
        TOW["Center tower O1–O5<br/>log-time tau-tower"]
        CLK["Clock equations<br/>UV / Mdef branches"]
    end

    subgraph Numerical["Numerical layer — double-null solver"]
        direction TB
        SOL["2nd-order characteristic solver<br/>flat space 1e-14"]
        ZM["Zoom machine<br/><b>z = 9.35 record</b>"]
        ECH["Echo measurement<br/><b>Delta = 3.44</b>"]
    end

    subgraph Theorems["Machine theorems"]
        direction TB
        CPT["Clock-pair theorem<br/><b>tau*(delta) = 27/(4-delta^2)</b><br/>12/12 bricks"]
        FAC["Factorization theorem<br/><b>S and chain = 3 families</b><br/>census exact"]
        DAE["Nonlinear DAE verdict<br/>flat line = the only manifold"]
    end

    subgraph Verdicts["Honest verdicts"]
        direction TB
        BRK["One brick closes the clock<br/><b>-2.57% to +0.062%</b>"]
        NEG["Negative results kept:<br/>tick does not select the brick;<br/>no static carrier of the clock"]
    end

    HIL --> EIN --> ROB
    EIN --> SOL --> ZM --> ECH
    EIN --> TOW --> CLK --> CPT
    TOW --> DAE
    CLK --> FAC
    CPT --> BRK
    FAC --> NEG
    DAE --> NEG

Loading

Implementation & CI/CD

flowchart TB
    subgraph Core["Mathematical Engine"]
        M["Core computations<br/>Klein curve · Dirac · Choptyuk"]
    end

    subgraph Impl["Four Independent Implementations"]
        direction LR
        PY["<b>Python 3.10+</b><br/>CLI + Interactive Menu<br/>NumPy · SciPy · mpmath"]
        JL["<b>Julia 1.9+</b><br/>REPL + Interactive Menu<br/>LinearAlgebra · Plots"]
        JV["<b>Java 17+</b><br/>Spring Boot REST API<br/>Commons Math · JFreeChart"]
        NX["<b>Next.js 15 + React 19</b><br/>Real-time Dashboard<br/>Recharts · MathJS · Tailwind"]
    end

    subgraph Out["Outputs"]
        direction LR
        RPT["<b>7 Report Formats</b><br/>DOCX · PDF · TXT · MD<br/>CSV · HTML · JSON"]
        PLT["<b>Publication Plots</b><br/>600 DPI PNG<br/>PDF · SVG vectors"]
        LOG["<b>Execution Logs</b><br/>Timestamped records<br/>Full provenance"]
    end

    subgraph CI["CI/CD & Reproducibility"]
        direction LR
        GHA["<b>GitHub Actions</b><br/>CI · Lint · Release<br/>Pages · Scorecard · Stale"]
        DOC["<b>Docker + Dev Container</b><br/>One-command setup<br/>Full toolchain"]
        HKS["<b>Pre-commit Hooks</b><br/>ruff · mypy · format<br/>YAML/JSON validation"]
        ZEN["<b>Zenodo DOI</b><br/>Permanent archive<br/>Versioned snapshots"]
    end

    M --> PY & JL & JV & NX
    PY & JL & JV & NX --> RPT & PLT & LOG
    M -.-> CI

    style Core fill:#2c3e50,stroke:#1a252f,color:#fff
    style Impl fill:#ecf0f1,stroke:#bdc3c7
    style Out fill:#e8f8f5,stroke:#1abc9c
    style CI fill:#fef9e7,stroke:#f1c40f

Loading

---

Project Structure

choptuik_ac_bc/
├── README.md                    # This file
├── LICENSE                      # Isaev Proprietary License (individual)
├── CITATION.cff                 # Citation metadata (single author)
├── CONTRIBUTING.md              # Contribution guidelines
├── CODE_OF_CONDUCT.md           # Conduct policy
├── SECURITY.md                  # Security policy
├── Makefile                     # Unified build system
├── .github/                     # GitHub templates & CI
│   ├── workflows/               # GitHub Actions CI/CD (ci, lint, pages, release, ...)
│   └── ISSUE_TEMPLATE/          # Issue templates
├── assets/
│   └── charts/                  # README charts generated from machine outputs
├── einstein_direct/             # ★ core verification laboratory (direct Einstein programme)
│   ├── README.md                # summary, file map, how to run (RU)
│   ├── README_EN.md             # deep 29-section technical ledger (EN)
│   ├── sympy_derivation.py      # Hilbert action → Einstein equations (machine-verified)
│   ├── roberts_test.py          # exact-solution regression
│   ├── choptuik_scaling.py      # critical amplitude A* by bisection
│   ├── solver.py, zoom_solver.py# double-null characteristic solver + zoom chain
│   ├── center_modes.py          # Thorne/MTW mass route, log-time tower, exact spectrum
│   ├── grid_machine_annulus.py  # PDE machine: annulus parity + relay + tower gates
│   ├── grid_machine_hexcheck.py # PDE machine: hexcheck stage
│   ├── grid_machine_mirror.py   # PDE machine: mirror cross-mode t := mirror(s)
│   ├── sympy_center*.py         # center hierarchy, O6+, nsolve audits
│   ├── sympy_second_flows.py    # quadratic pencil M(l), exact char poly
│   ├── sympy_third_order.py     # third-order tables, weight-rule theorem
│   ├── sympy_dd_closure.py      # dd-law closure, rank theorems
│   ├── dae_nonlinear_core.py    # nonlinear F(x)=0 + exact prolongation machinery
│   ├── march_dae_nonlinear.py   # nonlinear DAE march (v15 verdict)
│   ├── hexcycle_dae.py          # figure cycle in the DAE tower (static backbone)
│   ├── clock_closure_t1c.py     # clock-pair theorem + honest static map
│   ├── brick_scan_tick.py       # brick ladder: clocks, tick, phantom scan
│   ├── global_static_search.py  # global static census (G1a/G1/G2/G3)
│   ├── spinor_ladder.py, spinor_analysis.py, spinor_figures.py
│   ├── zoom_campaign_*.py       # zoom campaigns (regular / taylor)
│   ├── figures/                 # fig_ru/ and fig_en/ PNG sets
│   ├── results/                 # all campaign JSONs (machine outputs)
│   └── tests/                   # pytest suite re-checking the theorems (21/21)
├── verification/
│   └── README.md                # ★ the big verification dossier (English)
├── monograph/
│   ├── verification_monograph_bilingual.pdf   # ★ RU/EN honest account (no metadata)
│   ├── verification_monograph_bilingual.docx  # ★ same, DOCX (no metadata)
│   ├── choptyuk_qcd_bridge_ru.docx / _en.docx # QCD-bridge monographs
│   └── README.md                # folder guide
├── docs/                        # Documentation
│   ├── monograph/               # Monograph files (EN/RU, DOCX/PDF/LaTeX) + figures
│   ├── qcd_bridge/              # Strong-CP extension (v3.0): 40-page monograph + evidence
│   └── architecture/            # ARCHITECTURE.md
├── python/                      # Python implementation (CLI with interactive menu)
│   ├── run.py, setup.py, requirements.txt
│   ├── config/, presets/        # Configurations & preset parameter sets
│   ├── src/                     # core / verification / simulation / visualization / reporting / ui
│   └── tests/                   # Unit tests (25+ tests incl. enhanced)
├── julia/                       # Julia implementation (REPL with interactive menu)
│   ├── run.jl, Project.toml
│   ├── src/                     # incl. enhanced_verification.jl
│   └── test/                    # incl. 9 enhanced test sets
├── java-webapp/                 # Java Spring Boot web application (REST API + Web UI)
├── interactive-viz/             # Next.js real-time visualization dashboard
├── code/                        # compact cross-language QCD-bridge engines (Python/Julia/Java/web)
├── qcd_bridge/                  # QCD-bridge artifacts: figures, animations, configs, reports
├── audit_transfer/              # editorial verification appendix (audit, DSI closure, lemma Ш.3)
├── dsi_lab/                     # DSI laboratory: experiments exp1–exp7 + reports
├── docs-site/                   # MkDocs documentation site sources
├── notebooks/                   # Jupyter verification notebook
├── scripts/                     # repository-level runners and utility scripts
├── termux/                      # run the whole pipeline on Android and publish from the phone
├── docker/, .devcontainer/      # containerized environments
└── .pre-commit-config.yaml      # code quality hooks

Each directory carries its own detailed README.md (English).

---

Reproduction index: every headline claim → the exact command

Nothing in the tables above is taken on trust. Each headline claim maps to one command and one JSON output file in einstein_direct/results/; the pytest suite re-checks the theorem-level claims automatically.

Claim	Reproduce with	Machine output
Hilbert action → Einstein equations, residuals ≈ 10⁻⁴¹	python3 sympy_derivation.py	results/derivation_results.json
Exact-solution regression (Roberts–Oshiro)	python3 roberts_test.py	results/roberts_test.json
Critical amplitude A* = 0.0805333, honest scaling floor	python3 choptuik_scaling.py --n-bisect 1200	results/choptuik_scaling.json
Exact spectrum {0, −1, −1, −2, −3}; codim-1 window τ ≤ 27/80	python3 center_modes.py	results/center_modes.json
Zoom-depth record z = 9.35; Thorne link 0.3%	python3 grid_machine_annulus.py	results/grid_machine_annulus.json
Echo period Δ ≈ 3.44 in the data	zoom campaign + ring fits	results/zoom_campaign_regular.json
Nonlinear DAE verdict (flat line = the only manifold)	python3 march_dae_nonlinear.py	results/march_dae_nonlinear.json
Compensated book = static backbone of the figure cycle	python3 hexcycle_dae.py	results/hexcycle_dae.json
Clock-pair theorem (baseline + one brick, exact)	python3 clock_closure_t1c.py	results/clock_closure_t1c.json
Brick ladder: 12/12 clocks, tick non-monotone, phantom scan	python3 brick_scan_tick.py (~6 min)	results/brick_scan_tick.json
Global static census: factorization + 0 new branches	python3 global_static_search.py (~1 min)	results/global_static_search.json
Third-order weight-rule theorem; Jordan-2 annihilation	python3 sympy_third_order.py, python3 march_delta_mono.py	results/third_order_tables.json, results/march_delta_mono.json
Quadratic pencil M(l); δ_mono = 0 at linear order	python3 sympy_second_flows.py	results/second_flows_exact.json
Spinor ladder π/15, π/30	python3 spinor_ladder.py	results/spinor_ladder.json
All of the above at once	python3 -m pytest tests/ -q	21 passed

Run any of these from inside einstein_direct/. Every machine pins BLAS to one thread and writes its full configuration into the JSON next to the results, so each number carries its own provenance.

---

Scientific background in one minute

A spherically symmetric massless scalar field, numerically evolved in 1+1 double-null coordinates, shows critical collapse: below a critical amplitude A the pulse disperses, above it a black hole forms, and near the critical amplitude the black-hole mass scales as M ∝ (A − A*)^γ with a universal γ ≈ 0.374 (Choptuik). The same regime exhibits an echo — curvature spikes repeating with a log-period Δ ≈ 3.44.

This repository attacks the problem directly: derive the 1+1 double-null Einstein system from the Hilbert action symbolically (machine-verified), evolve it with a validated characteristic solver, push log-scale depth by multi-zoom regridding, and measure the echo, the clocks and the static backgrounds — reporting agreements and disagreements with equal honesty. Around the numerical core, a symbolic tower program derives the central (spinor) hierarchy, its log-time tower, spectra and static structure, and checks which parts of the observed phenomenology (including the septinial sector δ_C = π/7) can be closed from first principles.

The monograph part of the repository (python/, julia/, java-webapp/, interactive-viz/ and the audit appendix) verifies the spectral invariants of the Klein quartic curve used for the spinor corrections and their LIGO/Virgo quasi-normal-mode applications.

---

QCD Bridge Suite (v3.1, added 2026-08-10)

In addition to the original four-implementation monograph suite above, this release adds a self-contained QCD-bridge package under qcd_bridge/ and code/, with a parallel bilingual monograph and dynamic 4D visualizations.

What is added

Artifact	Path	Description
Bilingual monograph (DOCX)	monograph/	EN + RU, 11 sections, 18 embedded 3D/4D figures (~22 MB each)
600 DPI figures	qcd_bridge/figures/	54 files: 18 PNG @ 600 dpi + 18 PDF + 18 SVG, English labels, 9 sections × 3D + 4D variants
Dynamic 4D animations	qcd_bridge/animations/	18 files: 9 MP4 + 9 GIF, 60 frames each, replacing static surfaces with frame-based 4D evolution
Verification configs	qcd_bridge/configs/	verify_all.json, verify_section_3_8.json, verify_custom.json (arbitrary precision, N → ∞, any matrices)
Sample 7-format reports	qcd_bridge/reports/ + reports_java/	TXT, CSV, MD, PDF, HTML, DOCX, JSON — results first, then execution log

Four-language engine (each with interactive menu + 7-format reports)

Implementation	Path	Stack	Notes
Python (canonical)	code/python/	Python 3.10+, NumPy, Matplotlib, ReportLab, python-docx	9 sections, ReportEngine, CLI with 5 modes, web_runner bridge
Julia	code/julia/	Julia 1.9+, LinearAlgebra, Statistics	Full mirror of Python engine, hand-rolled PDF 1.4 + OOXML DOCX (stdlib has no zlib)
Java	code/java/	Pure Java 17+, no external deps	Jacobi eigensolver from scratch, hand-rolled PDF + DOCX via java.util.zip
Web app	code/web/	Next.js 16 + React 19 + TypeScript + Tailwind 4 + Plotly.js	Real-time 3D/4D viz, interactive dashboard with section-specific sliders for all 9 sections, EN/RU i18n, API routes for Python backend

The 9 QCD-bridge sections

1. O_χ random matrix theory — GUE-vs-Poisson spacing, Bayes factor
2. RMT sweep — κ_T scan over N and ensemble
3. K3 spectral staircase — 22×22 intersection form, E₈⊕E₈⊕U⊕U⊕U
4. N-scaling test — ⟨λ⟩ → 0 trend, θ̄_artifact ~ 1/√N
5. τ-relaxation dynamics — physical time-scale estimate
6. κ_T lattice physical estimate — Cabibbo-angle coincidence
7. Cabibbo angle coincidence — δ_C = π/7
8. CP 8-step solution chain — spectral CP solution audit
9. Jet wake bridge — CMS HIN-25-012 connection

Quick start (QCD bridge)

# Python — verify all 9 sections, generate 7-format reports + 600 dpi figures + 4D animations
cd code/python
python3 run.py --config ../../qcd_bridge/configs/verify_all.json

# Python — custom config (any N, any matrices, arbitrary precision)
python3 run.py --config ../../qcd_bridge/configs/verify_custom.json

# Python — single section
python3 run.py --section 3,6,8

# Julia — same 9 sections, 7 report formats
cd code/julia
julia qcd_bridge_engine.jl --section 1,2,3

# Java — same 9 sections, 7 report formats (no external deps)
cd code/java
javac qcd_bridge_engine.java && java qcd_bridge_engine --section 1,2,3

# Web app — interactive dashboard with sliders for all 9 sections
cd code/web
bun install && bun run dev   # → http://localhost:3000

Authorship (QCD bridge suite)

Same as the main monograph: Ishak Khamzatovich Isaev (GitHub: @wild8highlander, ORCID 0009-0003-7299-0701). Embedded in both DOCX monographs, all 7-format reports, the web app header/footer/About page, and CITATION.cff. The repository has a single author and maintainer; all commits on main are published under the wild8highlander account.

---

Documentation map (everything the repository carries)

Document	Content
verification/README.md	the verification dossier — very large, self-contained English dossier of every verification campaign: what is verified, by which machine, with which method, which numbers came out, what the verdict is, which caveats apply, and the exact commands to reproduce it
monograph/verification_monograph_bilingual.pdf	bilingual verification monograph (RU/EN) — the complete honest account from beginning to end: all hypotheses, all experiments, what was rejected, what was accepted, what was proven; open questions and the roadmap; published without any document metadata by design
monograph/verification_monograph_bilingual.docx	the same monograph in DOCX (also metadata-free)
einstein_direct/README.md	the core laboratory: summary, file map, how to run
einstein_direct/README_EN.md	the deep 29-section technical ledger
einstein_direct/INSTALL_AND_PUSH.md	installation and running notes
audit_transfer/README.md	the audit-and-transfer appendix write-up
folder README.md files	one detailed English readme per directory
docs-site/	the MkDocs documentation site sources

---

Report Formats

Every implementation generates reports in all of the following formats:

Format	Extension	Description
Microsoft Word	.docx	Formatted document with tables and figures
Portable Document	.pdf	Publication-ready PDF
Plain Text	.txt	Human-readable text report
Markdown	.md	GitHub-compatible markdown
Comma-Separated	.csv	Tabular data for analysis
HTML	.html	Styled web report
JSON	.json	Machine-readable structured data

Each report contains:

1. Results section — computed constants, deviations, comparison tables
2. Execution log — complete timestamped log of all computations

---

Visualization Output

All plots are generated in two high-resolution formats:

• PNG at 600 DPI — for screen display and documents
• PDF/SVG — vector format for publication

Plot types include:

• Spinor phase diagrams
• Spectral eigenvalue landscapes
• 64 spinor structure heatmaps
• QNM frequency comparison charts
• Deviation analysis plots
• Convergence diagrams
• Critical-collapse gauge-profile plots (double-null solver)
• Zoom-chain and echo diagnostics
• Brick-ladder clock curves and census maps

The README charts in assets/charts/ are generated directly from the machine outputs in einstein_direct/results/ — the same JSON files the pytest suite re-checks.

---

Verification Results (Reference)

Monograph constants

Constant	Computed	Observed	Deviation
Δ_bC	3.438710	3.443	0.125%
Δ_Ch (base)	3.437883	3.443	0.149%
Δ_Ch (full)	3.447040	3.443	0.117%
b_Ch	0.376510	0.377	0.130%

Direct Einstein programme — headline machine facts

Quantity	Machine value	Reference	Status
Roberts–Oshiro regression	~10⁻⁴¹	exact solution	machine-verified
Critical amplitude A*	0.0805333	—	fixed grid N = 1600
Echo period Δ	≈ 3.44	Gundlach–Hodgson 3.44 ± 0.02	measured in data
Thorne hoop link M3/(R1·t0²)	0.6687	2/3 = 0.6667	0.3% in data
Common clock (baseline)	τ* = 27/4 = 6.75	—	exact theorem
Common clock (one brick)	τ* = 1323/(196−π²) = 7.107920	—	exact theorem
ln τ* closure	−2.57% → +0.062%	κ_obs	one-brick screening
Non-degenerate static branches beyond the known families	0	—	census exact + 300 starts
Test suite	21/21 passing	—	pytest on JSON outputs

---

Citation

If you use this code in your research, please cite:

@book{isaev2024spinor,
  title     = {Spinor corrections b-C and a-C and the solution of the Choptyuk problem},
  author    = {Isaev, Ishak Khamzatovich},
  year      = {2024},
  address   = {Nalchik, Kabardino-Balkarian Republic},
  note      = {Monograph with verified computational implementations}
}

For the verification programme, cite the bilingual verification monograph:

@unpublished{isaev2026verification,
  title     = {What was verified, how, and with what verdict: the complete honest account of the verification programme},
  author    = {Isaev, Ishak Khamzatovich},
  year      = {2026},
  note      = {Bilingual RU/EN verification monograph, metadata-free edition; in this repository}
}

Zenodo Archive

A permanent DOI-backed archive of this software is available on Zenodo. When a new release is published on GitHub, Zenodo automatically creates a snapshot with a versioned DOI for exact reproducibility.

---

Author

wild8highlander — Ishak Khamzatovich Isaev (sole author and maintainer of this repository)

• GitHub: @wild8highlander — the only contributor account
• ORCID: 0009-0003-7299-0701
• Email: aslan08_05@mail.ru
• Location: Nalchik, Kabardino-Balkarian Republic

This is a single-author repository: all research, all code, all verification campaigns and all documentation are the work of one author, published exclusively under the wild8highlander account.

---

License

This project is licensed under the Isaev Proprietary License — see the LICENSE file for details.

Summary: This is a proprietary license. You may view and cite the work for academic reference, but you may NOT copy, modify, distribute, or use it commercially without the author's written permission. All intellectual property rights are retained by Ishak Khamzatovich Isaev.

---

Reproducibility

This project is designed for full computational reproducibility:

• Docker: One-command reproducible environment (make docker-run)
• Dev Containers: VS Code one-click setup with all tools pre-installed
• Makefile: Unified build system (make all)
• Pre-commit hooks: Automated code quality enforcement
• CI/CD: Every push is automatically verified across Python 3.10-3.12, Julia 1.9-1.10, Java 17, and Node 20
• Cross-implementation consistency: CI verifies that all implementations produce matching results
• Version pinning: All dependencies are version-pinned in requirements.txt, Project.toml, pom.xml, package.json
• BLAS single-thread discipline: numerical machines pin the BLAS thread count to 1 for bit-level reproducibility
• JSON result ledger: every campaign ships machine-readable outputs; the pytest suite re-checks the major theorems from those outputs (21/21)
• Zenodo DOI: Permanent archived snapshots for each release

---

Contributing

See CONTRIBUTING.md for detailed guidelines. Quick workflow:

1. Fork → Branch → Commit → PR
2. CI runs automatically (Python + Julia + Java + Viz)
3. All verification tests must pass
4. Deviations from reference values must remain within tolerance
5. New features require corresponding tests

Bug reports and reproduction issues are especially welcome — reproducing a number from the verification dossier is the fastest way to help.

---

Acknowledgments

• Bourque & Strohmaier (2024) for the rigorous computation of λ₁(Δ) on the Klein quartic
• Choptuik (1993) and the critical-collapse community — Gundlach, Garfinkle, Duncan, Brady, Hirschmann, Hod — for the phenomenology this programme attacks from first principles
• Gundlach & Hodgson for the echo-period reference 3.44 ± 0.02
• Thorne (hoop conjecture mass route) and Misner–Sharp (mass definitions) — the mass identities machine-derived in the fundamentals campaign
• LIGO/Virgo Collaboration for gravitational wave observational data
• The PSL(2,7) symmetry group and its role in the spinor structure classification
• The Sakharov conditions — the lens through which the tower's monodromy and phase structure is read