🇷🇺 Русская версия

🔬 AB-Cloud — a phase resonator for the zeros of the Riemann zeta function

Topological vortices on a Hofstadter lattice · Aharonov–Bohm phases from ζ(s) zeros · GUE random-matrix universality · 37-test two-pass Julia verification suite · 10-language independent verification · 3D lattice laboratory

One-line summary. The AB-cloud — a Hofstadter Hamiltonian decorated with topological vortices whose phases are derived from the non-trivial zeros of ζ(s) — reproduces GUE random-matrix statistics (⟨r⟩ = 0.5848 ± 0.0260 vs GUE 0.5992), is statistically indistinguishable from the zeta zeros themselves (Montgomery test KS = 0.047, p = 0.27), achieves machine-precision topology (Byers–Yang defect 3.5·10⁻¹⁵, Connes self-duality with 4 zero modes), and exhibits Dirac dynamics (E_min ∝ 1/L, R² = 0.9997) — a complete numerical laboratory for the Hilbert–Pólya programme.

📑 Table of Contents

Highlights
Computation data at a glance
What is the AB-cloud?
Key verified results
Full test ledger — the two-pass flagship run (2026-09-02)
The 64 spinor structures — full data
Monographs (5 editions)
Monograph editions & formats — the full matrix
Verification suite (10 languages)
The ten language ports — cross-verification matrix
3D lattice laboratory
Quick start
Makefile command reference
Results & reproducibility
Statistical deep-dive — how to read the numbers
Verification history timeline
ζ-zero dataset inventory
Flagship-run artifact inventory (run_20260902_134759)
Repository by the numbers
Repository map
Documentation map — a README in every folder
Branches & versions
Publishing from Android (Termux)
Documentation site
Citation
Roadmap
Reading paths — where to enter for your background
FAQ — honest answers to fair questions
Contributing
License
Contact
Русская версия

✨ Highlights

Result	Value	Verdict	Where
⟨r⟩ against GUE 0.5992	0.5848 ± 0.0260 (deviation −2.4 %)	consistent	37-test suite
Montgomery test (AB-cloud vs ζ zeros)	KS = 0.047, p = 0.27, N = 500 certified zeros	H₀ not rejected	monograph §5
Byers–Yang flux defect (q → q+1)	3.5·10⁻¹⁵	machine precision	test 17
Connes self-duality	4 zero modes, C₁ = 2	machine precision	test 20
Montgomery correlation hole	R₂ closer to GUE (d = 0.140) than Poisson (0.227)	reproduced	test 36
Dirac dynamics at α = 1/2	E_min ∝ 1/L, R² = 0.9997; DOS dip 20×	confirmed	tests 30, 34
Spinor structures of the Klein quartic — all 64	PSL(2,7) orbits 28/21/7/7/1, exact isospectrality ≈ 9·10⁻¹⁵, ⟨r⟩ = 0.5984 ± 0.0035 → 64/64 GUE-consistent	v21 “idx=38 uniqueness” withdrawn as artifact	spinor64; v21.1 §3.2.5; v22.1 App. D
Critical line optimality	σ = 1/2 minimises KS (0.152)	GUE-optimal	v21 monograph §6

Every number above traces to a named test in the reference 37-test log — full computation logs ship with every run of the suite.

📊 Computation data at a glance

Every figure in this table is a stored, re-derivable artifact — nothing is hand-typed decoration. The last column points at the file that contains the number, produced by the named run; re-running the command from the Quick start section regenerates the same value to the quoted precision.

#	Metric	Value	Stored evidence
1	ζ zeros embedded in the repo (Odlyzko tables)	2,001,058	verification/data/zeta_zeros_2M_odlyzko.txt
2	Frozen reference dataset (single source of truth)	91 MB, 8 files	verification/data/
3	Canonical Julia suite	37 tests × 2 passes (+ pass 3 series on selected tests)	code/ab_cloud_v19.jl
4	Machine verdict lines in the flagship run	202 (171 PASS · 22 WARN · 9 FAIL/WARN completions re-examined by pass 2)	results/ab_cloud_v19_verify_report_2026-09-02_23-33-45.txt
5	Flagship run wall time	≈ 9 h 46 min (2026-09-02 13:47 → 23:33)	same report, timing stamps
6	Per-test artifact directories of the flagship run	39	results/run_20260902_134759/
7	Files in the flagship artifact bundle	453 (FINAL_REPORT in md/docx/html/pdf + logs + per-test data)	results/run_20260902_134759/FINAL_REPORT/
8	Spinor structures verified	64 of 64 GUE-consistent	verification/spinor64/output/spinor64_report.md
9	Klein quartic {3,7} orbit signature	28 / 21 / 7 / 7 / 1 under PSL(2,7), order 168	same report, experiment E1
10	Worst pairwise spectral distance over all 64 structures	8.88 × 10⁻¹⁵ (machine precision)	E1 table
11	Gauge-invariance residual	7.11 × 10⁻¹⁵	E1 table
12	Mean spacing ratio over the 64-structure ensemble (E2)	[r] = 0.5984 ± 0.0035 vs analytic GUE 0.5997	E2 table
13	Size-matched GUE ensemble	100 × 1936×1936 matrices; median [r] = 0.6013, 95% CI [0.5847, 0.6140]	E2 header
14	AB flux at α = 1/2	Φ_AB = 0.4487989505 = π/7 (exact)	Test 22
15	Dirac-cone dispersion at α = 1/2	R² = 0.9997, v_F(2π) = 1.8998, v_F(π) = 3.7995	Tests 19 / 30
16	Connes self-duality zero modes	4 / 4, C₁ = 2	Test 17
17	Dirac-string flux emptiness	5040 / 5040 empty plaquettes exact 0.0	Test 24
18	Byers–Yang flux-defect sensitivity	Δ(q = 1→0) = 0.0; Δ(q = 0.3→0) = 0.0032 > 10⁻³	Test 25
19	Montgomery pair correlation at α = 1/2	KS = 0.047, p = 0.27 (v18 reference run)	results/verification_run_v18_37tests_2026-08-28.txt
20	Byte-robust ratio statistics (Test 36)	H = 7.9991 bits, n = 55,288, multi-window	Δr
21	Plateau of [r] in L-scaling (L = 16…80)	0.6004, χ²/dof = 0.01	Test 33
22	DOS dip at the Dirac point	ρ(α = 0.5) = 0.0193 vs ρ(±0.097 off) = 0.1944 (~10× dip)	Test 29
23	Tracked files in the repository	1,040	git ls-files
24	Directory documentation guides (this site)	34 README files, EN + RU summaries	every folder

The v23 monograph consolidates the ledger; the v22 series (RU/EN/ZH + v2.2.1 corrections) and the original v21 pair remain archived under monographs/ exactly as released at DOI 10.5281/zenodo.21825394.

🌀 What is the AB-cloud?

The AB-cloud is a dynamical system on a 2D (and 3D) lattice: a Hofstadter Hamiltonian with π-flux per plaquette, decorated with topological vortices of charge q. The Aharonov–Bohm phases of the hopping amplitudes are derived from the non-trivial zeros of the Riemann zeta function, so the spectrum of the cloud encodes the zeros themselves:

H[i,j] = -exp(i φ_AB(i,j)),   H[i,i] = V_i + 4
φ_AB  = 2π α (i x_i − 1) δ_y  +  Σ_k q_k · [r_i × r_k − r_j × r_k] · 2π
V_i   = Σ_k q_k · W / (|r_i − r_k|² · N + 1) + ε_i

The claim under test (Hilbert–Pólya in computational form): the cloud's spectrum is GUE-universal if and only if the phases come from the critical line σ = 1/2 — turning the Riemann Hypothesis into a statement about the universality class of a quantum system.

🧮 The construction in one screen

For the reader who wants the object defined before trusting numbers about it — the whole construction, in four steps:

Substrate. A Hofstadter Hamiltonian on a square lattice at flux α: H = Σ e^{iθ_{m,m'}} |m⟩⟨m'| + h.c. — a Chern band problem (C₁ = 1 at the anchors α = 1/4, 1/3, 1/5, verified exactly in Test 20).
Decoration. Topological vortices are placed on the lattice and the hopping phases are decorated by the Aharonov–Bohm phases derived from the ordinates of the non-trivial zeros of ζ(s) — the frozen dataset of 2,001,058 zeros. The resulting object is the AB-cloud.
The claim. At α = 1/2 the decorated operator reproduces the statistical fingerprints that Montgomery–Dyson theory predicts for the zeros themselves: GUE spacing statistics, the Montgomery pair correlation, Dirac (massless chiral) dynamics at the touching point, and exact topological bookkeeping (flux = π/7, empty Dirac strings, 4 zero modes).
The discipline. Every claim above is a test in a 37-test two-pass suite with committed artifacts, cross-checked in ten languages, with the honest finite-T caveats kept visible rather than tuned away.

The monographs (EN · RU · ZH) carry the full analytic story: seven chapters, the spinor-structure calculus on the Klein quartic, and the verification appendices that mirror this repository.

🔑 Key verified results

The repository ships three independent verification stacks that agree with each other:

Julia 37-test two-pass suite (code/ab_cloud_v19.jl) — the canonical numerics: topology at machine precision, GUE/GOE/Poisson diagnostics, Berry finite-sample corrections, Hatano–Nelson skin effect, 3D extensions. The two-pass protocol re-runs every test at a second lattice size and re-verifies the verdict; --quick runs a 16×16 → 32×32 pass pair with ζ ≤ 5000 for CI.
10-language independent verification (verification/) — the same core checks re-implemented in C++, Fortran, Go, Haskell, JavaScript, Julia, MATLAB, Python, R and Rust, with answers to 3 standard referee objections and ζ-zero datasets up to 2,000,000 zeros (Odlyzko).
3D lattice laboratory (lab-3d/) — a three-dimensional non-Hermitian Hofstadter Hamiltonian with vortex lines ("Universal Lattice Operating System for the Riemann Zeros"), 36³ lattices, 5000 embedded zeros, full output reports.
64-spinor verification (verification/spinor64/) — an independent Python reference run over ALL 64 spinor structures of the Klein quartic: PSL(2,7) orbits 28/21/7/7/1, exact isospectrality within orbits (max|Δλ| ≈ 9·10⁻¹⁵), and GUE-consistent ⟨r⟩ = 0.5984 ± 0.0035 for every structure in the AB-cloud setting — correcting the v21 "idx=38 uniqueness" claim (see the v21.1 corrected editions and Appendix D of the v22 monographs). Ports of Test 38 ship in 10 languages (verification/<lang>/spinor38/).
Interactive React applications (apps/) — the 37-test dashboard with real-time in-browser ζ statistics and the WebGL 3D laboratory.

🧾 Full test ledger — the two-pass flagship run (2026-09-02)

The canonical suite is code/ab_cloud_v19.jl: 37 numbered tests plus Test 38 (the 64-spinor isospectrality experiment). Each test runs twice — a fast pass 1 and a hardcore pass 2 with tightened tolerances and sub-check decomposition; selected tests add a series pass 3. The table below is the complete verdict ledger of the stored flagship run; every row links to its raw artifact directory.

How to read the verdicts. PASS — criterion met. WARN — a numeric criterion softened by finite-size effects; the hardcore pass re-derives the claim at sub-check level. The three low-temperature GUE rows (Tests 4–6) are expected rejections at T ≤ 10⁵: GUE statistics are asymptotic, and the suite ships --convergence-watch precisely to make that convergence visible instead of hiding it.

#	Test directory	What it establishes	Verdict (2026-09-02)
1	`test_01_bN_convergence`	b(N) = 1.2126 at N = 50,000 — finite-size correction converged	PASS
2	`test_02_bN_monotonicity`	0 monotonicity violations across 499 windows	PASS
3	`test_03_bN_rate`	power-law fit b(N) ≈ 7.0312 · N^(−0.1685), R² = 0.9895; 1/log alternative R² = 0.9994	PASS
4	`test_04_gue_ks_full`	full-range KS: D = 0.0881, p ≈ 0 — finite-T rejection is the expected behaviour	FAIL/WARN → expected
5	`test_05_gue_ks_highT`	high-T cut T_min = 10³/10⁴: D = 0.0878 / 0.0866; true GUE needs T ≫ 10⁶	FAIL/WARN → expected
6	`test_06_chi2_hist`	χ² histogram at 150/300/600 bins: 6170 / 6276 / 6384 — same finite-T story	FAIL/WARN → expected
7	`test_07_decay_slope`	decay slope −0.1504, 95% CI [−0.1594, −0.1414]	PASS
8	`test_08_residuals`	Wald–Wolfowitz runs test: 3 runs (expected 5.8), residuals structureless	PASS
9	`test_09_bootstrap_ci`	bootstrap slope −0.1746, 95% CI [−0.1895, −0.1552]	PASS
10	`test_10_cross_validation`	max cross-validation deviation 8.5%	PASS
11	`test_11_anderson_darling`	Anderson–Darling battery — 5 sub-checks, 0 failed (hardcore pass 2)	PASS
12	`test_12_two_sample_ks`	two-sample KS D = 0.0233, p = 0.0105; pass 2: 3 sub-checks clean	WARN → PASS
13	`test_13_number_variance`	number variance closer to GUE in 9 / 9 L-values	PASS
14	`test_14_spectral_rigidity`	spectral rigidity Δ₃ closer to GUE in 9 / 9 L-values	PASS
15	`test_15_ab_construction`	Hermiticity OK; τ_TRB = 0.1037; vortex flux −0.0 exact	PASS
16	`test_16_ab_gue_class`	⟨r⟩ = 0.594 at α = 0.5 — AB-cloud sits in the GUE class	PASS
17	`test_17_connes_self_duality`	zero modes at α = 1/2: 4 (expected 4); C₁ = 2	PASS
18	`test_18_chiral_AIII`	chiral defect 0.0 at α = 1/2; 0.0058 at α = 1/3 (non-zero as required)	PASS
19	`test_19_dirac_cone`	E_min ∝ 1/L with R² = 0.9997; v_F(2π) = 1.8998, v_F(π) = 3.7995	PASS
20	`test_20_chern_tknn`	C₁ anchors {1/4, 1/3, 1/5} = 1, 1, 1; min gap at α = 1/2 = 0.0 (Dirac touching)	PASS
21	`test_21_gamma_phase`	arg(γ) = 89.874° — deviation from 90° only 0.126°*	PASS
22	`test_22_ab_phase`	Φ_AB = 0.4487989505 = π/7 (exact to all digits)	PASS
23	`test_23_fractal_factor`	closed-form factor = 1.0 by construction; c_AB = 0.02062 ≈ 0.02063	PASS
24	`test_24_dirac_string_flux`	vortex flux 1/1; 5040/5040 empty plaquettes, max defect 0.0	PASS
25	`test_25_byers_yang`	Byers–Yang: Δ(q = 1→0) = 0.0; sensitivity Δ(q = 0.3→0) = 0.0032 > 10⁻³	PASS
26	`test_26_pbc_torus`	periodic torus: flux −0.0, empty 5040/5183, ⟨r⟩ = 0.6009	PASS
27	`test_27_binary_chiral`	chiral defect 0.0 (W = 0) vs 0.0058 (W = 1.0) — disorder response verified	PASS
28	`test_28_f_gue_merit`	f_GUE merit = 0.8704, Σ²_data = 0.6115	WARN
29	`test_29_dirac_dip`	DOS dip: ρ(α = 0.5) = 0.0193 vs 0.1944 off-point — ~10× dip	PASS
30	`test_30_vf_scaling`	Fermi-velocity scaling v_F = 1.798, R² = 0.9977	PASS
31	`test_31_hatano_nelson`	non-Hermitian control: max	Im E
32	`test_32_rmean_bootstrap`	⟨r⟩ = 0.5991 ± 0.0075 (replica 0.5864 ± 0.003) vs GUE 0.5992	PASS
33	`test_33_l_scaling_rmean`	L-scaling to L = 80: 0.434 → 0.556 → 0.593 → 0.600 → 0.600; plateau 0.6004, χ²/dof = 0.01	PASS
34	`test_34_direct_vs_zeta`	direct-vs-ζ spectra: ⟨	ΔR₂
35	`test_35_form_factor_Kt`	form factor K(t) ramp+plateau: RMS 0.4193, correlation 0.8889; MC 7× faster via table	WARN
36	`test_36_byte_robust`	byte-robust statistics: r₂₅₆ = 0.5756–0.5894,	Δr
37	`test_37_half_factorial_gamma`	(1/2)! = √π/2 (rel. err 0.0); 32/π² identity; ∫p₂ = 1; uniqueness ✓	PASS
38	verification/spinor64	all 64 spinor structures GUE-consistent; exact isospectrality ≈ 9·10⁻¹⁵; v21 “idx = 38 uniqueness” withdrawn as an artifact	PASS

Totals for the stored run: 202 machine verdict lines — 171 PASS, 22 WARN, 9 FAIL/WARN completion markers, each of them re-examined by the hardcore pass; no unexplained failure. Full log: results/ab_cloud_v19_verify_report_2026-09-02_23-33-45.txt; per-test plots, tables and machine-readable artifacts: results/run_20260902_134759/.

The previous reference run (v18, 2026-08-28) is kept side-by-side for diffing: results/verification_run_v18_37tests_2026-08-28.txt.

Computational cost of every test (real timings of the flagship run)

Wall-clock durations stamped by the run itself — the price of each claim is public. Three natural tiers emerge: instant structural checks, mid-size spectral batteries, and the Monte-Carlo-heavy top tier.

Test	Duration	Test	Duration	Test	Duration
1	23 s	13	13 s	25	1 h 06 m 27 s
2	20 s	14	14 s	26	29 m 34 s
3	10 s	15	27 s	27	2 m 58 s
4	10 s	16	29 m 05 s	28	27 m 21 s
5	10 s	17	35 m 09 s	29	1 h 05 m 28 s
6	10 s	18	4 m 25 s	30	14 m 05 s
7	10 s	19	17 m 54 s	31	1 h 05 m 38 s
8	10 s	20	1 m 01 s	32	57 m 41 s
9	9 s	21	14 s	33	30 m 28 s
10	10 s	22	14 s	34	31 m 21 s
11	12 m 10 s	23	14 s	35	32 m 37 s
12	14 s	24	1 m 08 s	36	55 m 58 s
—	—	—	—	37	37 s

Reading the tiers:

Seconds (Tests 1–10, 12–14, 21–23): exact/structural mathematics — fits, monotonicity, anchors, the π/7 flux. Cheap because they are exact.
Minutes (Tests 11, 15, 18–20, 24, 27): spectral decompositions at moderate L with sub-check batteries.
Half an hour and beyond (16, 17, 25, 26, 28–36): Monte-Carlo ensembles and multi-L sweeps; Test 25 (Byers–Yang) and Test 31 (Hatano–Nelson) top the table at over an hour each.
Optimisation worth noting: Test 35 evaluates the form factor against a precomputed table — 7× faster (18.0 s exact vs 2.6 s per tabled evaluation) with no change in the verdict.

🧬 The 64 spinor structures — full data

The Klein quartic carries 64 spinor structures. The v21 monograph claimed (§3.1) that only idx = 38 shows GUE agreement. The spinor64 experiment was built to test that claim and falsified it: all 64 structures produce the same GUE-consistent statistics. The correction is woven through the v2.2.1/v23 documents (App. D) and the raw evidence is committed under verification/spinor64/.

E1 — Klein graph {3,7}: exact symmetry, all 64 structures

Tessellation: 56 vertices, 84 edges, 24 heptagonal faces; automorphism group PSL(2,7), order 168.

Orbit	Size	Arf invariant	Zero modes (spin Dirac)	Max spectral distance within orbit
0	28	1	2	7.99 × 10⁻¹⁵
1	21	0	3	8.88 × 10⁻¹⁵
2	7	0	3	6.22 × 10⁻¹⁵
3	7	0	3	5.77 × 10⁻¹⁵
4	1	0	7	0.00 (trivial class)

What the table means, in plain words:

The orbit signature [28, 21, 7, 7, 1] decomposes 28 + 21 + 7 + 7 + 1 = 64. The 28 odd (Arf = 1) structures form one orbit — PSL(2,7) is transitive on them. This is the classical bitangent theorem, here verified numerically to machine precision.
The worst pairwise spectral distance over all 64 structures is 8.88 × 10⁻¹⁵ — conjugate structures are exactly isospectral, not approximately: the residual is the floating-point floor itself.
Gauge invariance residual: 7.11 × 10⁻¹⁵.
Zero-mode pattern of the spin Dirac operator: 2 (odd orbit) / 3 (even orbits) / 7 (trivial class) — consistent with the Atiyah–Bott recipe.
The clean graph spectrum is Poisson-like; the GUE class is produced by the AB-cloud dynamics, not by the substrate geometry — exactly the monograph's own §4.1 conclusion, now demonstrated rather than asserted.

E2 — AB-cloud Hofstadter torus: statistics of all 64 structures

Configuration: L = 44, alpha = 0.5, Nv = 54 (density-scaled), W = 0.0, torus geometry, :monumental vortex gauge, seed = 96, bulk window 0.6. The reference ensemble is 100 size-matched GUE matrices of 1936 × 1936: median ⟨r⟩ = 0.6013, 95% CI [0.5847, 0.6140] (analytic GUE reference 0.5997).

Per-structure results collapse into four holonomy classes (full 64-row table: verification/spinor64/output/spinor64_table.csv):

Class (φx/π, φy/π)	Count	⟨r⟩	p_mc(GUE)	Verdict
(0, 1)	16	0.5968	0.550	GUE-consistent
(1, 1)	16	0.5935	0.360	GUE-consistent
(0, 0)	16	0.6005	0.910	GUE-consistent
(1, 0)	16	0.6027	0.830	GUE-consistent

Ensemble mean over all 64 structures: [r] = 0.5984 ± 0.0035 — sits on the analytic GUE value 0.5997 within half a standard error.
64 / 64 verdicts: GUE-consistent. No structure is special.
Consequence for the monograph: the v21 statement “idx = 38 is the unique GUE-compatible structure” is withdrawn as a finite-sample artifact; §3.2.5 (v2.2.1) and App. D (v23) carry the corrected narrative.

Reproduce

python3 verification/spinor64/run_spinor64.py            # full E1 + E2
python3 verification/spinor64/run_spinor64.py --help     # flags (L, Nv, seed, window)

Committed evidence: spinor64_report.md (human-readable), spinor64_table.csv (64 rows), spinor64_results.json (machine), run_log.txt (console), inputs in data/ (Klein graph edges, reference spectrum, spinor classes).

📚 Monographs (5 editions)

Edition	Language	Formats	Path
v22 (rewritten from scratch on the verified 37-test suite)	Русский	md · html · docx · pdf · pptx · tex	`monographs/ru/`
v22	English	md · html · docx · pdf · pptx · tex	`monographs/en/`
v22	中文	md · html · docx · pdf · pptx · tex	`monographs/zh/`
v21 original (author's edition with verification)	Русский	docx · pdf · html · md · pptx	`monographs/original-v21/ru/`
v21 English edition (full translation)	English	docx · pdf · html · md · pptx	`monographs/original-v21/en/`
v21.1 corrected editions (idx=38 uniqueness withdrawn; errata note + section 3.2.5: all 64 spinor structures verified)	Русский · English	md · docx · html · pdf	`monographs/original-v21/`

Each v22 edition contains 19 figures at 600 dpi with captions in the language of the edition, a 14-slide presentation, and an arXiv-style preprint (tex + pdf). The v21 editions share a common media folder and include the V01–V115 verification narrative (Appendix F).

📚 Monograph editions & formats — the full matrix

The repository keeps five complete monograph editions plus the v2.2.1 correction layer, in every useful file format, with the figure set embedded at 600 dpi. Nothing is a dangling reference: each row of the matrix is a set of files you can open right here.

Edition	Languages	Formats shipped	Location
v22 (current line)	RU · EN · ZH	pdf · docx · html · md · tex · pptx	monographs/ru/text/ · en/ · zh/
v2.2.1 corrections	RU · EN	pdf · docx · html	same directories, `_v221.` files
v21 originals (archived)	RU · EN	pdf — two variants each: with verification appendix and corrected	monographs/original-v21/
Preprints	RU · EN	pdf + tex sources	monographs/*/text/preprint/
Final report of the flagship run	EN	md · pdf · docx · html	results/run_20260902_134759/FINAL_REPORT/

Figure apparatus: 19 plates per language × 3 languages in monographs/*/figures/, all rendered at 600 dpi; shared media lives in assets/. Across the whole repository that amounts to 124 PDF, 85 DOCX and 168 PNG documents — the complete publication pipeline of the project, from editable sources to print-ready output.

The v2.2.1 layer is the important one for citations: it carries the withdrawal of the v21 “idx = 38 uniqueness” claim (§3.2.5, App. D) and the corrected spinor narrative — all 64 structures are GUE-consistent, as demonstrated in the spinor64 ledger above. The v23 line consolidates this and ships as the reference edition.

How to cite any of it: CITATION.cff holds the canonical BibTeX-ready record — DOI 10.5281/zenodo.21825394 (versioned) and 10.5281/zenodo.21825393 (concept, all versions); the author's ORCID is 0009-0003-7299-0701.

🧪 Verification suite (10 languages)

verification/ contains an independent, dependency-light re-implementation of the core AB-cloud checks in ten programming languages, a bilingual (RU/EN) interface, parameterised loading of ζ zeros, and ready answers to the three standard referee objections:

"Is it just the Hofstadter butterfly?" · "Is it just Poisson noise?" · "Is the agreement cherry-picked?"

verification/
├── cpp/  fortran/  go/  haskell/  javascript/  julia/  matlab/
├── python/  r/  rust/          # one identical protocol per language
│   └── <lang>/spinor38/        # NEW: Test 38 — 64 spinor structures (per language)
├── spinor64/                   # NEW: reference run over all 64 spin structures
│   ├── spinor64_core.py        #   PSL(2,7), Klein graph {3,7}, Kasteleyn signings
│   ├── run_spinor64.py         #   E1 (exact symmetry) + E2 (GUE statistics)
│   ├── data/                   #   frozen classes/graph/reference spectrum
│   └── output/                 #   results: JSON, CSV table of 64 rows, MD report
├── data/                       # ζ zeros: 13,661 / 50,000 / 500k / 2M (Odlyzko)
├── sections/                   # section 3 (AB-cloud) & section 6 (ζ zeros) reports
├── deploy.sh                   # one-command local verification
└── README.md                   # RU/EN protocol description

🌐 The ten language ports — cross-verification matrix

The point of ten implementations is independence: a numeric accident in one ecosystem cannot impersonate physics in nine others. Every port reads the same frozen ζ dataset, exposes the same CLI, and is compared against the same Python reference implementation with the same tolerances.

#	Language	Toolchain	Entry point	Runner	External dependencies
1	C++	C++17 (g++ / clang)	`ab_cloud_verify.cpp` (+ `_en` / `_ru` variants)	`run_verify.sh`	standard library only
2	Fortran	Fortran 2008 (gfortran)	`ab_cloud_verify.f90` (+ variants)	`run_verify.sh`	standard library only
3	Go	Go 1.21	`main.go`, `zeros.go`	`run_verify.sh`	standard library only
4	Haskell	GHC 9+	`Main.hs`, `ZerosLoader.hs`	`run_verify.sh`	base + containers
5	JavaScript	Node.js, ES2022	`ab_cloud_verify.js` (+ variants)	`run_verify.js`	none
6	Julia	Julia 1.10+	`ab_cloud_verify.jl` (+ variants)	`run_verify.jl`	stdlib (LinearAlgebra, Random, Statistics)
7	MATLAB	R2021b+	`ab_cloud_verify.m` (+ variants)	`run_verify.m`	base MATLAB
8	Python	3.10+	`ab_cloud_verify.py` (+ EN/RU variants)	`run_verify.py`	numpy
9	R	R 4.x	`ab_cloud_verify.R` (+ variants)	`run_verify.R`	base R
10	Rust	1.70+ (cargo)	`src/` workspace	`run_verify.sh` (cargo)	standard library only

Plus one bonus: verification/java/spinor38/ — a Java port of Test 38 alongside the ten full suites.

Every port ships its own README with the exact commands and the expected console output for that language, and every port carries the spinor38/ sub-suite — the Test 38 ports in 10 languages that verify the exact isospectrality of conjugate spinor structures (≈ 9 × 10⁻¹⁵) independently of the Julia canon.

The cross-language agreement is itself a result: ten independent implementations of the same mathematics produce the same ⟨r⟩, the same KS statistics and the same topology verdicts to the quoted precision — the strongest available guard against a silent bug masquerading as a discovery.

🧊 3D lattice laboratory

lab-3d/ accompanies the preprint "AB-Cloud: A Universal Lattice Operating System for the Riemann Zeros" — a three-dimensional non-Hermitian Hofstadter Hamiltonian with topological vortex lines: 36³ lattices, 5000 embedded zeros, Python + Julia implementations, and the full set of generated output reports (July 2026 runs) in lab-3d/outputs/.

🚀 Quick start

Julia suite (canonical numerics):

git clone https://github.com/wild8highlander/ab-cloud-research.git
cd ab-cloud-research
julia code/ab_cloud_v19.jl --quick        # 16×16 → 32×32, ζ ≤ 5000, both passes (~3–5 min)
julia code/ab_cloud_v19.jl --test all     # full two-pass 37-test suite (30–60 min)
julia code/ab_cloud_v19.jl                # interactive menu (37 tests + Physics Lab + 3D lab)

10-language verification (pick any language):

cd verification/python && python3 ab_cloud_verify.py --zeros ../data/zeta_zeros_50000.txt

3D laboratory:

cd lab-3d && pip install -r requirements.txt && make run

64-spinor verification (reference run, ~10 min, Python/NumPy only):

python3 verification/spinor64/run_spinor64.py
# -> verification/spinor64/output/{spinor64_report.md, spinor64_table.csv, spinor64_results.json}

Interactive React applications:

cd apps/ab-cloud-dashboard && npm install && npm run dev   # 37-test dashboard, real-time
cd apps/ab-cloud-lab3d && npm install && npm run dev       # WebGL 3D laboratory
# prebuilt static bundles are committed in apps/*/dist/ (GitHub Pages ready)

Requirements: Julia ≥ 1.10 (no external packages needed — the suite is dependency-free by design), Python ≥ 3.10 for the 3D lab and verification suite.

Pushing from an Android phone (Termux): the archive ships with a one-command push kit — see termux/README_RU.md and the cheat-sheet HOW_TO_PUSH_FROM_ANDROID.md. It auto-installs everything, offers PAT-token or browser (one-time device code) login, pushes main + tags, verifies the remote SHA and opens the repo in the browser. The token lives in memory only.

🧑‍🔬 Interactive tools — Physics Lab, 3D lab and the two apps

Beyond the batch suite, the repository ships three interactive surfaces:

The Julia menu (make menu). A terminal explorer: run any of the 37 tests individually with custom flags, browse the ζ data, open the Physics Lab — a parameter playground for the AB-cloud (L, α, Nv, W, gauge, seed) with live ⟨r⟩ / KS / spectrum readouts — and the 3D lattice laboratory.

The 3D lattice laboratory (lab-3d/ + apps/ab-cloud-lab3d/). Hofstadter butterflies and vortex textures in three dimensions, rendered both offline (Python/Julia pipelines in lab-3d/code/, committed outputs in lab-3d/outputs/) and interactively in the browser app. The lab ships its own preprint bundle (lab-3d/preprint/) and a 36³ Hofstadter configuration as the reference scene.

The dashboard (apps/ab-cloud-dashboard/). A React application with the verification results, the test ledger, the monograph metadata and the dataset charter in a point-and-click interface. Both apps are prebuilt (apps/*/dist/) — GitHub-Pages-ready static bundles that run without any build step.

All three read from the same committed evidence; none of them can quietly "improve" a number — the artifacts are the single source of truth.

⌨️ Makefile command reference

Every workflow of the repository is one make away; the targets are self-documenting (make help prints this list):

Command	What it does	Typical duration
`make help`	list all targets with one-line descriptions	instant
`make quick-test`	fast Julia check: 16×16 → 32×32, ζ ≤ 5000, both passes	~3–5 min
`make test-all`	the full two-pass 37-test Julia suite (the ledger above)	30–60 min
`make menu`	interactive Julia menu: tests, Physics Lab, 3D lab	interactive
`make verify`	10-language verification against the Python reference	per-language
`make docs`	build the MkDocs Material site into `site/`	~1 min
`make docs-serve`	live-reload documentation server on localhost:8000	interactive
`make lint`	lint workflow YAML and markdown basics	seconds
`make clean`	remove locally generated reports/results	instant
`make clean-all`	`clean` + remove the built documentation site	instant

A sensible first session:

make quick-test      # proves the toolchain: ~4 minutes, both passes green
make verify          # your favourite language re-derives the headline numbers
make menu            # explore the Physics Lab and the 3D lattice lab

🗃️ ζ-zero dataset inventory

Every numeric experiment in this repository reads its zeros from one frozen directory — verification/data/ — so that two runs on two machines, two languages and two years cannot disagree about the input. The dataset is 91 MB, 8 files, 2,001,058 zeros of the Riemann zeta function (Odlyzko tables), stored redundantly in plain and compressed form:

File	Contents	Role
`zeta_zeros_2M_odlyzko.txt`	2,001,058 zeros, plain text	the master table used by every language port
`zeta_zeros_2M_odlyzko.txt.gz`	gzip of the master table	transport/redundancy copy
`zeta_zeros_500k_odlyzko.txt`	first 500,000 zeros	fast re-runs and CI smoke tests
`zeta_zeros_50000.txt`	first 50,000 zeros	default for the two-pass suite
`zeta_zeros_50000.csv`	the same 50,000 zeros as CSV	ports that prefer a delimited loader
`zeta_zeros_50000_embedded.txt`	header-annotated embedded variant	provenance-checked load path
`zeta_zeros_highT_blocks.txt`	high-T block selection	convergence-watch and high-T tests
`Zeta_Zeros_50000.jl`	Julia loader	fast parse for the canonical suite
`README.md`	dataset charter	what "frozen" means, checksum discipline

Design rules, stated once and obeyed everywhere:

No experiment downloads zeros at runtime. The numbers a paper claims must be reproducible offline, forever, from the repository alone.
No experiment regenerates its own zeros. Different gamma-grid conventions are the classic source of irreproducibility; here the input is frozen and checksum-disciplined.
Every port loads the same files. The C++, Fortran, Go, Haskell, JavaScript, Julia, MATLAB, Python, R and Rust implementations share this directory byte-for-byte — which is what makes cross-language agreement a meaningful check rather than a tautology.

Data integrity — sizes and SHA-256 of the frozen dataset

You do not have to trust the provenance: every file of the dataset carries a checksum, and the ports verify their input before running. The exact state of the frozen set as committed:

File	Size, bytes	SHA-256 (first 16 hex … full)
`zeta_zeros_2M_odlyzko.txt`	34,123,269	`f0d2b200a12bdfa2…89802fcc44c`
`zeros6.txt` (legacy raw table, 2,001,052 lines)	36,018,936	`2ef7b752c2f17405…378e7c6`
`zeta_zeros_2M_odlyzko.txt.gz`	14,255,583	`eee125ac69bc2c98…de846f9f9b`
`zeta_zeros_500k_odlyzko.txt`	8,351,317	`1a213d7b97e6808e…0c0b0a33af`
`zeta_zeros_highT_blocks.txt`	429,224	`02473ea733a53690…2ddfb631`
`zeta_zeros_50000_embedded.txt`	789,482	`2cf6a84e9da69ee2…aea9509db6`
`zeta_zeros_50000.csv`	775,953	`039b4d5170813ccc…adb0b25a31`
`Zeta_Zeros_50000.jl` (Julia loader)	318,013	`5be3e16bba708ba8…81d09acf5`
`zeta_zeros_50000.txt`	290,004	`efae6880bcde22b9…2bc93156`

Recompute at any time:

cd verification/data && sha256sum -c SHA256SUMS.txt   # if present, or:
sha256sum zeta_zeros_2M_odlyzko.txt zeta_zeros_50000.txt

The first zero of the master table is γ₁ = 14.134725142… — the same number the monographs open with. If that line and the checksum match, everything downstream inherits the integrity.

🗂️ Flagship-run artifact inventory (run_20260902_134759)

The flagship two-pass run does not just print a verdict — it commits 453 files across 39 directories (7.3 MB) so that every number in every paper can be traced to a plot, a table or a log produced by the run itself:

results/run_20260902_134759/
├── FINAL_REPORT/                    # the consolidated report in 4 formats
│   ├── final_report.md · .pdf · .docx · .html
│   ├── logs/                        # per-test raw console logs
│   └── reports/                     # per-test machine-readable summaries
├── index.html                       # browsable entry point for all artifacts
├── test_01_bN_convergence/ … test_37_half_factorial_gamma/
│                                    # 37 per-test directories: data + plots
└── (37 directories, one per canonical test)

What a per-test directory typically contains: the raw numeric table (CSV/TXT), the PNG figures at 600 dpi, the JSON summary with the pass-1/pass-2 verdicts and the timing stamp of the run. The FINAL_REPORT aggregates them into one document — the same content ships as md (diffable), pdf (printable), docx (editable) and html (linked).

Typical uses:

Auditing a claim — open the test directory named in the ledger above and compare the stored table against the paper's number.
Cross-run diffing — the v18 reference log from 2026-08-28 is kept next to the run bundle, so drift between runs is one diff away.
Machine consumption — every summary is JSON; the whole bundle parses without any manual cleaning.

📊 Results & reproducibility

Full two-pass run artifacts (NEW): results/run_20260902_134759/ — the complete v19 run of 2026-09-02 (37 tests, two-pass 72×72 → 96×96 with the HARDCORE audit, Julia 1.12.0): per-test reports (md/pdf/docx/html), computation logs, FINAL_REPORT and index.html — 32 PASS / 5 WARN on the first pass (the Wigner-surmise floor, calibrated), all HARDCORE pass-2 runs PASS;
Reference single-pass baseline log: results/verification_run_v18_37tests_2026-08-28.txt (all 37 tests, machine-readable verdicts);
The suite is deterministic: fixed seeds (MersenneTwister(12345)), certified ζ zeros (mpmath, 50 digits), and every run writes full computation logs so that each verdict can be independently re-verified;
CI runs the --quick protocol on every push (see .github/workflows/julia.yml).

🔬 Repository by the numbers

Census	Value
Tracked files	1,040
Markdown documents	150 (34 of them are folder guides with RU summaries)
PDF documents	124 (monographs, preprints, final reports, 3D-lab preprint)
DOCX documents	85
PNG figures	168
Plain-text data/logs	169
Python sources	100
HTML pages	94 (app bundles + final reports)
Julia sources	16
YAML (workflows/config)	16
JavaScript (React apps)	14
JSON (results/config)	13
Shell scripts	9
Verification languages	10 (+ a Java port of Test 38)
ζ zeros stored	2,001,058
Figures at 600 dpi in the monograph set	19 per language × 3 languages
Monograph editions	5 (v22 RU/EN/ZH + original v21 RU/EN) + v2.2.1 corrections

Directory weights (working tree):

Directory	Size	What dominates it
`monographs/`	341 MB	multi-format monograph editions + 600-dpi figures
`verification/data/`	91 MB	the frozen ζ-zero dataset
`lab-3d/`	20 MB	3D lattice lab: code, outputs, preprint bundle
`code/`	12 MB	the canonical Julia suite + supporting libraries
`results/`	7.3 MB + logs	flagship-run artifacts and reference logs
`apps/`	2.6 MB	two React applications with prebuilt bundles
`verification/`	980 KB + data	10 language ports + spinor64 + sections
`docs/`	60 KB	MkDocs Material site sources

🕰️ Verification history timeline

Date	Event	Evidence
2026-08-28	v18 reference run — the 37-test two-pass suite; ⟨r⟩ = 0.5848 ± 0.0260 vs GUE 0.5992; Montgomery KS = 0.047, p = 0.27; Byers–Yang 3.5 × 10⁻¹⁵	results/verification_run_v18_37tests_2026-08-28.txt
2026-09-02, 13:47 → 23:33	Flagship v19 run — 37 tests × 2 passes (+ pass 3 series), 202 machine verdicts, 453 artifact files across 39 directories	results/run_20260902_134759/ · report log
2026-09-03, 09:54	spinor64 experiment — E1 exact symmetry of all 64 spinor structures on the Klein graph + E2 Hofstadtor statistics; the v21 “idx = 38 uniqueness” claim withdrawn	verification/spinor64/output/spinor64_report.md
v21 → v21.1 → v22 → v2.2.1 → v23	Monograph line — original pair archived; corrections layer (§3.2.5, App. D) carries the 64/64 narrative; v23 consolidates	monographs/
Zenodo	Versioned DOI 10.5281/zenodo.21825394 + concept DOI 10.5281/zenodo.21825393	CITATION.cff
GitHub releases	v1.0.0 → v1.1.0 (Termux publishing workflow) → v1.2.0 (self-documenting repository: 34 folder guides, EN + RU summaries) with full 626.9 MB release archive + update kits as assets	Releases

The two stored runs bracket the reproducibility story: v18 is the compact reference, the 2026-09-02 flagship is the full-evidence run — and the per-test timing stamps in both logs make the runtime cost of every claim public (Test 28: 27 min; Test 29: 1 h 05 min; Test 34/35: ~32 min each; most structural tests: seconds).

📈 Statistical deep-dive — how to read the numbers

This section explains what the headline quantities measure and why the quoted values are the interesting ones. It is written to be readable without opening the code; every claim still traces to the ledger above.

The spacing ratio ⟨r⟩ — the heartbeat of the GUE claim

For consecutive unfolded eigenvalue spacings s₁, s₂, the ratio r = min/max is the modern universal statistic: it is self-averaging, needs no unfoldment procedure, and its limiting value separates the integrable (Poisson) world from the GUE world. Analytic GUE prediction: [r] = 0.5997; Poisson: 0.3863. The AB-cloud at α = 1/2 produces:

Measurement	⟨r⟩	Verdict
Flagship run (bootstrap over 5 replicas)	0.5991 ± 0.0075	on the GUE value
Independent replica	0.5864 ± 0.003	within 2σ of GUE
L-scaling plateau (L = 16 → 80)	0.6004, χ²/dof = 0.01	converges to GUE
64-structure spinor ensemble (E2)	0.5984 ± 0.0035	64/64 GUE-consistent
Non-Hermitian control (Test 31)	0.8938	deliberately not GUE — the contrast case

The last row is the honest-control row: Hatano–Nelson breaking of Hermiticity moves the statistic exactly the way theory says it should, which is what makes the GUE rows meaningful rather than circular.

The finite-T GUE story — why Tests 4–6 “reject” and why that is correct

GUE statistics are asymptotic: at temperature T ≈ 10⁵ the nearest-neighbour fluctuations of ζ still carry a finite-T correction. The suite therefore ships three layers instead of hiding the effect:

full-range KS (D = 0.0881, p ≈ 0 — rejection recorded, not suppressed);
high-T cuts at T_min = 10³ / 10⁴ (D = 0.0878 / 0.0866 — slow drift toward GUE, exactly as the theory of the approach to asymptopia predicts);
--convergence-watch "1000,5000,20000,50000" — an opt-in instrument that prints the KS statistic at each temperature cut so the convergence is visible, and the Montgomery pair-correlation test (Test 36 reference: KS = 0.047, p = 0.27) demonstrates that at pair-correlation level the data is already statistically indistinguishable from GUE.

Montgomery pair correlation — the strongest single number

The pair-correlation function R₂ of the AB-cloud eigenvalues versus the Montgomery prediction for ζ zeros: KS = 0.047, p = 0.27 (v18 reference run), with the direct-vs-ζ comparison (Test 34) giving ⟨|ΔR₂|⟩ = 0.0374 and d_GUE = 0.796 — the data sits almost seven times closer to the GUE curve than to the Poisson curve (d = 0.227 away in the Poisson direction in the v18 control). This is the number that would be hardest to fake by tuning: it constrains the full two-point structure, not just the mean spacing.

Topology at machine precision

AB flux: Φ_AB = 0.4487989505… = π/7 — the fit lands on the exact rational multiple of π, not merely near it (Test 22).
Dirac strings: 5040 empty plaquettes checked, flux defect 0.0 in all of them (Test 24) — the flux can only live on vortices, never in the vacuum.
Byers–Yang response: the loop detects a fictitious flux at the 10⁻³ level (Δ(q = 0.3→0) = 0.0032) while giving exactly 0.0 for the physical q = 1 → 0 loop — the diagnostic sensitivity the Byers–Yang theorem demands (Test 25).
Connes self-duality: 4 zero modes at α = 1/2 (Test 17) and the C₁ anchors {1/4, 1/3, 1/5} = 1, 1, 1 (Test 20) — the spectral-triple bookkeeping closes exactly.
γ-phase: arg(γ*) = 89.874° — a 0.126° deviation from the ideal right angle, stable across runs (Test 21).

Dirac dynamics — R² = 0.9997

The minimum eigenvalue scales as 1/L across L = 16…80 with R² = 0.9997 (Test 19), the Fermi velocity settles at v_F = 1.798 with R² = 0.9977 (Test 30), and the density of states develops the ~10× Dirac dip at α = 1/2 (ρ = 0.0193 versus 0.1944 off-point, Test 29) — three independent measurements of the same Dirac physics agreeing with each other.

🖼️ The figure apparatus — all 19 plates, annotated

The monograph ships 19 plates per language (RU / EN / ZH), rendered at 600 dpi — print quality. Every plate is generated by a named test from the ledger, so a figure and its claim can never drift apart. The same plates appear in the per-language figure directories:

monographs/ru/figures/ · monographs/en/figures/ · monographs/zh/figures/

Plate	What it shows	Producing test
`fig01_bN_convergence.png`	b(N) finite-size correction converging — 1.2126 at N = 50,000	Test 1
`fig02_spacing_hist.png`	spacing histogram vs GUE Wigner surmise	Tests 4–6
`fig03_decay_fits.png`	power-law vs 1/log decay fits (R² = 0.9895 / 0.9994)	Test 3/7
`fig04_bootstrap_slope.png`	bootstrap distribution of the decay slope with 95% CI	Test 9
`fig05_ks_convergence.png`	KS statistic marching toward GUE as T_min grows	Test 5 + convergence-watch
`fig06_sigma2_L.png`	number variance Σ²(L) vs GUE/Poisson envelopes	Test 13
`fig07_delta3_L.png`	spectral rigidity Δ₃(L) — GUE in 9/9 L-values	Test 14
`fig08_r2_pair.png`	pair correlation R₂ against Montgomery prediction	Test 34/36
`fig09_K_form_factor.png`	form factor K(t): ramp + plateau spectral form factor	Test 35
`fig10_r_L_scaling.png`	⟨r⟩ L-scaling to the 0.6004 plateau (χ²/dof = 0.01)	Test 33
`fig11_r_bootstrap.png`	bootstrap of ⟨r⟩ — 0.5991 ± 0.0075 vs GUE 0.5992	Test 32
`fig12_dirac_cone.png`	Dirac cone at α = 1/2: E_min ∝ 1/L, R² = 0.9997	Test 19
`fig13_dirac_dip.png`	the ~10× density-of-states dip at the Dirac point	Test 29
`fig14_byers_yang.png`	Byers–Yang flux response: exact 0.0 vs sensitive 0.0032	Test 25
`fig15_berry_R2_cutoff.png`	Berry–Keating-type R₂ cutoff comparison	Test 34
`fig16_hatano_nelson.png`	non-Hermitian control:	Im E
`fig18_gamma_phase.png`	arg(γ*) = 89.874° — the phase portrait of γ	Test 21
`fig19_vortex_texture.png`	vortex texture of the monumental gauge — where the flux lives	Tests 22–24
`fig20_hofstadter_butterfly.png`	the Hofstadter butterfly of the substrate lattice	Physics Lab

Reuse note: the plates are part of the strictly-personal-licensed monograph apparatus — viewing and citing is welcome; republishing them needs the author's written consent (see the license section).

🗺️ Repository map

ab-cloud-research/
├── code/
│   ├── ab_cloud_v19.jl           # canonical 37-test two-pass Julia suite (menu, labs)
│   └── julia/                    # NEW: v19 / v19_v1 / v20 / v21 full sources
├── apps/                         # NEW: React applications
│   ├── ab-cloud-dashboard/       #   37-test dashboard, real-time ζ statistics (+ dist/)
│   └── ab-cloud-lab3d/           #   WebGL 3D laboratory: lattice, Dirac cone, ζ strip (+ dist/)
├── monographs/
│   ├── ru/  en/  zh/             # v22 editions: md + html + docx + pdf + pptx + preprint
│   │   ├── text/                 #   + 19 figures @ 600 dpi per language
│   │   └── figures/
│   └── original-v21/             # author's original monograph (RU) + English edition
│       ├── ru/  en/              #   docx + pdf + html + md + pptx (16 slides each)
│       └── media/                #   shared figures
├── verification/                 # 10-language verification + spinor64 + ζ data
├── lab-3d/                       # 3D lattice laboratory (code + outputs + preprint)
├── results/                      # 455 files: run_20260902_134759 artifacts + reference logs
├── docs/                         # MkDocs Material documentation site
├── termux/                       # push-from-phone kit (Android/Termux)
├── assets/                       # banner & repo art
└── .github/                      # CI, templates, funding, release automation

📚 Documentation map — a README in every folder

Wherever you land, the folder you are in explains itself: what lives there, what it does, what the stored results mean, and how to run the code. All READMEs are in English and end with a short Russian summary.

Enter here	Read this	You will learn
`code/`	`code/README.md`	the canonical 37-test two-pass Julia suite: all test groups, flags, two-pass protocol, what a run writes
`code/julia/`	`code/julia/README.md`	the author's historical versions v19/v19_v1/v20/v21 and what each contributed
`verification/`	`verification/README.md`	the three referee objections, identical CLI on 10 languages, data auto-selection, tolerances
`verification/<lang>/`	e.g. `verification/python/README.md`	per-language files, build/run commands, expected output, spinor38 port
`verification/spinor64/`	`verification/spinor64/README.md`	the 64-spinor experiment E1+E2, orbits 28/21/7/7/1, why idx=38 uniqueness was withdrawn
`verification/data/`	`verification/data/README.md`	every ζ-zero dataset, formats, provenance, the loader contract
`verification/sections/`	`verification/sections/README.md`	per-section closed-form micro-verifications
`monographs/`	`monographs/README.md`	the five editions, format guide, what physics each document stores, how to rebuild
`monographs/{ru,en,zh}/`	`monographs/en/README.md`	per-edition file tables, reading order, appendices B/D
`monographs/original-v21/`	`monographs/original-v21/README.md`	the original v21, its claims, and the exact v21.1 corrections
`lab-3d/`	`lab-3d/README.md`	the 3D lattice OS: key numbers, modes A–J, the four committed runs
`lab-3d/code/`, `lab-3d/outputs/`	`README.md` inside each	the 69-module map; how to read/regenerate the 2026-07-31 runs
`results/`	`results/README.md`	the 455-file run `run_20260902_134759` and the two reference logs
`apps/`	`apps/README.md`	the two React apps and how to run/deploy them
`apps/ab-cloud-dashboard/`, `apps/ab-cloud-lab3d/`	`README.md` inside each	tab-by-tab feature guide, architecture, build commands
`docs/`	`docs/README.md`	the MkDocs site pages and how to build them
`termux/`	`termux/README.md` · `termux/README_RU.md`	publishing to GitHub from an Android phone (EN quick guide + full RU manual)
`assets/`	`assets/README.md`	banner provenance and figure reuse rules
`.github/`	`.github/WORKFLOWS.md`	what every CI workflow, template and automation file does

🌿 Branches & versions

main — the only content branch; everything below ships from it.
dependabot/github_actions/* (5 branches: markdownlint-cli2-action-24, actions/checkout-7, actions/stale-11, julia-actions/setup-julia-3, release-drafter/release-drafter-7) — automated CI-action bumps, each open as a PR (#1–#5); merge at your leisure, they never touch science content.
Tags: v1.0.0 — the first Zenodo-mirrored release; the current state corresponds to the v1.2.0 entry of CHANGELOG.md (v1.1.0 — spinor64 + run artifacts + React apps + Termux kit; v1.2.0 — this documentation deep dive).

📱 Publishing from Android (Termux)

The repository updates itself from a phone: termux/install_and_push.sh installs everything, offers PAT-token (hidden input, API-verified) or browser login (one-time device code at github.com/login/device), pushes main + tags, verifies the remote SHA and opens the repo in the browser — token in memory only. Guides: termux/README.md (EN), termux/README_RU.md (RU, full manual), HOW_TO_PUSH_FROM_ANDROID.md (cheat sheet).

⚙️ CI/CD — what runs on every push

Six automated pipelines (configured in .github/workflows/) guard the repository; their live status is the first badge row of this page.

Workflow	Trigger	What it verifies
CI (`ci.yml`)	every push / PR	markdownlint + link sanity + smoke-run of the section micro-verifications (`verification/sections/*/python/verify.py`)
Julia tests (`julia.yml`)	push / PR / nightly	`code/ab_cloud_v19.jl --quick` — 16×16 → 32×32, ζ ≤ 5000, both passes: the canonical suite must always run
Docs deploy (`deploy-docs.yml`)	push to main	builds the MkDocs Material site and publishes it to GitHub Pages
CodeQL (`codeql.yml`)	push / weekly	static security analysis of the JavaScript/Python surfaces
Link checker (`link-checker.yml`)	scheduled	crawls all repository markdown for dead links — this page's 218 links included
Release drafter (`release-drafter.yml`)	merged PRs	assembles release notes and tags versions

Plus Dependabot keeping the GitHub-Actions and ecosystem pins fresh, a labeler auto-triaging PRs, issue templates and CODEOWNERS.

🖥️ What success looks like — expected console outputs

So that "it works" is never a matter of taste, the expected faces of the fast commands:

$ make quick-test
  [suite] pass 1: 16x16 -> 32x32, zeta <= 5000
  Test 16 [MONTGOMERY] α=0.5: ⟨r⟩ mean=0.594 → PASS
  pass 1 result: PASS (elapsed: 0.71s)
  [suite] pass 2 (hardcore): tightened tolerances
  Test 16b [HARDCORE pass 2]: 2 sub-checks, 0 failed → PASS
  pass 2 result: PASS
  SUITE: ALL GREEN

$ python3 verification/python/ab_cloud_verify.py --alpha 0.5
  loading frozen zeros: verification/data/zeta_zeros_50000.txt
  N = 50000 | window = bulk 0.6 | gauge = monumental
  ⟨r⟩ = 0.5xx (GUE ref 0.5997)          → PASS
  KS pair-correlation vs Montgomery ...  → PASS
  Φ_AB = 0.4487989505 (π/7 exact)       → PASS
  VERDICT: consistent with GUE / Hilbert–Pólya instrumentation

(Exact digits vary with the chosen L/α/seed; verdicts do not. The flagship values in the tables above are the committed evidence.)

📖 Documentation site

The full documentation (quick start, per-edition guides, verification protocol, figure galleries) is built with MkDocs Material and published to GitHub Pages:

https://wild8highlander.github.io/ab-cloud-research

📖 Citation

If this work is useful to you, please cite it (see also CITATION.cff):

BibTeX

@software{isaev2026abcloud,
  author  = {Isaev, Iskhak Khamzatovich},
  title   = {AB-Cloud Research: a phase resonator for the zeros of the Riemann zeta function},
  year    = {2026},
  doi     = {10.5281/zenodo.21825394},
  url     = {https://github.com/wild8highlander/ab-cloud-research},
  note    = {Monographs (RU/EN/ZH + original v21), 37-test Julia suite, 10-language verification, 3D lattice lab}
}

APA

Isaev, I. K. (2026). AB-Cloud Research: a phase resonator for the zeros of the Riemann zeta function (Version 1.0.0) [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.21825394

🛣️ Roadmap

📖 Glossary — every term used on this page

Term	Meaning in this repository
AB-cloud	the Hofstadter operator decorated with vortex phases derived from ζ zeros — the central object
α (flux)	magnetic flux per plaquette; α = 1/2 is the critical line analogue and the Dirac point
Φ_AB	the fitted Aharonov–Bohm phase; equals π/7 exactly at the reference configuration (Test 22)
⟨r⟩	mean adjacent-spacing ratio; GUE predicts 0.5997, Poisson 0.3863 — the core statistic
GUE	Gaussian Unitary Ensemble — the random-matrix universality class of ζ zeros (after unfolding)
Poisson	the integrable-world alternative: uncorrelated spacings; the control curve
KS test	Kolmogorov–Smirnov distance between distributions; the go-to verdict machine here
Δ₃ / Σ²(L)	spectral rigidity / number variance — two-point statistics across window L
R₂(s)	pair correlation function; Montgomery's prediction connects it to ζ zeros
K(t)	spectral form factor — the Fourier-space two-point statistics (ramp + plateau)
C₁	first Chern number of the band; anchors 1, 1, 1 at α = 1/4, 1/3, 1/5 (Test 20)
Dirac point	α = 1/2 touching of bands: zero gap, zero modes, ~10× DOS dip
Dirac string	the flux-carrying plaquette of a vortex; emptiness of all other plaquettes is exact (Test 24)
Byers–Yang	flux-quantisation theorem used as a falsification instrument (Test 25)
Arf invariant	the ℤ₂ invariant separating odd (28) from even (36) spinor structures on the Klein quartic
PSL(2,7)	the order-168 automorphism group of the Klein quartic; orbit signature 28/21/7/7/1
spinor structure	one of the 64 spin bundles on the quartic; exactly isospectral within orbits
zero mode	an exact E = 0 state; 4 at α = 1/2 in the bulk Dirac operator (Connes row)
two-pass	the suite discipline: fast pass 1, then hardcore pass 2 with tightened sub-checks
convergence-watch	the opt-in instrument printing KS at temperature cuts — honesty about finite-T
frozen data	the ζ dataset committed once, checksummed, never re-downloaded or regenerated
monumental gauge	the vortex gauge convention used by E2 and the flagship run
Termux	the Android terminal emulator the whole project is developed and published from
FAIR	findable–accessible–interoperable–reusable; the reason 600+ MB of evidence lives in git

🧭 Reading paths — where to enter for your background

Twenty-eight sections is a lot of surface. Four curated routes through the repository, each starting where you are:

🔍 The reviewer in a hurry (15 minutes). Highlights → Computation data at a glance → the test ledger → spot-check two numbers of your choice against FINAL_REPORT → the license if the verdict matters to your use case.

🧑‍🔬 The physicist (half a day). What is the AB-cloud → key results → the statistical deep-dive → the English monograph PDF (v22, 7 chapters, 19 plates) → reproduce one figure from lab-3d/ → the 3D lab preprint.

🧮 The mathematician (at your own pace). The 64 spinor structures and the Klein quartic orbit theorem → Connes self-duality and Chern anchors in the ledger → the .tex sources of the monograph (monographs/*/text) → ζ dataset provenance in verification/data/README.md.

👨‍💻 The engineer / reproducibility auditor (one evening). Quick start → Makefile reference → run make quick-test (~4 min) → pick your language from the cross-verification matrix → audit the data charter → check the CI workflows in .github/WORKFLOWS.md.

🎓 The student (guided tour). The hosted documentation site → the interactive dashboard app and 3D lab app → make menu for the interactive Julia explorer → the figures gallery (monographs/ru/figures/) → the FAQ below.

❓ FAQ — honest answers to fair questions

Does this repository prove the Riemann Hypothesis? No — and it never claims to. It is a numerical laboratory for the Hilbert–Pólya programme: a concrete, fully verifiable Hamiltonian whose spectrum reproduces GUE statistics, pair correlation and Dirac physics with quantitative precision. A proof would require exact spectral identity with ζ(s) — the repository gives the systematic numerical evidence and the instrumentation to search for it, and is explicit about the difference throughout the monographs.

Why do Tests 4–6 “fail” in the ledger? Because GUE statistics are asymptotic in temperature, and the full-range KS test at T ≲ 10⁵ must reject — any suite that hides this is lying. The repository does the opposite: it records the rejection, splits the high-T sub-ranges, and ships --convergence-watch so you can watch the statistic march toward GUE. The pair-correlation level (Montgomery, KS = 0.047, p = 0.27) is where finite-T noise is already below the signal.

What exactly changed between v21 and v2.2.1? One real correction, found by the project's own instrumentation: the v21 claim that spinor structure idx = 38 is the unique GUE-compatible one was a finite-sample artifact. The spinor64 experiment (E1 + E2) showed all 64 structures are exactly isospectral and GUE-consistent. The correction is documented in §3.2.5 and App. D; the raw evidence is committed and re-runnable. A project that catches and publishes its own corrections in full detail is doing science the right way around.

Can I reproduce the headline numbers on a laptop? Yes. make quick-test (~4 minutes, ζ ≤ 5000, 16×16 → 32×32, both passes) proves the toolchain. python3 verification/python/ab_cloud_verify.py re-derives ⟨r⟩, KS and the topology verdicts in minutes. The full flagship ledger is make test-all (30–60 min per pass tier on a modern laptop).

And on a phone? Yes — the whole project is developed and published from Android via Termux; the Termux guide covers installation, the Julia toolchain and the push workflow end to end.

Why ten programming languages for the same math? Because a numerical artifact that survives translation through ten independent ecosystems (compilers, BLAS stacks, floating-point orders, parser quirks) is very unlikely to be a bug — and a discrepancy between ports is the cheapest early-warning system a numerical project can buy. The ports agree to the quoted precision; that agreement is itself part of the evidence.

Where do the ζ zeros come from — and why “frozen”? From the Odlyzko tables, committed into the repository (2,001,058 zeros, 91 MB). Frozen means: no experiment downloads zeros at runtime, no experiment regenerates them, every language port loads byte-identical files. Reproducibility that depends on a live internet resource is not reproducibility — it is a hope.

What did the flagship run cost in compute? ≈ 9 h 46 min of wall time for the full two-pass suite with artifacts (Test 29 alone: 1 h 05 min; the MC-heavy Test 35 cuts its cost 7× via a precomputed table — 18.0 s exact vs 2.6 s tabulated per evaluation). Every per-test duration is stamped in the stored logs.

How do I cite this? CITATION.cff — DOI 10.5281/zenodo.21825394 (this version) or 10.5281/zenodo.21825393 (all versions); author ORCID 0009-0003-7299-0701. For the 64-structure correction, cite the v2.2.1 layer / v23 edition specifically.

What is the license, in one sentence? Strictly personal (Custom Research License): all exclusive rights belong to the author — you may read, clone, run and cite with attribution, while redistribution, rehosting and commercial use require his prior written consent (see LICENSE, EN + RU).

Why is the full 600+ MB of evidence committed to git? Because the FAIR principles the project subscribes to are about independent re-derivation years later: figures, logs, tables and the exact data that produced them travel together, offline, forever. Git history then doubles as the audit trail of every correction.

🤝 Contributing

Contributions of verification code (new languages for the 10-language suite, performance ports), bug reports and numerical reproducibility reports are welcome — see CONTRIBUTING.md and the issue templates. Substantive changes to the monographs' scientific content are made by the Author.

📄 License

This project is licensed under a Custom Research License — all rights belong fully and exclusively to Isaev Iskhak Khamzatovich. You may read, clone, run and cite the work with attribution; redistribution and commercial use require the Author's written consent. See LICENSE (EN/RU).

What “strictly personal” means, precisely

This repository is distributed under the author's Custom Research License, and the operative phrase is strictly personal: publication here is a scientific communication, not an offer of rights. All copyright, related and other exclusive rights to every asset — the monographs in all languages and formats, the verification suites in all ten languages, the source code, the 600-dpi figure apparatus, the frozen ζ datasets, the applications, the presentation and preprint bundles — belong fully and exclusively to Isaev Iskhak Khamzatovich.

Concretely and without loopholes:

✅ Allowed without permission — reading and studying any part of the repository; cloning it locally; running the verification suites, the apps and the 3D laboratory for verification, teaching or your own understanding; citing the work with attribution (DOI + author).

⛔ Requires the author's prior written consent — any redistribution or rehosting of code, data, figures or text (in whole, in part, or in modified form); any commercial use; any derivative monograph, translation or course built on the monograph content; any claim of authorship beyond citation.

The publication of this repository does not create joint ownership, does not grant a back-license, and does not imply any transfer of rights. The full legal text — in English and in Russian, with identical force — is in LICENSE; permission requests go through the contact channel below. If in doubt whether your use case is “reading” or “redistributing”, ask first: the author grants written permissions readily for proper scientific use.

📬 Contact

🇷🇺 Русская версия

AB-Cloud — фазовый резонатор для нулей дзета-функции Римана

AB-облако — гамильтониан Хофштадтера с топологическими вихрями, фазы Ааронова–Бома которого выведены из нетривиальных нулей дзета-функции Римана. Проект полностью посвящён одной теме: численной проверке программы Гильберта–Поля в вычислимой форме.

Ключевые верифицированные результаты

Результат	Значение	Статус
⟨r⟩ против GUE 0.5992	0.5848 ± 0.0260 (отклонение −2.4 %)	согласуется
Тест Монтгомери (облако vs нули ζ)	KS = 0.047, p = 0.27, N = 500 сертифицированных нулей	H₀ не отвергается
Дефект потока Байерса–Янга (q → q+1)	3.5·10⁻¹⁵	машинная точность
Самодуальность Конна	4 нулевые моды, C₁ = 2	машинная точность
Корреляционная дыра Монтгомери	R₂ ближе к GUE (d = 0.140), чем к Пуассону (0.227)	воспроизведена
Дираковская динамика при α = 1/2	E_min ∝ 1/L, R² = 0.9997; провал DOS 20×	подтверждена
Спинорные структуры квартики Клейна — все 64	орбиты PSL(2,7) 28/21/7/7/1, изоспектральность ≈ 9·10⁻¹⁵, ⟨r⟩ = 0.5984 ± 0.0035 — 64/64 GUE-согласованы	утверждение v21 об «уникальности idx=38» снято как артефакт
Оптимальность критической прямой	σ = 1/2 минимизирует KS (0.152)	GUE-оптимальность

Каждое число трассируемо до именованного теста в эталонном 37-тестовом логе.

Что в репозитории

code/ab_cloud_v19.jl — каноническая 37-тестовая двухпроходная сюита на Julia (без внешних пакетов): интерактивное меню, физическая лаборатория (22 эксперимента), 3D-лаборатория (30 тестов), быстрый режим --quick (16×16 → 32×32, ζ ≤ 5000).
monographs/ — пять изданий монографии: v22, переписанная с нуля на верифицированной сюите (русский, английский, китайский — md/html/docx/pdf/pptx/препринт tex+pdf, по 19 рисунков 600 dpi), и оригинальная авторская монография v21 с полной английской версией (docx/pdf/html/md + презентации по 16 слайдов).
verification/ — независимая 10-языковая верификация (C++, Fortran, Go, Haskell, JavaScript, Julia, MATLAB, Python, R, Rust), двуязычный интерфейс RU/EN, ответы на 3 стандартных возражения рецензентов, данные нулей ζ до 2 000 000 (Одлыжко); spinor64 — все 64 спинорные структуры GUE-согласованы, порты Test 38 на 10 языках.
lab-3d/ — трёхмерная лаборатория: 3D-гамильтониан Хофштадтера с вихревыми линиями, решётки 36³, 5000 встроенных нулей, полные отчёты прогонов.
results/ — 455 файлов: полный двухпроходной прогон run_20260902_134759 (37 тестов) + эталонные логи.
apps/ — два React-приложения: дашборд 37 тестов с живыми ζ-статистиками и WebGL 3D-лаборатория.
termux/ — публикация репозитория с Android-телефона одной командой (PAT-токен или вход через браузер).
В каждом каталоге лежит подробный README (по-английски + краткое резюме по-русски) — см. «Documentation map» выше.

Быстрый старт — что вы должны увидеть

make quick-test     # ~3–5 минут: 16×16 → 32×32, ζ ≤ 5000, оба прохода
make verify         # десятиязычная перекрёстная проверка
make menu           # интерактивное меню: тесты + Physics Lab + 3D-лаборатория
python3 verification/spinor64/run_spinor64.py   # эксперимент E1+E2 по 64 структурам

Признак успеха make quick-test — строки pass 1 result: PASS, pass 2 result: PASS, финал SUITE: ALL GREEN. Признак успеха run_spinor64.py — таблица орбит 28/21/7/7/1 и вердикт GUE-consistent по всем 64 строкам. Точные команды для каждого из десяти языков — в verification/<язык>/README.md; полное руководство по публикации с телефона — в termux/README_RU.md.

Быстрый старт

git clone https://github.com/wild8highlander/ab-cloud-research.git
cd ab-cloud-research
julia code/ab_cloud_v19.jl --quick     # быстрая проверка: оба прохода, ~3–5 мин
julia code/ab_cloud_v19.jl             # интерактивное меню

📊 Большие данные вычислений

Ключевые числа проекта — не декорация, а извлечённые из артефактов результаты; для каждой строки указан файл, в котором число хранится.

Показатель	Значение	Источник
Нулей ζ, встроено в репозиторий	2 001 058 (таблицы Одлыжко)	`verification/data/`
Замороженный набор данных	91 МБ, 8 файлов	`verification/data/`
Канонический сюит	37 тестов × 2 прохода + серийный проход 3	`code/ab_cloud_v19.jl`
Машинных вердиктов в флагманском прогоне	202 (171 PASS · 22 WARN · 9 FAIL/WARN, все перепроверены)	`results/ab_cloud_v19_verify_report_2026-09-02_23-33-45.txt`
Время флагманского прогона	≈ 9 ч 46 мин (2026-09-02)	метки времени в логе
Артефактов прогона	453 файла / 39 каталогов (7,3 МБ)	`results/run_20260902_134759/`
Спинор-структуры	64 из 64 GUE-согласованы	`verification/spinor64/`
Орбиты квартки Клейна	28 / 21 / 7 / 7 / 1 (PSL(2,7), порядок 168)	отчёт E1
Максимальное спектральное расстояние	8,88 × 10⁻¹⁵	отчёт E1
Калибровочная инвариантность	7,11 × 10⁻¹⁵	отчёт E1
⟨r⟩ по ансамблю 64 структур	0,5984 ± 0,0035 против GUE 0,5997	E2
GUE-ансамбль	100 матриц 1936×1936; медиана ⟨r⟩ = 0,6013	E2
Поток Ааронова–Бома	Φ_AB = 0,4487989505 = π/7 (точно)	тест 22
Динамика Дирака	R² = 0,9997; v_F(2π) = 1,8998	тесты 19/30
Нулевые моды Конна	4 из 4, C₁ = 2	тест 17
Пустые плакетки (струны Дирака)	5040/5040, дефект ровно 0,0	тест 24
Монпгомери, парная корреляция	KS = 0,047, p = 0,27	v18-лог
Байт-устойчивая статистика	H = 7,9991 бит; n = 55 288	тест 36
Отслеживаемых файлов	1 040	git ls-files
Монографии	5 изданий (RU/EN/ZH + v21 RU/EN) + слой v2.2.1	`monographs/`
Рисунков при 600 dpi	19 × 3 языка	`monographs/*/figures/`

Полный реестр тестов флагманского прогона (2026-09-02)

№	Каталог теста	Что устанавливает	Вердикт
1	`test_01_bN_convergence`	b(N) = 1,2126 при N = 50 000	PASS
2	`test_02_bN_monotonicity`	0 нарушений монотонности на 499 окнах	PASS
3	`test_03_bN_rate`	степенной закон b(N) ≈ 7,0312·N^(−0,1685), R² = 0,9895	PASS
4	`test_04_gue_ks_full`	KS на всём диапазоне: D = 0,0881 — ожидаемое отклонение при конечном T	FAIL/WARN → ожидаемо
5	`test_05_gue_ks_highT`	высокие T: D = 0,0878 / 0,0866 — дрейф к GUE	FAIL/WARN → ожидаемо
6	`test_06_chi2_hist`	χ²-гистограмма: 6170 / 6276 / 6384 по бинам	FAIL/WARN → ожидаемо
7	`test_07_decay_slope`	наклон −0,1504, ДИ95 [−0,1594, −0,1414]	PASS
8	`test_08_residuals`	критерий серий: 3 серии (ожидалось 5,8)	PASS
9	`test_09_bootstrap_ci`	бутстреп-наклон −0,1746, ДИ95 [−0,1895, −0,1552]	PASS
10	`test_10_cross_validation`	максимальное отклонение 8,5%	PASS
11	`test_11_anderson_darling`	батарея Андерсона–Дарлинга: 5/5 под-проверок чисто	PASS
12	`test_12_two_sample_ks`	двухвыборочный KS: D = 0,0233, p = 0,0105	WARN → PASS
13	`test_13_number_variance`	дисперсия числа точек ближе к GUE в 9/9 L	PASS
14	`test_14_spectral_rigidity`	жёсткость спектра Δ₃ ближе к GUE в 9/9 L	PASS
15	`test_15_ab_construction`	эрмитовость ОК; τ_TRB = 0,1037; поток −0,0 точно	PASS
16	`test_16_ab_gue_class`	⟨r⟩ = 0,594 при α = 0,5 — класс GUE	PASS
17	`test_17_connes_self_duality`	нулевые моды: 4 (ожидание 4); C₁ = 2	PASS
18	`test_18_chiral_AIII`	киральный дефект: 0,0 при α=1/2; 0,0058 при α=1/3	PASS
19	`test_19_dirac_cone`	E_min ∝ 1/L, R² = 0,9997; v_F(2π) = 1,8998	PASS
20	`test_20_chern_tknn`	якоря C₁: {1/4, 1/3, 1/5} = 1, 1, 1; зазор 0,0 в точке Дирака	PASS
21	`test_21_gamma_phase`	arg(γ*) = 89,874° (отклонение 0,126°)	PASS
22	`test_22_ab_phase`	Φ_AB = 0,4487989505 = π/7 (точно)	PASS
23	`test_23_fractal_factor`	замкнутая форма = 1,0; c_AB = 0,02062 ≈ 0,02063	PASS
24	`test_24_dirac_string_flux`	5040/5040 пустых плакеток, дефект 0,0	PASS
25	`test_25_byers_yang`	Δ(q=1→0) = 0,0; чувствительность 0,0032 > 10⁻³	PASS
26	`test_26_pbc_torus`	тор: поток −0,0; пустых 5040/5183; ⟨r⟩ = 0,6009	PASS
27	`test_27_binary_chiral`	киральный дефект 0,0 (W=0) против 0,0058 (W=1,0)	PASS
28	`test_28_f_gue_merit`	merit f_GUE = 0,8704; Σ²_data = 0,6115	WARN
29	`test_29_dirac_dip`	провал DOS: 0,0193 против 0,1944 (~10×)	PASS
30	`test_30_vf_scaling`	масштабирование v_F = 1,798, R² = 0,9977	PASS
31	`test_31_hatano_nelson`	неэрмитов контроль: max	Im E
32	`test_32_rmean_bootstrap`	⟨r⟩ = 0,5991 ± 0,0075 против GUE 0,5992	PASS
33	`test_33_l_scaling_rmean`	L-масштаб до L=80: плато 0,6004, χ²/dof = 0,01	PASS
34	`test_34_direct_vs_zeta`	⟨	ΔR₂
35	`test_35_form_factor_Kt`	форм-фактор K(t): RMS 0,4193, корреляция 0,8889	WARN
36	`test_36_byte_robust`	r₂₅₆ = 0,5756–0,5894; H = 7,9991 бит; n = 55 288	PASS
37	`test_37_half_factorial_gamma`	(1/2)! = √π/2 (ошибка 0,0); 32/π²; ∫p₂ = 1	PASS
38	`verification/spinor64`	64/64 GUE-согласованы; изоспектральность ≈ 9·10⁻¹⁵	PASS

Итог: 202 машинных вердикта — 171 PASS, 22 WARN, 9 FAIL/WARN-маркеров

64 спинор-структуры квартки Клейна — итог

Эксперимент spinor64 (E1 — точная симметрия на графе Клейна {3,7}: 56 вершин, 84 ребра, 24 семиугольные грани; E2 — статистика на хофштадтеровском торе, L = 44, α = 0,5, калибровка :monumental) показал:

разбиение 64 структур по орбитам PSL(2,7): 28 / 21 / 7 / 7 / 1 (28 нечётных, Arf = 1, образуют одну орбиту — классическая теорема о битангенсах, подтверждена численно до машинной точности);
максимальное спектральное расстояние внутри орбит: 8,88 × 10⁻¹⁵ — сопряжённые структуры изоспектральны точно;
калибровочная инвариантность: 7,11 × 10⁻¹⁵;
по ансамблю всех 64 структур: [r] = 0,5984 ± 0,0035 против аналитического GUE 0,5997 — 64 из 64 GUE-согласованы;
следствие: утверждение v21 об уникальности структуры idx = 38 отозвано как артефакт конечной выборки (§3.2.5 v2.2.1, Прил. D v23).

Полные 64 строки: verification/spinor64/output/spinor64_table.csv; отчёт с таблицами E1/E2: spinor64_report.md.

, каждый перепроверен «hardcore»-проходом; необъяснённых провалов нет.

Три правила воспроизводимости, общие для всего репозитория: нули не скачиваются во время счёта; нули не пересоздаются; все десять языковых портов читают побитово одни и те же файлы. Английская часть этого README (разделы Full test ledger, The 64 spinor structures, Statistical deep-dive) содержит полные таблицы всех 38 тестов и 64 структур.

Целостность данных — контрольные суммы

Набор нулей заморожен и защищён контрольными суммами; все десять языковых портов читают побитово одни и те же файлы. Реальные SHA-256 состояния, закоммиченного в репозиторий:

Файл	Размер	SHA-256 (начало)
`zeta_zeros_2M_odlyzko.txt`	34 123 269	`f0d2b200a12bdfa2…`
`zeros6.txt`	36 018 936	`2ef7b752c2f17405…`
`zeta_zeros_2M_odlyzko.txt.gz`	14 255 583	`eee125ac69bc2c98…`
`zeta_zeros_500k_odlyzko.txt`	8 351 317	`1a213d7b97e6808e…`
`zeta_zeros_highT_blocks.txt`	429 224	`02473ea733a53690…`
`zeta_zeros_50000_embedded.txt`	789 482	`2cf6a84e9da69ee2…`
`zeta_zeros_50000.csv`	775 953	`039b4d5170813ccc…`
`Zeta_Zeros_50000.jl`	318 013	`5be3e16bba708ba8…`
`zeta_zeros_50000.txt`	290 004	`efae6880bcde22b9…`

Первая строка главной таблицы — γ₁ = 14,134725142… — то же число, которым открываются монографии. Совпала сумма и первая строка — вся цепочка воспроизводимости унаследовала целостность. Время каждого из 37 тестов флагманского прогона опубликовано в английской части (таблица Computational cost): от 9 секунд у структурных проверок до 1 ч 06 мин у теста Байерса–Янга.

Мини-словарь

⟨r⟩ — среднее отношение соседних зазоров (GUE: 0,5997; Пуассон: 0,3863); KS — статистика Колмогорова–Смирнова; Δ₃, Σ²(L) — жёсткость спектра и дисперсия числа точек; R₂ — парная корреляция (прогноз Монтгомери); C₁ — первое число Черна; α — поток на плакетку (α = 1/2 — точка Дирака); Arf — ℤ₂-инвариант нечётных/чётных спинор-структур; PSL(2,7) — группа автоморфизмов квартки Клейна порядка 168; двухпроходность — быстрый проход 1 + «hardcore»-проход 2 с под-проверками; замороженные данные — единственный источник нулей для всех портов, без скачивания и пересоздания.

Лицензия

Действует персональная лицензия автора: все права полностью и исключительно принадлежат Исаеву Исхаку Хамзатовичу. Разрешены чтение, клонирование, локальный запуск и цитирование с атрибуцией; распространение и коммерческое использование — только с письменного согласия автора. Полный текст (RU/EN): LICENSE.

Лицензия — строго персональная. Все исключительные права на материалы репозитория — монографии на всех языках и во всех форматах, верификационные сюиты на десяти языках, исходный код, графика, данные, приложения — принадлежат в полном объёме и исключительно автору, Исаеву Исхаку Хамзатовичу. Разрешено без разрешения: читать, клонировать локально, запускать сюиты и приложения для проверки и обучения, цитировать с атрибуцией (DOI + ORCID). Требуется предварительного письменного согласия автора: любое перераспространение или повторный хостинг (целиком, частично или в изменённом виде), любое коммерческое использование, любые производные монографии, переводы и учебные курсы на их основе. Публикация репозитория не создаёт совместной собственности, обратной лицензии или подразумеваемой передачи прав. Полный текст с равной юридической силой на русском и английском — в файле LICENSE; запросы разрешений — через каналы связи ниже.

Контакты

Исаев Исхак Хамзатович · aslan08_05@mail.ru · ORCID 0009-0003-7299-0701 · DOI 10.5281/zenodo.21825394

«Гипотеза Римана как условие универсальности квантового пространства»
The Riemann Hypothesis as a universality condition of quantum space

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🔬 AB-Cloud — a phase resonator for the zeros of the Riemann zeta function

📑 Table of Contents

✨ Highlights

📊 Computation data at a glance

🌀 What is the AB-cloud?

🧮 The construction in one screen

🔑 Key verified results

🧾 Full test ledger — the two-pass flagship run (2026-09-02)

Computational cost of every test (real timings of the flagship run)

🧬 The 64 spinor structures — full data

E1 — Klein graph {3,7}: exact symmetry, all 64 structures

E2 — AB-cloud Hofstadter torus: statistics of all 64 structures

Reproduce

📚 Monographs (5 editions)

📚 Monograph editions & formats — the full matrix

🧪 Verification suite (10 languages)

🌐 The ten language ports — cross-verification matrix

🧊 3D lattice laboratory

🚀 Quick start

🧑‍🔬 Interactive tools — Physics Lab, 3D lab and the two apps

⌨️ Makefile command reference

🗃️ ζ-zero dataset inventory

Data integrity — sizes and SHA-256 of the frozen dataset

🗂️ Flagship-run artifact inventory (run_20260902_134759)

📊 Results & reproducibility

🔬 Repository by the numbers

🕰️ Verification history timeline

📈 Statistical deep-dive — how to read the numbers

The spacing ratio ⟨r⟩ — the heartbeat of the GUE claim

The finite-T GUE story — why Tests 4–6 “reject” and why that is correct

Montgomery pair correlation — the strongest single number

Topology at machine precision

Dirac dynamics — R² = 0.9997

🖼️ The figure apparatus — all 19 plates, annotated

🗺️ Repository map

📚 Documentation map — a README in every folder

🌿 Branches & versions

📱 Publishing from Android (Termux)

⚙️ CI/CD — what runs on every push

🖥️ What success looks like — expected console outputs

📖 Documentation site

📖 Citation

🛣️ Roadmap

📖 Glossary — every term used on this page

🧭 Reading paths — where to enter for your background

❓ FAQ — honest answers to fair questions

🤝 Contributing

📄 License

What “strictly personal” means, precisely

📬 Contact

🇷🇺 Русская версия

AB-Cloud — фазовый резонатор для нулей дзета-функции Римана

Ключевые верифицированные результаты

Что в репозитории

Быстрый старт — что вы должны увидеть

Быстрый старт

📊 Большие данные вычислений

Полный реестр тестов флагманского прогона (2026-09-02)

64 спинор-структуры квартки Клейна — итог

Целостность данных — контрольные суммы

Мини-словарь

Лицензия

Контакты

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