🔬 hexa-cern

HEXA-CERN family — particle physics · benchtop accelerator · σ-cascade · n=6 substrate

particle-physics · accelerator · laser-plasma · LWFA · σ-cascade · LHC · DESY · n=6 lattice · benchtop

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💫 hexa-cern

hexa-cern — n=6 sigma-cascade 6-order benchtop accelerator (100 MeV / 1 GeV/m, mini + parent + classical 3-pillar).

A petite, peer-of-Lumière standalone repo from the dancinlab org. Where Lumière takes the camera/character axes, hexa-cern takes the accelerator axis: three pillars distilled from the canon physics domain into a single MIT-licensed bundle.

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Why — benchtop CERN

LHC fills a 27 km tunnel for 7 TeV. DESY runs a 1 GeV/m laser-plasma prototype on a research-lab footprint. hexa-cern's design target is a benchtop σ-φ=10 GeV/m continuous-mode accelerator at 100 MeV total, threaded by the n=6 perfect-number lattice (σ(6)=12, τ(6)=4, φ(6)=2).

The design ceiling — what the spec claims if Stage-1+ empirical builds confirm the σ-cascade — is 6 orders of practical change vs current tech:

effect	LHC/DESY current	hexa-cern design ceiling
precision	1.0 unit	σ-φ = 10× gain
throughput	1.0×	σ² = 144×
energy cost	100%	1/σ ≈ 8.3%
equipment size	1.0 L (or 27 km)	1/(σ-φ) = 0.1 L benchtop
error rate	1%	1/σ² ≈ 0.7%
lifetime	1 year	σ·τ = 48 months

This is the why: a CERN you can put on a bench, drawn from the same n=6 invariant that threads the rest of the HEXA family.

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Status

• v1.1.0 RSC code-layer FINAL on main (2026-05-13)
• 29/29 verify scripts PASS · 353/353 row-level checks PASS · 4/4 tests PASS
• 100% bookkeeping closure across F-PCERN-1/2/3 (T1+T2+T3 locked)
• __HEXA_CERN_RSC_SATURATED__ STOP signal active (17/17 saturation conditions met)
• 3 pillars: HEXA-MINI-ACCEL (벤치톱 100 MeV / 1 GeV/m laser-plasma) + HEXA-PACCEL (integrated parent) + HEXA-CLASSIC-ACCEL
• n=6 invariant: σ(6)=12 · τ(6)=4 · φ(6)=2 · J₂=24 · σ·φ = n·τ = 24
• Zero .py in the runnable surface — 100% .hexa end-to-end (verify + tests + firmware sim)
• LHC 7 TeV/27km & DESY 1 GeV/m baselines compared paper-only; empirical raw-data fit (Stage-1+ benchtop) UNVERIFIED until hardware lands
• Closure is bookkeeping — closed-form algebra + closed-form numerics + archival paper-existence; not bench measurement
• Real-limits authority: LIMIT_BREAKTHROUGH.md (CERN public TDR/CDR values L1..L12; no n=6 lattice fit on CERN vendor numbers)
• Parent: dancinlab/echoes; GitHub canonical at https://github.com/dancinlab/hexa-cern

What it does not ship: actual particle acceleration, Geant4/MAD-X bridge, real-time beam diagnostics, LHC/DESY data ingestion. The σ-cascade 6-order claim is a design-target ceiling, not a measurement.

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Verification

v1.1.0 RSC code-layer FINAL on main (2026-05-13): 29/29 verify scripts PASS · 353/353 row-level checks PASS · 4/4 tests PASS · 100% bookkeeping closure across F-PCERN-1/2/3 (T1+T2+T3 locked) · __HEXA_CERN_RSC_SATURATED__ STOP signal active.

v1.0.0 ships (frozen 2026-05-06):

• 3 pillar specs (.md, extracted from canon@c0f1f570)
• a cli/hexa-cern.hexa dispatcher with 3 pillar verbs + status / selftest

v1.1.0-pre adds (on main, 2026-05-07):

• verify/ — 12 .hexa scripts auditing n=6 lattice + per-pillar derivations + numerical solvers
• build/ — pandoc + xelatex Makefile that regenerates 3 pillar PDFs (clean)
• tests/ — 4 .hexa test cases (+ test_all.hexa aggregator); 4/4 PASS
• cli/hexa-cern.hexa verify [<sub>] — 6-runner aggregator subcommand
• hexa.toml v1.1.0-pre [closure] block: verify_pass: 6/6, tests: 4/4

Zero .py was added — the runnable surface is 100% .hexa. This is deliberate: hexa-cern is a hexa-family member, and the migration target across dancinlab repos is .hexa-native tooling.

The verify/ surface (all .hexa) audits n=6 closure + per-pillar derivations. Current state (2026-05-13): 29/29 scripts PASS, 353/353 row-level checks PASS — 100% bookkeeping closure. F-PCERN-1/2/3 all at T1+T2+T3 locked. __HEXA_CERN_RSC_SATURATED__ STOP signal active (17/17 saturation conditions met).

script	check	result
verify/lattice_check.hexa	σ(6)·φ(6) = n·τ(6) = J₂ = 24 across roadmap + 3 pillars	23/23 PASS
verify/cross_doc_audit.hexa	LHC / DESY / OEIS / BT cross-link + firmware HDL/MCU skeleton	15/15 PASS
verify/calc_wakefield.hexa	mini — E_peak = σ·(σ-φ) = 120 GV/m, a₀ = n = 6, R = 10 cm	6/6 PASS
verify/numerics_wakefield.hexa	mini — closed-form plasma numerics (n_e, L_d via math_pure)	4/4 PASS
verify/numerics_lwfa_solver.hexa	mini — Verlet LWFA ODE solver	7/7 PASS
verify/numerics_lwfa_relativistic.hexa	mini — KDK leapfrog relativistic LWFA (γ → 200)	9/9 PASS
verify/numerics_beam_dynamics.hexa	mini — LWFA betatron + emittance preservation	8/8 PASS
verify/numerics_lwfa_scaling.hexa	mini — Lu/Esarey/TD scaling-law parity	10/10 PASS
verify/calc_sigma_cascade.hexa	parent — E_0..E_6 chain (10 MeV → 100 TeV)	8/8 PASS
verify/numerics_sigma_cascade.hexa	parent — relativistic γ progression numerics	10/10 PASS
verify/numerics_bending.hexa	parent — collider bending-radius R = E/(ecB), LHC/Tev/FCC	8/8 PASS
verify/calc_classical.hexa	classical — DOF = n = 6, phase-space dim = σ = 12	11/11 PASS
verify/numerics_classical.hexa	classical — symplectic leapfrog (τ=4 quadrants)	9/9 PASS
verify/numerics_liouville.hexa	classical — Liouville volume preservation (det(J)=1)	8/8 PASS
verify/numerics_se3_partial.hexa	classical — 2-DOF symplectic (1→2→6-DOF)	8/8 PASS
verify/numerics_cross_pillar.hexa	cross-pillar consistency (mini ↔ parent ↔ classical)	8/8 PASS
verify/numerics_lhc_parity.hexa	F-PCERN-1 collider parity (LEP/Tevatron/LHC/FCC)	10/10 PASS
verify/numerics_lwfa_parity.hexa	F-PCERN-3 LWFA parity (BELLA/FACET/ATHENA/FLASHFwd)	7/7 PASS
verify/numerics_lattice_arithmetic.hexa	n=6 lattice float arithmetic (math_pure stability)	12/12 PASS
verify/lint_numerics.hexa	meta-lint: every numerics_*.hexa follows conventions	71/71 PASS
verify/saturation_check.hexa	RSC saturation (sat-1 + sat-2 + sat-3 → STOP)	17/17 PASS
verify/empirical_lhc_api.hexa	F-PCERN-1 T3 — CERN Open Data API archival feed	7/7 PASS
verify/empirical_lwfa_hepdata.hexa	F-PCERN-3 T3 — Inspire-HEP LWFA paper milestones	10/10 PASS
verify/empirical_classical_arxiv.hexa	F-PCERN-2 T3 — arXiv classical-mechanics milestones	6/6 PASS
verify/falsifier_check.hexa	F-PCERN-1/2/3 preregister + closure progress (100% bookkeeping)	21/21 PASS
firmware/sim/timing_chain.hexa	§A.6.1 step C — master clock + trigger sim	10/10 PASS
firmware/sim/dac_chain.hexa	§A.6.1 step C — 16-bit DAC chain	10/10 PASS
firmware/sim/adc_chain.hexa	§A.6.1 step C — ADC chain (BPM/diamond)	9/9 PASS
firmware/sim/control_loop.hexa	§A.6.1 step C — closed PID loop	9/9 PASS

Run them all with the unified CLI subcommand or the standalone orchestrator:

HEXA_LANG=$HOME/core/hexa-lang hexa-cern verify all       # 29/29 expected
HEXA_LANG=$HOME/core/hexa-lang hexa run verify/run_all.hexa  # same; orchestrator (.hexa)

HEXA_LANG points the interpreter at the hexa-lang stdlib root that ships self/runtime/math_pure. Required when numerics scripts run outside the hx package shim.

Or build the 3 pillar PDFs:

make -C build check       # verify pandoc + xelatex + hexa available
make -C build all         # rebuild all 3 pillar PDFs into build/out/

Empirical wiring (laser-plasma sandbox, parent integration, classical baseline solver) is deferred to Stage-1+ benchtop builds. See docs/cern_baseline.md for the LHC 7 TeV/27 km vs DESY 1 GeV/m vs HEXA σ-φ=10 GeV/m comparison table, and docs/numerics_methodology.md for how the verify surface is structured (3-tier evidence ladder, F-PCERN closure pct, math_pure conventions, recipe for adding new numerics).

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Install

# 1. Install hexa-lang (gives you `hexa` + `hx` package manager)
/bin/bash -c "$(curl -fsSL https://raw.githubusercontent.com/dancinlab/hexa-lang/main/install.sh)"

# 2. Install hexa-cern
hx install hexa-cern

Run

hexa-cern status          # 0/3-wired pillar table + verdict + caveats
hexa-cern selftest        # full 3-pillar sentinel sweep
hexa-cern verify          # n=6 invariant + per-pillar calculators (29/29)
hexa-cern --version       # show version
hexa-cern --help          # full usage

# orchestrator (.hexa, no CLI wrapper):
HEXA_LANG=$HOME/core/hexa-lang hexa run verify/run_all.hexa

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Repo layout

hexa-cern/
├── README.md                     ← this file
├── LICENSE                       ← MIT
├── hexa.toml                     ← package manifest (hx install hexa-cern)
├── install.hexa                  ← hx install hook (post-install selftest)
├── .roadmap.hexa_cern            ← cross-cutting state (lattice / cycles / falsifiers)
├── CHANGELOG.md                  ← release history
├── RELEASE_NOTES_v1.0.0.md       ← v1.0.0 cut notes
│
├── mini/doc/mini-accelerator.md                            ← pillar 1 (47 KB)
├── parent/doc/particle-accelerator.md                      ← pillar 2 (14 KB)
├── classical/doc/classical-mechanics-accelerator.md        ← pillar 3 (47 KB)
│
├── cli/
│   └── hexa-cern.hexa            ← CLI router (status/selftest/verify/mini/parent/classical)
├── verify/                       ← v1.1.0-pre — n=6 audit surface (.hexa)
│   ├── lattice_check.hexa            ← σ·φ = n·τ = J₂ = 24 closure   (23/23)
│   ├── cross_doc_audit.hexa          ← LHC/DESY/OEIS/BT cross-pillar (11/11)
│   ├── calc_wakefield.hexa           ← mini — laser-wakefield n=6   ( 6/ 6)
│   ├── numerics_wakefield.hexa       ← mini — closed-form n_e/L_d   ( 4/ 4)
│   ├── numerics_lwfa_parity.hexa     ← mini — vs DESY/SLAC LWFA refs ( 7/ 7)
│   ├── calc_sigma_cascade.hexa       ← parent — E_0..E_6 chain      ( 8/ 8)
│   ├── numerics_sigma_cascade.hexa   ← parent — relativistic γ      (10/10)
│   ├── numerics_lhc_parity.hexa      ← parent — vs LEP/Tev/LHC/FCC  (10/10)
│   ├── calc_classical.hexa           ← classical — Lagrange/Hamilton(11/11)
│   ├── numerics_classical.hexa       ← classical — symplectic leap. ( 9/ 9)
│   ├── numerics_cross_pillar.hexa    ← mini ↔ parent ↔ classical    ( 8/ 8)
│   └── falsifier_check.hexa          ← F-PCERN-1/2/3 + closure %    (11/11)
├── build/
│   ├── Makefile                  ← pandoc + xelatex 3-PDF rebuild
│   ├── header.tex                ← LaTeX include (CJK + monospace; soft-guarded)
│   └── out/*.pdf                 ← generated, .gitignore'd
├── tests/                        ← v1.1.0-pre — regression suite (.hexa)
│   ├── test_selftest.hexa
│   ├── test_lattice.hexa
│   ├── test_calculators.hexa
│   ├── test_cli_verify.hexa
│   └── test_all.hexa             ← runs everything above (4/4 PASS)
└── docs/cern_baseline.md         ← LHC vs DESY vs hexa-cern comparison

The verify/ + build/ + tests/ triad is the canonical runnable surface for hexa-cern: every audit + every PDF + every test is .hexa end-to-end (no Python, no shell-only logic).

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Cross-link

dependency / cousin	repo	role
SC magnet substrate	dancinlab/hexa-rtsc	superconducting magnet primitive
cousin (PET cyclotron, antimatter)	dancinlab/hexa-antimatter	parallel acceleration use case
Stage-3 propulsion dependent	dancinlab/hexa-ufo	downstream propulsion consumer

Provenance: extracted from canon at SHA c0f1f570 on 2026-05-06.

Sister repo (peer extraction): dancinlab/lumiere — camera-filter + hexa-main-character apps-axis.

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License

MIT — see LICENSE.

Copyright (c) 2026 dancinlab (박민우 nerve011235@gmail.com)