🌌 hexa-cosmos

HEXA-Cosmos family — cosmology · particle-cosmology · cosmic observatory · n=6 ΛCDM closed-form candidate

cosmology · ΛCDM · n=6 lattice · particle-cosmology · observatory · BBN · CMB · candidate-closed-form

---

Cosmos substrate — cosmology + particle-cosmology + cosmic observatory. n=6 ΛCDM (LambdaCDM) closed-form comparison candidate.

3-pillar Cosmos substrate organized around the n=6 invariant lattice: COSMOLOGY / PARTICLE / OBSERVATORY. All 3 pillars ship as theoretical spec at v1.0.0; the n=6 ΛCDM 6-parameter mapping is a candidate, not a measurement.

Distribution: GitHub canonical at https://github.com/dancinlab/hexa-cosmos.

Why — n=6 우주론 substrate

hexa-cosmos는 3-pillar Cosmos substrate로, write-side 우주론 spec을 공개한다. ΛCDM의 핵심 좌표 — 6개 독립 파라미터, Ω_m : Ω_Λ ≈ 1/3 : 2/3, T_CMB ≈ 2.725 K, CMB 1st peak l₁ = 220 — 가 모두 n = 6 substrate의 number-theoretic identity로 closed-form 후보 표현을 가진다는 가설을 검증가능한 형태로 노출하는 것이 v1.0.0의 목적이다.

3개 pillar는 tetrahedron이 아닌 triangle로 구성된다 (자매 substrate hexa-bio는 4-verb tetrahedron):

                ┌──────────────┐
                │  COSMOLOGY   │
                │  (ΛCDM 6-par)│
                └──────┬───────┘
                       │
               ┌───────┴───────┐
               │               │
        ┌──────▼─────┐  ┌──────▼──────┐
        │  PARTICLE  │  │ OBSERVATORY │
        │ (BBN/CMB)  │  │  (telescope)│
        └────────────┘  └─────────────┘
           [SPEC]            [SPEC]

n=6 invariant lattice가 ΛCDM와 만나는 지점 — n_s = 27/28 = (n/φ)³/((n/φ)³+μ) (0.9643 vs 측정 0.9649 ± 0.0042) — 이 substrate의 가장 tight한 후보 매치이다. 전체 비교표는 docs/lambda_cdm_vs_n6.md 참고.

Status

이론 + 후보 spec. 작동 .hexa CLI TBD. ΛCDM (LambdaCDM) baseline에 대한 n=6 closed-form 비교 후보 (candidate, not measurement).

• 0/3 pillars empirically wired. All 3 ship as theoretical spec only. The .hexa CLI is a placeholder router (subcmd dispatch + audit logging landed; numerical wiring TBD).
• n=6 ΛCDM closed-form comparison is a CANDIDATE, not a measurement. See docs/lambda_cdm_vs_n6.md for the side-by-side parameter table with honest σ-bounds vs candidate n=6 derivation, plus 6 falsifiers (F1~F6).
• n=6 invariant lattice verified via OEIS A000203 / A000005 / A000010 / A001414 cross-derivation only.
• Numerical pipelines (CMB, BBN, N-body, telescope) deferred post-v1.0.

1. 0/3 pillars empirically wired. All 3 ship as theoretical spec only.
2. n=6 ΛCDM closed-form comparison is a CANDIDATE, not a measurement.
3. n=6 invariant lattice (σ=12, τ=4, φ=2, J₂=24) is verified via OEIS sequence cross-derivation only.
4. Numerical pipelines (CMB, BBN, N-body, telescope) are out of scope for v1.0.0 — empirical wiring deferred to post-v1.0 cycles.
5. Cross-link cousins (see §Cross-link below) ship independently.

Install

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

# 2. Install hexa-cosmos
hx install hexa-cosmos          # global, pulls latest from registry

Run

hexa-cosmos cosmology           # cosmology spec (ΛCDM 6-param closed-form candidate)  [SPEC]
hexa-cosmos particle            # particle-cosmology spec                              [SPEC]
hexa-cosmos observatory         # cosmic-observatory spec                              [SPEC]
hexa-cosmos status              # 0/3-wired pillar table + verdict + caveats
hexa-cosmos selftest            # full 3-pillar markdown presence sweep
hexa-cosmos --version           # show version
hexa-cosmos --help              # full usage

Cross-link

Sister substrates (each independent, MIT/Apache-2.0 standalone):

• dancinlab/hexa-space — observation-side ops (aerospace + astronomy + astrobiology). hexa-cosmos provides the theoretical Cosmos substrate; hexa-space provides the observational ops that ground it.
• dancinlab/hexa-millennium — math substrate cousin. n=6 invariant lattice provenance lives here.
• dancinlab/hexa-bio — sister extraction template (4-verb molecular toolkit, same n=6 lattice).

Provenance

Extracted 2026-05-06 from canon@c0f1f570:

• cosmology/ ← domains/physics/cosmology/
• particle/ ← domains/physics/cosmology-particle/
• observatory/ ← domains/physics/cosmic-observatory/

The originating spec lives at canon@c0f1f570 (read-only); this repo is a thin standalone wrapper that exposes the 3 pillars + a placeholder .hexa CLI router + the ΛCDM-vs-n=6 candidate comparison table.

Verify

hexa-cosmos ships a 4-script SPEC_FIRST verify suite (Wave N, 2026-05-13). All scripts live under verify/ and aggregate via run_all.hexa:

# Run the full sweep (4/4 scripts, exit 0 = all PASS)
hexa run verify/run_all.hexa

# Or run individual checks
hexa run verify/spec_presence.hexa        # 9 spec docs on disk (3 pillars + 6 nav)
hexa run verify/lattice_arithmetic.hexa   # n=6 self-consistency (aux only)
hexa run verify/real_limits_anchor.hexa   # LIMIT_BREAKTHROUGH.md anchors (Planck/DESI/SH0ES)
hexa run verify/closure_consistency.hexa  # scoreboard cross-check (CLI · toml · README · AGENTS)

Closure shape (SPEC_FIRST):

Component	Count	Status
CLI pillars	3	cosmology · particle · observatory
Nav specs	6	holography · calabi-yau-nav · m-theory-11d · meta-closure-nav · multiverse-nav · simulation-theory
Spec docs total	9	9/9 markdown files present
Verify scripts	4	4/4 PASS
Verdict	—	SPEC_FIRST (no measurement claim)

SPEC_FIRST verdict — honest red preserved: cosmology specs are NOT measurements made by this repo. H₀ tension (SH0ES vs Planck), σ₈ tension, and dark matter/energy fractions use observational Λ-CDM values from Planck 2018 / DESI 2024 / SH0ES / JWST / Vera Rubin / Euclid / SPT / Roman — NOT lattice-derived. The n=6 ΛCDM 6-parameter mapping is a candidate closed-form comparison, not a measurement. Hubble tension and σ₈ tension remain UNRESOLVED open observational problems.

Per LATTICE_POLICY.md §1.2: cosmological observables are anchored against Planck/DESI/SH0ES/COBE-FIRAS published values + NIST CODATA 2022 constants, never against the n=6 lattice. See LIMIT_BREAKTHROUGH.md for the per-limit HARD_WALL / SOFT_WALL / BREAKABLE assessment (L1–L12).

Repo layout

hexa-cosmos/
├── README.md
├── LICENSE                       MIT
├── hexa.toml                     package manifest
├── install.hexa                  bootstrap
├── cli/                          .hexa CLI router (placeholder)
├── cosmology/                    pillar 1 spec — ΛCDM 6-param candidate
├── particle/                     pillar 2 spec — BBN/CMB cosmology
├── observatory/                  pillar 3 spec — telescope ops
├── holography/                   nav spec
├── calabi-yau-nav/               nav spec
├── m-theory-11d/                 nav spec
├── meta-closure-nav/             nav spec
├── multiverse-nav/               nav spec
├── simulation-theory/            nav spec
├── origins/                      cosmic origins notes
├── breakthroughs/                LIMIT_BREAKTHROUGH evidence
├── verify/                       4-script SPEC_FIRST verify suite
├── tests/                        test scaffolding
├── docs/
│   ├── logo.svg                  hexagon + cosmos glyph
│   └── lambda_cdm_vs_n6.md       ΛCDM vs n=6 candidate comparison table
├── LATTICE_POLICY.md             n=6 lattice policy
├── LIMIT_BREAKTHROUGH.md         L1–L12 wall assessment
├── CHANGELOG.md
├── CITATION.cff
├── AGENTS.tape                   agent identity (.tape v1.2)
└── state/                        runtime markers (gitignored)

License

MIT — Copyright (c) 2026 박민우 nerve011235@gmail.com. Use freely.