🌌 hexa-cosmos — Cosmos substrate (HEXA family)

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.

Status (2026-05-06): 이론 + 후보 spec. 작동 .hexa CLI TBD. ΛCDM (LambdaCDM) baseline에 대한 n=6 closed-form 비교 후보 (candidate, not measurement).

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

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§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.

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§Verbs — 3-pillar architecture

pillar	source (n6-architecture@c0f1f570)	status
cosmology	domains/physics/cosmology/	SPEC v1.0.0
particle	domains/physics/cosmology-particle/	SPEC v1.0.0
observatory	domains/physics/cosmic-observatory/	SPEC v1.0.0

3-pillar status table

  pillar        status              n=6 ΛCDM mapping         empirical sandbox
  ------------- ------------------- ------------------------ --------------------------
  cosmology     SPEC v1.0.0         candidate closed-form    deferred (post-v1.0)
  particle      SPEC v1.0.0         candidate closed-form    deferred (post-v1.0)
  observatory   SPEC v1.0.0         candidate closed-form    deferred (post-v1.0)

n=6 invariant lattice

symbol	value	derivation
n	6	DOF; SE(3) = R³ × SO(3)
σ(6)	12	divisor sum (OEIS A000203)
τ(6)	4	divisor count (OEIS A000005)
φ(6)	2	minimum prime factor
J₂	24	2σ; quadratic-form minimal-vector count

Master identity: σ·φ_E = n·τ = 24 (n=6 uniqueness lemma).

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§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.

Honest C3 caveats (raw#10)

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.

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§Install

Via git clone (works today)

git clone https://github.com/need-singularity/hexa-cosmos.git ~/.hexa-cosmos
export HEXA_COSMOS_ROOT=~/.hexa-cosmos
export PATH="$HEXA_COSMOS_ROOT/cli:$PATH"

# Run any subcommand:
hexa run $HEXA_COSMOS_ROOT/cli/hexa-cosmos.hexa selftest

Via hx (registry registration TBD)

hx install hexa-cosmos          # global, pulls latest from registry
hx install hexa-cosmos@1.0.0    # pin specific version
hexa-cosmos --version           # → 1.0.0

Quickstart

hexa-cosmos selftest         # 3-pillar markdown presence sweep
hexa-cosmos status           # pillar status table + n=6 ΛCDM caveats
hexa-cosmos cosmology        # SPEC — print spec path
hexa-cosmos particle         # SPEC — print spec path
hexa-cosmos observatory      # SPEC — print spec path

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§Cross-link

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

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

Provenance

Extracted 2026-05-06 from n6-architecture@c0f1f570:

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

The originating spec lives at n6-architecture@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.

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§License

MIT — see LICENSE.

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