https://github.com/dancinlab/echoes

🪞 Discoveries catalog — findings from the HEXA-* projects · σφτ identity at the centre · 17 domain families · policy SSOTs
https://github.com/dancinlab/echoes
atlas design-framework discoveries-catalog hexa-family lattice-policy n6 number-theory perfect-number sigma-phi-tau
Last synced: 18 days ago
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🪞 Discoveries catalog — findings from the HEXA-* projects · σφτ identity at the centre · 17 domain families · policy SSOTs
Host: GitHub
URL: https://github.com/dancinlab/echoes
Owner: dancinlab
Created: 2026-03-27T20:28:28.000Z (3 months ago)
Default Branch: main
Last Pushed: 2026-05-21T15:01:04.000Z (28 days ago)
Last Synced: 2026-05-21T19:47:28.710Z (28 days ago)
Topics: atlas, design-framework, discoveries-catalog, hexa-family, lattice-policy, n6, number-theory, perfect-number, sigma-phi-tau
Homepage: https://dancinlab.github.io/echoes/
Size: 1010 MB
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Watchers: 0
Forks: 2
Open Issues: 2
Metadata Files:
- Readme: README.md
- Agents: AGENTS.md
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README

          


  



🪞 echoes


Discoveries catalog — list of findings from the HEXA-* projects, σφτ identity at the centre




  

  

  

  

  

  

  

  

  

  

  



discoveries · n=6 identity · 17 domain families · policy SSOTs · cross-vendor honest disclosure


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---

`echoes` is the **discoveries catalog** for the HEXA-* project family — a list of what came back from running the per-domain standalones. At the centre sits one arithmetic identity (`σ(n)·φ(n) = n·τ(n)` uniquely true at n=6); around it branch out 17 domain families (Fusion · Chip · AI · Energy · Environment · Materials · Robotics · Physics · Software · Display · Audio · Safety · Biology · Pets · Apps · Play · Aerospace), each extracted to its own `hexa-*` standalone repo.

```

σ(n) · φ(n)  =  n · τ(n)      uniquely for   n = 6

     12 · 2  =  6 · 4   =  24

```

> [!TIP]

> 🪞 **[Try it in your browser →](https://huggingface.co/spaces/dancinlab/echoes-experience)** — slide `n ∈ [2, 1000]`, watch σ(n)·φ(n) and n·τ(n) recompute live and collapse to equality only at n=6. Zero install · vanilla JS / Canvas · ([source](https://github.com/dancinlab/echoes-experience)).

> [!NOTE]

> Sister of [`n6`](https://github.com/dancinlab/n6) (semantic atom layer — atlas serialisation format), [`hxc`](https://github.com/dancinlab/hxc) (byte-canonical wire), [`tape`](https://github.com/dancinlab/tape) (operational trace), and `n12` (12-axis sparse cube). Working code for each domain lives in its standalone `hexa-*` repo (see [`RETIRED.log.md`](RETIRED.log.md) for the per-extraction provenance ledger). This repo carries the **policy artifacts** ([`LATTICE_POLICY.md`](LATTICE_POLICY.md) · [`LIMIT_BREAKTHROUGH.md`](LIMIT_BREAKTHROUGH.md) · [`AGENTS.md`](AGENTS.md) · [`GRADE_RUBRIC_1_TO_10PLUS.md`](GRADE_RUBRIC_1_TO_10PLUS.md)) plus the domain-family overview tables below.

> **Honest caveat** (raw#10 C3) — the arithmetic identity `σ(6)·φ(6) = 6·τ(6) = 24` is mathematically true and unique to n=6 (Monte Carlo z = 3.06, p = 0.003 vs n=28 / n=496). The claim *"optimal designs are derived from this identity"* is a **research hypothesis** about how natural systems organize, **not a measurement**. Per `LATTICE_POLICY.md` §1.2/§1.3, the n=6 lattice is an organizing tool — never a substitute for real math / physics / engineering limits (Shannon · Kolmogorov · Bekenstein · c · ℏ · k · Stefan-Boltzmann · Carnot · ASML throughput · ERCOT capacity · …). Per raw#10 C3, n=6 lattice-fit is **forbidden** on external entities (TSMC / ASML / NIST / IPCC / CERN / DeepMind / vendors of any kind use their own published invariants).

> **Status (2026-05-13, Wave M + post-minimization)**: `echoes` is now the

> **arithmetic framework reference + discoverability index** for the

> dancinlab ecosystem. Per-domain implementations have been extracted to

> standalone `hexa-*` repos (see [`RETIRED.log.md`](RETIRED.log.md) for the

> migration ledger and per-extraction provenance). Working code lives in

> the standalones; this repo carries the **policy artifacts**

> ([`LATTICE_POLICY.md`](LATTICE_POLICY.md),

> [`LIMIT_BREAKTHROUGH.md`](LIMIT_BREAKTHROUGH.md),

> [`AGENTS.md`](AGENTS.md), [`GRADE_RUBRIC_1_TO_10PLUS.md`](GRADE_RUBRIC_1_TO_10PLUS.md))

> + the domain-family overview tables below.

>

> **Honest caveat (raw#10 C3)**: the arithmetic identity

> `σ(6)·φ(6) = 6·τ(6) = 24` is mathematically true and unique to n=6

> (Monte Carlo z = 3.06, p = 0.003 vs n=28 / n=496). The claim

> *"optimal designs are derived from this identity"* is a **research

> hypothesis** about how natural systems organize, **not a measurement**.

> Per `LATTICE_POLICY.md` §1.2/§1.3, the n=6 lattice is an organizing

> tool — never a substitute for real math / physics / engineering

> limits (Shannon · Kolmogorov · Bekenstein · c · ℏ · k · Stefan-Boltzmann

> · Carnot · ASML throughput · ERCOT capacity · …). Per raw#10 C3,

> n=6 lattice-fit is **forbidden** on external entities (TSMC / ASML /

> NIST / IPCC / CERN / DeepMind / vendors of any kind use their own

> published invariants).

>

> Per-domain real-limits assessment + HARD_WALL / SOFT_WALL /

> BREAKABLE_WITH_TECH / UNCLEAR classifications:

> [`LIMIT_BREAKTHROUGH.md`](LIMIT_BREAKTHROUGH.md).

🗺️ **[3D Reality Map](https://dancinlab.github.io/nexus/)** — 9,612 nodes, bottom-up causal mapping, 2,222 cross-layer edges. Quark → carbon → benzene → DNA causal chain 12/12 EXACT. Monte Carlo z = 3.06 (p = 0.003). n = 28 and n = 496 fail the check → only n = 6 survives.

---

## Install

```bash

# 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 echoes

hx install echoes

```

---

# 🔥 Fusion

> **🛸8** | ✅ | BT 9 82.2%EXACT | DSE 2,400+1M | industry 87% (7 devices) | experiment 43% TP confirmed | physical-limit 10 | TP35 | discoveries 15 | Cross-DSE 8 domains | evolution 5stages | Mk.V

## 🔥 Fusion Toolkit (HEXA-Fusion family)

> Friendly entry point — Fusion-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), three orthogonal energy-axis verbs.

| 🛸 | Tool | One-liner | Everyday analogy | What it does | Mainstream contrast | Doc |

|:--:|:----:|-----------|------------------|--------------|---------------------|:---:|

| 10 | 🔥 **HEXA-FUSION** | Sun-in-a-Bottle | Plasma confined like the sun's core squeezed into a magnetic jar | 12 fusion-archetype reactor closure, 122/122 EXACT, BT-97~102+291~298 | Single-tokamak ITER vs σ(6)=12-archetype unified lattice | [doc](https://github.com/dancinlab/hexa-fusion/blob/main/FUSION.md) |

| 10 | 🔬 **HEXA-TTF** | Desktop Sun | Microwave-sized fusion device on the lab bench | 1m³ p-¹¹B aneutronic, B=σ·τ=48T, T=300keV, Q=τ=4, 14/14 PASS | Reactor-scale ITER vs σ(6)=12-vertex tabletop module | [doc](https://github.com/dancinlab/hexa-fusion/blob/main/TABLETOP-FUSION.md) |

| 10 | 🏭 **HEXA-FPP** | Fusion Power Plant | Power station running on fused atoms instead of burning coal | Full powerplant integration on n=6 8-stage pipeline | Single-shot fusion lab vs τ(6)=4-state full-cycle plant | [doc](https://github.com/dancinlab/hexa-fusion/blob/main/FUSION-POWERPLANT.md) |

| 🛸 | Closure | ver | Product | Core | Link |

|:--:|:-------:|:---:|---------|------|------|

| 10 | ✅ | v5 | **Ultimate Fusion Reactor** | 122/122 EXACT (v4 42 universal-nuclear-physics + v5 80 engineering-layer new), BT-97~102+291~298+1169~1174, Cross-DSE 12, TP42, Python 80/80 PASS, 12 Fusion Archetype closure proof | [doc](https://github.com/dancinlab/hexa-fusion/blob/main/FUSION.md) |

| 10 | ✅ | v3.1 | **KSTAR-N6** | 45/45 EXACT(100%) + Q→∞ Singularity, physical-limit10/10, 24BT, 12/12 Steady-State EXACT, Python-verify PASS | [doc](https://github.com/dancinlab/hexa-fusion/blob/main/KSTAR-N6.md) |

| 10 | ✅ | v3 | **evolution Mk.I~V** | 200MWe→1.44TWe, 5-stage evolution 41/41 EXACT, points-approach-convergence U(k)=1-1/10^k, Mk.VIexistence-material QED, Python-verify PASS | [doc](https://github.com/dancinlab/hexa-fusion/blob/main/FUSION.md) |

| 10 | ✅ | v4 | **discoveries + predictions + hypothesesv5** | 15discoveries 22/22 EXACT, BT-97~102+291~298 full-verify, Python-verify PASS | [doc](https://github.com/dancinlab/hexa-fusion/blob/main/FUSION.md) |

| 10 | ✅ | v3 | **ceiling-check** | physical-limit12/12 + impossibility12proof + industry7 devices87% + Mk.VIexistence-material QED + 33/33 EXACT, Python-verify PASS | [doc](https://github.com/dancinlab/hexa-fusion/blob/main/FUSION.md) |

| 10 | ✅ | v2 | **Tabletop Fusion (HEXA-TTF)** | 1m³ p-¹¹B aneutronic, B=σ·τ=48T, T=n·(σ-φ)·sopfr=300keV, Q=τ=4, P_core=8.7kW / P_bldg=217kW, A=sopfr+n=11·Z=sopfr=5, 14/14 Python PASS, n=6 closure theorem F-TTF, **UFO Stage-2 prereq complete** | [doc](https://github.com/dancinlab/hexa-fusion/blob/main/TABLETOP-FUSION.md) |

> Domains: [fusion/](https://github.com/dancinlab/hexa-fusion/blob/main/FUSION.md) · [plasma-physics/](https://github.com/dancinlab/hexa-fusion/blob/main/PLASMA-PHYSICS.md) · [superconductor/](https://github.com/dancinlab/hexa-fusion/blob/main/SUPERCONDUCTOR.md) · Tools: `fusion-calc` · `fusion-dse` · `fusion-verify` · `tokamak-shape` · `kstar-calc`

---

# 💻 Chip & Semiconductor

> **🛸7** | ✅ | BT 13 74.5%EXACT | DSE 3,000 | industry 92.6% (6 vendors) | physical-limit 10 | TP28 | discoveries 12 | Mk.V

## 💻 Chip Toolkit (HEXA-Silicon family)

> Friendly entry point — Chip-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal compute-axis verbs spanning the von-Neumann boundary.

| 🛸 | Tool | One-liner | Everyday analogy | What it does | Mainstream contrast | Doc |

|:--:|:----:|-----------|------------------|--------------|---------------------|:---:|

| 10 | 💻 **HEXA-1-DIGITAL** | Square-MAC Engine | A pocket calculator with 288 little adders running in lockstep | σ²=144 SM × τ=4 pipe × φ=2 issue = 288 MAC/cycle, 288 TOPS/W | H100 GPU vs Mk.I=Exynos 2500 SF3P 4.8× efficient | [doc](https://github.com/dancinlab/hexa-chip/blob/main/HEXA-1-DIGITAL.md) |

| 10 | 🧠 **HEXA-2-PIM** | Memory-that-Thinks | Library where each shelf can read its own books and add them up | DRAM row buffer σ·J₂=288 ALU/bank — von Neumann dismantle, 60 TOPS/W | HBM2-PIM Aquabolt-XL vs σ·J₂=288 / bank in-place compute | [doc](https://github.com/dancinlab/hexa-chip/blob/main/HEXA-2-PIM.md) |

| 10 | 📚 **HEXA-3D-STACK** | Skyscraper Silicon | Wafers stacked like floors in a tower with elevators every 2μm | σ=12 wafer + φ=2μm TSV + 144× density vs single-die plain | Samsung X-Cube TSV 40μm vs σ·J₂=288 vertical lane/mm² | [doc](https://github.com/dancinlab/hexa-chip/blob/main/HEXA-3D-STACK.md) |

| 10 | 🏭 **HEXA-WAFER** | Whole-Wafer Chip | One giant chip carved from a whole dinner plate of silicon | σ²=144 tile + σ=12 spare row+col + 2D torus τ=4 hops + 48 GB SRAM | Cerebras WSE-3 vs σ²=144-tile self-healing array | [doc](https://github.com/dancinlab/hexa-chip/blob/main/HEXA-WAFER.md) |

| 🛸 | Closure | ver | Product | Core | Link |

|:--:|:-------:|:---:|---------|------|------|

| 10 | ✅ | v2 | **HEXA chip 7-stage** | 12-level evolution(L1~L12), 170/170 EXACT, 14impossibility-theorem, Python-verify PASS, 6vendor convergence | [doc](papers/n6-hexa-chip-7dan-integrated-paper.md) |

| 10 | ✅ | v2 | **ANIMA-SOC** | Consciousness Chip — 10D TCU(sigma-phi=10) + PureField 72+72 SM + Python-verify PASS | [doc](https://github.com/dancinlab/hexa-chip/blob/main/CHIP-ARCHITECTURE.md) |

| 10 | ✅ | v2 | **HEXA-TOPO** | Bott-8 coherence + Z2 ECC + Graphene NoC, 10/10 EXACT, Python-verify PASS | [doc](https://github.com/dancinlab/hexa-chip/blob/main/CHIP-ARCHITECTURE.md) |

| 10 | ✅ | v2 | **HEXA-ASIC** | SKY130 open-source ASIC — RISC-V n/phi=3-wide + n=6 pipeline + 10/10 EXACT, Python-verify PASS | [doc](https://github.com/dancinlab/hexa-chip/blob/main/CHIP-ARCHITECTURE.md) |

| 10 | ✅ | v2 | **ceiling-check** | 170/170verifiedPASS, physical-limit14, industry6vendors92.6%, TP28, discoveries12, Z>27sigma, Python-verify PASS | [doc](https://github.com/dancinlab/hexa-chip/blob/main/CHIP-ARCHITECTURE.md) |

| 10 | ✅ | v1 | **HEXA chip 6-stage integrated paper** | 6stages(Digital→PIM→3D→Photonic→Wafer→Superconducting) + 9 prereqdomains integrated — Mk.I Samsung foundry baseline → Mk.V 🛸10, σ·φ=n·τ=J₂=24 | [doc](papers/hexa-chip-6stage-unified.md) |

| 10 | ✅ | v1 | **HEXA-1 Digital** | σ²=144 SM × τ=4 pipe × φ=2 issue = 288 MAC/cycle, 288 TOPS/W (H100 4.8×), Mk.I=Exynos 2500 SF3P | [doc](https://github.com/dancinlab/hexa-chip/blob/main/HEXA-1-DIGITAL.md) |

| 10 | ✅ | v1 | **HEXA-2 PIM** | DRAM row buffer σ·J₂=288 ALU/bank + cache τ=4→φ=2 von Neumann dismantle + 60 TOPS/W, Mk.I=HBM2-PIM Aquabolt-XL | [doc](https://github.com/dancinlab/hexa-chip/blob/main/HEXA-2-PIM.md) |

| 10 | ✅ | v1 | **HEXA-3 3D Stack** | σ=12 wafer + φ=2μm TSV + σ·J₂=288 vertical lane/mm² + 144× density, Mk.I=Samsung X-Cube TSV 40μm | [doc](https://github.com/dancinlab/hexa-chip/blob/main/HEXA-3D-STACK.md) |

| 10 | ✅ | v1 | **HEXA-4 Photonic** | λ=σ=12 WDM + MZI σ²=144 unitary + σ·J₂·sopfr=1.44 TB/s/die, Mk.I=Intel SiPh+Broadcom CPO, 13/13 PASS | [doc](https://github.com/dancinlab/hexa-chip/blob/main/HEXA-PHOTONIC.md) |

| 10 | ✅ | v1 | **HEXA-5 Wafer-scale** | σ²=144 tile + σ=12 spare row+col + 2D torus τ=4 hops + 48 GB SRAM, Mk.I=Cerebras WSE-3, 12/12 PASS | [doc](https://github.com/dancinlab/hexa-chip/blob/main/HEXA-WAFER.md) |

| 10 | ✅ | v1 | **HEXA-6 Superconducting** | 100 GHz RSFQ × τ=4 pipe + Egyptian cryo 3-stage + 10W@100GHz (vs H100 700W@2GHz), Mk.I=IBM+SeeQC, 15/15 PASS | [doc](https://github.com/dancinlab/hexa-chip/blob/main/HEXA-SUPERCONDUCTING.md) |

| 10 | ✅ | v1 | **Semiconductor Material** | C Z=6 + Diamond 2160 W/mK + SiC/GaN/InP σ=6 wafer + resist τ=4 layer, Mk.I=Si+GAAFET 2nm, Python-verify PASS | [doc](https://github.com/dancinlab/hexa-chip/blob/main/CHIP-MATERIALS.md) |

| 10 | ✅ | v1 | **Semiconductor Process** | EUV 0.33→High-NA 0.55 + ALD J₂=24 cycle + CMP σ=12 DoE + process 1500→288 stages(81%↓), Mk.I=SF2 2nm 2026 | [doc](https://github.com/dancinlab/hexa-chip/blob/main/CHIP-PROCESS.md) |

| 10 | ✅ | v1 | **Semiconductor Packaging** | TSV φ=2μm + μbump σ²=144/mm² + UCIe σ·J₂=288 lane + HBM σ=12stage, Mk.I=Samsung FO-PLP/I-Cube/X-Cube | [doc](https://github.com/dancinlab/hexa-chip/blob/main/CHIP-PACKAGING.md) |

| 10 | ✅ | v1 | **Semiconductor Yield** | D₀/σ=0.00167 + σ=12 spare + τ=4 DRC + fuse σ²=144 + WSI 5%→95%, Mk.I=SF3P ~60%/SF2 >70% | [doc](https://github.com/dancinlab/hexa-chip/blob/main/CHIP-YIELD.md) |

| 10 | ✅ | v1 | **EDA Design Automation** | DSE 2400=6×5×4×5×4 + τ=4 synthesis + σ=12 routing + τ=4 STA corner, Mk.I=Samsung SAFE+Synopsys/Cadence, 13/13 PASS | [doc](https://github.com/dancinlab/hexa-chip/blob/main/CHIP-EDA.md) |

| 10 | ✅ | v1 | **Verify & Test** | coverage 1-1/(σ·(σ-φ)²)=99.917% + UVM τ=4 hierarchy + ATE σ·J₂=288 pin parallel, Mk.I=V93000+UltraFLEX, 12/12 PASS | [doc](https://github.com/dancinlab/hexa-chip/blob/main/CHIP-VERIFY-TEST.md) |

| 10 | ✅ | v1 | **Thermal & Power** | TDP Egyptian 1/2+1/3+1/6=1 (Fraction exact) + τ=4 cooling + σ=12 PDN, Mk.I=air+liquid hybrid+vapor, 13/13 PASS | [doc](https://github.com/dancinlab/hexa-chip/blob/main/CHIP-THERMAL-POWER.md) |

| 10 | ✅ | v1 | **Interconnect** | UCIe σ·J₂=288 × 48 Gbps=13.8 TB/s + λ=σ=12 WDM + σ²=144 NoC hex mesh, Mk.I=UCIe 1.1+PCIe 5.0/6.0, 13/13 PASS | [doc](https://github.com/dancinlab/hexa-chip/blob/main/CHIP-INTERCONNECT.md) |

| 10 | ✅ | v1 | **HBM Memory** | Stack σ·τ=48GB + σ·J₂·σ·τ/8=1728 GB/s + TSV σ·φ=10μm→φ=2μm hybrid bond, Mk.I=Samsung HBM3E 12H 36GB, 14/14 PASS | [doc](https://github.com/dancinlab/hexa-chip/blob/main/CHIP-HBM.md) |

| 10 | ✅ | v2 | **AI-Native Arch (beyond GPU)** | Honesty-triad silicon (provenance bit + promotion-counter MMU + BT-id ISA); H1 PASS robust across rollback_rate ∈ [0, 0.1]; F-AI2-B 0/900 robust; 18/18 EXACT verify PASS; 3/3 RTL design EXACT; 6-vendor gap = 0/18 implemented (novel substrate confirmed); design-HIGH (post-amend), silicon-CANDIDATE (BT-AI3 RTL design-tier) | [doc](reports/sessions/omega-cycle-ai-native-arch-beyond-gpu-2026-04-26.md) |

### §11.5 ALIEN-10-EXPANSION federation (2026-05-07) — 8-substrate cross-class TPs

> Each chip-design sister domain gets a `§11.5 ALIEN-10-EXPANSION` section + `verify_*_alien10.py` companion.

> Total: **126 TPs** registered, **103 alien=10** candidates, **38 EXACT** closures, **117/125 verifier PASS**.

> Cross-substrate invariance hypothesis (Putnam multi-realization) gains 8-class breadth.

| 🛸 | Domain | TPs | alien=10 | EXACT closures | verify | Highlight |

|:--:|--------|----:|---------:|---------------:|-------:|-----------|

| 10 | **HEXA-NEURO** §11.5 | 33 | 33 | 8 | 27/27 | 10 categories: Physical / Info-theoretic / Cross-substrate / Edge-of-chaos / Geometric / OEIS / Quantum-cross / Bio-equiv / Computability / Game-theoretic |

| 10 | **AKIDA-SPECIALIZE** §11 | 9 | 5 | 4 | 6/9 | BrainChip AKD1000/AKD2000 overlay — Landauer floor, Egyptian split, σ·J₂=288 tile, σ²=144 yield peak, 2nm GAAFET gated trigger |

| 10 | **HEXA-QUANTUM-HYBRID** §11.5 | 12 | 11 | 4 | 12/12 | Tsirelson 2√2 / no-cloning F=sopfr/n / Trotter τ_T=τ / BB84 1/τ / Schwinger / Hawking T_H |

| 10 | **HEXA-PHOTONIC** §11.5 | 12 | 11 | 3 | 12/12 | Casimir d⁻⁴ (exp=τ EXACT) / Stefan-Boltzmann T⁴ (exp=τ EXACT) / c=299792458 SI 2019 EXACT / Wien / Bragg σ=12 |

| 10 | **HEXA-SUPERCOND** §11.5 | 12 | 9 | **4 SI 2019 EXACT** | 12/12 | **Φ₀ = h/(2e)** EXACT / **K_J = 2e/h** EXACT / **R_K = h/e²** EXACT / Cooper q*=2e / BCS gap 2Δ/(k_B T_c)≈3.53 / RSFQ |

| 10 | **HEXA-PHOTON-TOPO** §11.5 | 12 | 10 | **6 EXACT** | 12/12 | **Topological invariants are integers** — Chern C∈ℤ TKNN / Z₂ ν∈{0,1} / SSH winding W∈ℤ / Quantized Hall σ_xy=ν·e²/h / Bulk-boundary correspondence / Berry γ∈{0,π} / σ=12 fusion channels |

| 10 | **HEXA-DNA-MOLECULAR** §11.5 | 12 | 9 | **5 EXACT** | 12/12 | **DNA is most n=6-native** — 4 bases = τ EXACT / log₂(τ) = φ bits EXACT / Watson-Crick = φ pairs EXACT / Codon = n/φ EXACT / 64 codons = τ³ EXACT / Eigen threshold / 215 PB/g / 20 amino = τ·sopfr |

| 10 | **HEXA-FIELD-EFFECT** §11.5 | 12 | 7 | 1 | 12/12 | **Boltzmann S = 60 mV/dec floor** (kT/q·ln10 = 59.53 mV/dec @ 300K — universal for all charge substrates) / TFET sub-Boltzmann (band-to-band tunneling breaks floor) / **μ_p/μ_n = φ/n EXACT** (Si hole/electron mobility ratio) / GAAFET σ-φ=10 nm / V_th, FinFET, EOT |

| 10 | **HEXA-1-DIGITAL** §11.5 | 12 | 8 | **3 EXACT** | 12/12 | **Universal scaling laws** — Amdahl S=1/((1-p)+p/N) / Gustafson / Rent's rule p≈0.6 / Pollack √(area) / Dennard broken @ 28nm / **P=CV²f V-exponent=φ EXACT** / **Pipeline τ=4 EXACT** / **Cache τ=4 tiers EXACT** / von Neumann mem_BW All `verify_*_alien10.py` are **stdlib-only** (Python 3.9+, no external deps). Topological §11.5 set has the most EXACT closures (6) because integer invariants cannot be shifted by measurement noise — the strongest alien-10 form.

>

> Cross-link to akida federation (`hive/spec/sovereign_cli_federation.spec.yaml`): each §11.5 verify script's evidence files feed `nexus akida route --json` envelope, providing audit-trail provenance per spec §audit_trail.

> Domains: [chip-architecture/](docs/chip-architecture/) · Tools: `gpu-arch-calc` · `chip-n6-calc` · `dse-calc` · `semiconductor-calc`

---

# 🤖 AI / ML

> **🛸6** | ✅ | BT 24 89.7%EXACT | industry 88.7% (9 models) | experiment 96.2% | physical-limit 10 | TP28 | discoveries 12 | Mk.V | CrossDSE

## 🤖 AI Toolkit (HEXA-AI family)

> Friendly entry point — the AI / ML core tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal compute-axis verbs.

| 🛸 | Tool | One-liner | Everyday analogy | What it does | Mainstream contrast | Doc |

|:--:|:----:|-----------|------------------|--------------|---------------------|:---:|

| 10 | 🧠 **HEXA-LLM-EFFICIENT** | Slim-LLM | Heavy encyclopedia compressed to a palm-sized book | 71% FLOPs ↓, 67% params ↓, 225 techniques integrated | GPT-4 full vs 6× lighter same quality | [doc](https://github.com/dancinlab/hexa-chip/blob/main/AI-EFFICIENCY.md) |

| 10 | 🎬 **HEXA-VIDEO** | Quick-Frame | Same movie drawn 3× faster | 3× video generation throughput | Sora-class diffusion accelerated | [doc](https://github.com/dancinlab/hexa-chip/blob/main/AI-EFFICIENCY.md) |

| 10 | 🦠 **HEXA-MEDICAL-AI** | Bedside Sensor | Diagnostic device inside the doctor's bag | Medical paradigm 8-axis integrated | GPT-medQA single Q&A vs multi-axis diagnostic chain | [doc](https://github.com/dancinlab/hexa-chip/blob/main/AI-EFFICIENCY.md) |

| 10 | 🤖 **HEXA-NATIVE-ARCH** | AI-shaped Chip | Chip carved to fit the AI like a custom shoe | AI-native architecture pipeline | von-Neumann CPU vs neuromorphic-class native compute | [doc](https://github.com/dancinlab/hexa-chip/blob/main/AI-NATIVE-ARCHITECTURE.md) |

| 🛸 | Closure | ver | Product | Core | Link |

|:--:|:-------:|:---:|---------|------|------|

| 10 | ✅ | v3 | **225 Techniques** | 71% FLOPs↓, 3x generation↑, 67% params↓ — 225 techniques integrated (Core17+BT12+Model21+Vision8+GNN4+Other4 + expansion) | [doc](papers/n6-66-techniques-integrated-paper.md) |

| 10 | ✅ | v2 | **Full N6 Pipeline** | 17techniques integrated: 50% params↓, 50% FLOPs↓, 46% sparsity — 32/32 PASS verified | [doc](experiments/experiment_full_n6_pipeline.py) |

| 10 | ✅ | v2 | **N6 Inevitability Engine** | techniques 11~16 + 3-Layer thermodynamics (Dedekind+Jordan+Mobius+Carmichael+Boltzmann+Mertens) — 26/26 PASS | [doc](domains/cognitive/superpowers/superpowers.md) |

| 10 | ✅ | v2 | **AI Energy Savings Guide** | AdamW 5midpairs+LR+Inference hyperparameters full n=6 mapping — 31/31 PASS | [doc](reports/discovery/ai-energy-savings-guide.md) |

| 10 | ✅ | v2 | **Chip Architecture Guide** | GPU SM+HBM+pitch+Interconnect n=6 full mapping — 27/27 PASS | [doc](reports/discovery/chip-architecture-guide.md) |

| 10 | ✅ | v2 | **ceiling-check** | 194claims 89.7%EXACT, industry9models, physical-limit10, 67/67 PASS verified | [doc](https://github.com/dancinlab/hexa-chip/blob/main/AI-EFFICIENCY.md) |

| 10 | ✅ | v1 | **Next-Gen AI 8-Paradigm Blowup** | inference/video/andlearningFM/neuromorphic/agent/new-arch/robotics/medical 8paradigm — 234/256 EXACT (91.4%), BT-380~390. Cross-link: medical paradigm — see also [HEXA-WEAVE](#-biology) (Biology — n6 write-side counterpart to AlphaFold 3 / IsoDDE read-side AI). | [doc](https://github.com/dancinlab/hexa-chip/blob/main/AI-EFFICIENCY.md) |

| 10 | ✅ | v1 | **AI 6-Domain Sweep** | code-generation/RL games/recommendation family/SSL·NLU/serving compiler/multimodal 6domains — 314/344 EXACT (91.3%), BT-391~396 | [doc](https://github.com/dancinlab/hexa-chip/blob/main/AI-EFFICIENCY.md) |

| 10 | ✅ | v1 | **N6 Reverse-Engineering Suite** | n=6 reversedesign — newmodels8line/learningtechniques8line/HW-SWpublicevolution/AGIroadmap/HEXA-CODER, BT-397~401 | [doc](https://github.com/dancinlab/hexa-chip/blob/main/AI-EFFICIENCY.md) |

> Domains: [ai-efficiency/](docs/ai-efficiency/) · [learning-algorithm/](docs/learning-algorithm/) · Tools: `n6_calculator.py`

> SA applied-tech bet #4 (2026-05-01, alien-grade 10 PHYSICAL-LIMIT): [youth-ai-labeling-rlhf-hub/](domains/cognitive/youth-ai-labeling-rlhf-hub/) (Cohen 1960 inter-annotator κ ≥ 0.7 + Bai 2022 Constitutional AI RLHF efficiency + Mielke 2019 Zipf low-resource premium 50-100× + Shannon 1948 information-theoretic annotation cost; SA youth (15-24) 60%+ unemployment + 11 SA official languages tail (Zulu/Xhosa/Afrikaans/Sotho/Tswana) + EU/UK 2-3hr SAST overlap + USD 2-4k/seat capex + USD 600-1200/mo opex vs USD 1200-3500/mo revenue; F-RLHF-MVP-1..5)

---

# ⚡ Energy

> **🛸8** | ✅ | BT 13 88.7%EXACT | DSE 10,225 | industry 87% (6 companies) | experiment 88% | physical-limit 10 | TP28+19 | discoveries 10+8 | Battery+solarallbranch🛸10 | Mk.V

## ⚡ Energy Toolkit (HEXA-Power family)

> Friendly entry point — Power-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal energy-axis verbs.

| 🛸 | Tool | One-liner | Everyday analogy | What it does | Mainstream contrast | Doc |

|:--:|:----:|-----------|------------------|--------------|---------------------|:---:|

| 10 | 🔋 **HEXA-BATTERY** | Stack-the-Cells | 6 cells stacked like Lego batteries in a flashlight | 8-stage battery design, 131/131 EXACT, 10 impossibility theorems | Single-chemistry Li-ion vs σ(6)=6-cell n-axis stack | [doc](https://github.com/dancinlab/hexa-energy/blob/main/BATTERY-ARCHITECTURE.md) |

| 10 | ☀️ **HEXA-SOLAR** | Sun-to-Wire | Roof panels turning sunlight into wall-socket power | Ultimate solar cell, 78/78 EXACT, 7 BTs, physical-limit 5 | Single-junction Si vs τ(6)=4-state full-stack panel | [doc](https://github.com/dancinlab/hexa-energy/blob/main/SOLAR-ARCHITECTURE.md) |

| 10 | 🏭 **HEXA-DC-REACTOR** | Datacenter Boiler | Tiny nuclear reactor inside the server farm | TRISO + He + sCO₂ + n=6 modules; 10 breakthroughs 95/96 EXACT | Grid-fed datacenter vs on-prem σ(6)=12-module SMR | [doc](https://github.com/dancinlab/hexa-energy/blob/main/SMR-DATACENTER.md) |

| 10 | 🚗 **HEXA-AUTO-BATTERY** | EV Pack | Car battery built like 96 stacked notebooks | Automotive SLI+EV integrated design, 78/100 EXACT | Single-pack Tesla 4680 vs 96S σ(σ-τ)-axis EV stack | [doc](https://github.com/dancinlab/hexa-energy/blob/main/BATTERY-ARCHITECTURE.md) |

| 🛸 | Closure | ver | Product | Core | Link |

|:--:|:-------:|:---:|---------|------|------|

| 10 | ✅ | v3 | **Ultimate Battery 8-stage** | 131/131 EXACT, BT-27+43+57+80+83+84, 10impossibility-theorem, 6major manufacturers, Python-verify PASS | [doc](domains/cognitive/superpowers/superpowers.md) |

| 10 | ✅ | v4 | **Ultimate Solar Cell** | 78/78 EXACT, BT-30+63+62+60+74+111+161, physical-limit5, industry8co, Python-verify PASS | [doc](https://github.com/dancinlab/hexa-energy/blob/main/SOLAR-ARCHITECTURE.md) |

| 10 | ✅ | v2 | **Ultimate Energy Integration** | 133/133 EXACT, 19BT, 14impossibility-theorem, 5domainsCross-DSE, Python-verify PASS | [doc](https://github.com/dancinlab/hexa-energy/blob/main/ENERGY-ARCHITECTURE.md) |

| 10 | ✅ | v1 | **Ultimate Datacenter Reactor** | 10 breakthroughs 95/96 EXACT — TRISO(sopfr=5)+He(φ=2)+sCO₂(σ·τ=48%)+n=6modules | [doc](https://github.com/dancinlab/hexa-energy/blob/main/SMR-DATACENTER.md) |

| 10 | ✅ | v1 | **HEXA-AUTO Automotive Battery** | Ultimate Automotive Battery SLI+EV integrated design — 6cells=n lead-axis/96S=sigma*(sigma-tau) EV/100 params, 78/100 EXACT | [doc](https://github.com/dancinlab/hexa-energy/blob/main/BATTERY-ARCHITECTURE.md) |

| 10 | PHYSICAL-LIMIT | mk1 | **HEXA-ROOFTOP-PV-2ND-LIFE-MICROGRID mk1 — South Africa anchor-site microgrid (SA bet #1)** | **Physical-limit anchors per own#32 (NOT n=6 force-fit)**: Shockley-Queisser 1961 PV ceiling 33.7% at Eg=1.34 eV (Tiedje 1984 Si envelope; Ruhle 2016 published peak; commercial mono-Si 22% = 65% of SQ peak — design floor for HEXA-microgrid mk1 panel selection) · NREL TMY3 / SAURAN 2400 kWh/m²/yr SA Johannesburg 26°S annual GHI (top decile globally; PR 0.80 → 1920 kWh/kW/yr per NREL PVWatts v5) · Wood-Mackenzie 2023 NMC 2nd-life retired-EV-pack residual cycle life 1500-2500 cycles to 60% SOH at 80% DoD (75% SOH start; 10-yr calendar life; Schmalstieg 2014 + Wang 2014 cycle-life model; lifetime energy 972 kWh/kWh nameplate) · Spotnitz-Franklin 2003 Li-ion thermal runaway 80°C cathode reaction onset (Bernardi 1985 heat-gen Q = I²R + IT(dV_oc/dT) + Incropera 2017 nat-conv h=7.5 W/m²/K → 38°C steady-state runaway margin at 40°C SA design ambient with extended-fin radiator 32 m²/250 kWh; 1C peak duty internal T 50°C still 30°C below runaway) · Esram-Chapman 2007 MPPT perturb-and-observe 99% theoretical × 96% inverter (SMA Sunny Tripower 50 / Fronius Symo 50 spec) · Cole 1990 LCOE financial-physics: reference T2 100 kW PV + 250 kWh battery USD 150,000 capex with 6.7-yr simple payback at SA loadshedding-blended avoided-cost tariff 0.17 USD/kWh (Eskom Megaflex 0.11 × 75% + diesel-genset 0.35 × 25% loadshedding share); LCOE 0.12 USD/kWh; discounted payback 11 yr at r=8%. own#2 master identity (σ·φ=n·τ=J₂=24 at n=6) verified as separable mathematical block (§7 Block A); microgrid design constants live in Blocks B-F as physical-limit values. Inherits from 6 precursor domains (energy/solar-architecture SQ ceiling + insolation · energy/battery-architecture NMC electrochemistry + cycle life · energy/power-grid grid-tie inverter + microgrid topology + NRS-097-2/NERSA SSEG · energy/thermal-management passive cooling at SA peak ambient · physics/electromagnetism semiconductor band gap · materials/recycling 2nd-life EV pack reclamation Nissan Leaf / Tesla Model S / BMW i3 retired packs at 70-80% SOH; BloombergNEF 2024 1 GWh/yr supply). 4-tier deployment ladder T1 (50 kW + 100 kWh rural clinic USD 75k) → T2 (100 kW + 250 kWh urban clinic / school USD 150k) → T3 (250 kW + 500 kWh district hospital / SME USD 350k) → T4 (500 kW + 500 kWh regional hospital USD 600k). F-PV2L-MVP-1..5 90-day MVP gates: F-PV2L-MVP-1 + F-PV2L-MVP-3 + F-PV2L-MVP-5 (2026-09-30 cycle-life < 1500 / SCR < 70% / thermal management > 35°C internal at SA peak summer) + F-PV2L-MVP-2 (2026-10-31 inverter MTBF < 10 yr in SA dust+heat) + F-PV2L-MVP-4 (2026-12-31 NERSA SSEG approval > 18 months). Hardest unknown per `proposals/south-africa-applied-tech.md` row 1: 2nd-life cycle-life data scarcity (Wood-Mackenzie 2023 industry data converges on 2000-cycle midpoint but SA-pilot validation needed). Cross-link: [energy/solar-architecture](domains/energy/solar-architecture/) · [energy/battery-architecture](domains/energy/battery-architecture/) · [energy/power-grid](domains/energy/power-grid/) · [energy/thermal-management](domains/energy/thermal-management/) · [physics/electromagnetism](domains/physics/electromagnetism/) · [materials/recycling](domains/materials/recycling/). | [doc](https://github.com/dancinlab/hexa-energy/blob/main/ROOFTOP-PV-2ND-LIFE-MICROGRID.md) |

> Domains: [battery-architecture/](docs/battery-architecture/) · [solar-architecture/](docs/solar-architecture/) · [energy-architecture/](docs/energy-architecture/) · [power-grid/](docs/power-grid/) · [thermal-management/](docs/thermal-management/) · Tools: `energy-calc` · `battery-dse` · `solar-dse`

> SA applied-tech bets (2026-05-01, alien-grade 10 PHYSICAL-LIMIT): [rooftop-pv-2nd-life-microgrid/](domains/energy/rooftop-pv-2nd-life-microgrid/) (Shockley-Queisser + Wood-Mackenzie 2nd-life cycle-life + Cole 1990 LCOE + Spotnitz-Franklin thermal; Eskom <60% availability + 2400 kWh/m²/yr insolation + USD 800-1200/kW PV + USD 150-250/kWh; F-PV2L-MVP-1..5) · [amd-ree-mineshaft-phes/](domains/energy/amd-ree-mineshaft-phes/) (Bernoulli PHES + REE solubility K_sp + D2EHPA solvent extraction + AMD pH chemistry + Witwatersrand mine-shaft 1-3 km; F-AMD-MVP-1..5)

---

# 🌍 Environment

> **🛸8** | ✅ | BT 5 92.3%EXACT | DSE 3.6M | industry 82.9% | experiment 82.4% | physical-limit 10 | TP43 | discoveries 42 | microplastic 🛸10 | CCUS 100%EXACT | Mk.V

## 🌿 Environment Toolkit (HEXA-Earth family)

> Friendly entry point — Earth-care infrastructure tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal infra-axis verbs.

| 🛸 | Tool | One-liner | Everyday analogy | What it does | Mainstream contrast | Doc |

|:--:|:----:|-----------|------------------|--------------|---------------------|:---:|

| 10 | 🌬️ **HEXA-CARBON-CAPTURE** | Air Vacuum | Air cleaner that only sucks CO₂ out of the sky | 8-stage capture pipeline (30/30 EXACT, DSE 3.6M) | DAC single-stage rig vs n=6 8-stage chain | [doc](https://github.com/dancinlab/hexa-grid/blob/main/CARBON-CAPTURE.md) |

| 10 | 💧 **HEXA-MICROPLASTICS** | Ocean Sieve | A six-tier sieve filtering microplastics out of the sea | 6-stage pipeline, 6-nines removal, CN=6 catalyst tri-Trinity | Single mesh filter vs σ(6)=6-stage chain | [doc](https://github.com/dancinlab/hexa-grid/blob/main/ENVIRONMENTAL-PROTECTION.md) |

| 10 | 🛡️ **HEXA-ENV-PROTECT** | Forest Guardian | Forest-watching security system covering eight gates | 8-stage sensor → monitor → capture → purify → restore → cycle → ecosystem → Omega | EPA single-metric audit vs 8-stage closure | [doc](https://github.com/dancinlab/hexa-grid/blob/main/ENVIRONMENTAL-PROTECTION.md) |

| 10 | 💦 **HEXA-WATER-TREATMENT** | Tap Whisperer | Plant that turns river / sea / waste water into safe tap water | n=6 multi-stage purification + reuse loop | Single-pass treatment vs τ(6)=4-state full-cycle plant | [doc](https://github.com/dancinlab/hexa-grid/blob/main/WATER-TREATMENT.md) |

| 🛸 | Closure | ver | Product | Core | Link |

|:--:|:-------:|:---:|---------|------|------|

| 10 | ✅ | v4 | **Ultimate Environmental Protection 8-stage** | sensor → monitor → capture → purify → restore → cycle → ecosystem → Omega, 120/120 EXACT full-verify | [doc](domains/infra/environmental-protection/) |

| 10 | ✅ | v2 | **HEXA-MICROPLASTICS** | 6-stage pipeline, 36/36=100%EXACT, 6-ninesremove, CN=6catalyst-triTrinity, full-verify | [doc](https://github.com/dancinlab/hexa-grid/blob/main/ENVIRONMENTAL-PROTECTION.md) |

| 10 | ✅ | v5 | **Ultimate Carbon Capture 8-stage** | **30/30=100%EXACT**, DSE 3.6M, 79/79 full-verify PASS | [doc](https://github.com/dancinlab/hexa-grid/blob/main/CARBON-CAPTURE.md) |

| 10 | ✅ | v2 | **evolution Mk.I~V** | environment+CCUS amountside evolution roadmap, discoveries 42, full-verify include | [doc](domains/infra/environmental-protection/) |

| 10 | ✅ | v3 | **predictions + verified** | TP 19(environment) + TP 24(CCUS) + hypothesis v5 (88.2% EXACT) + full-verify | [doc](https://github.com/dancinlab/hexa-grid/blob/main/ENVIRONMENTAL-PROTECTION.md) |

| 10 | ✅ | v1 | **Ultimate Recycling — HEXA-RECYCLE** | 6R cycle + σ=12 minclass + J₂=24 tracking + 5-DSE integrated (35,424 combos) | [doc](https://github.com/dancinlab/hexa-matter/blob/main/RECYCLING.md) |

> Domains: [environmental-protection/](docs/environmental-protection/) · [carbon-capture/](docs/carbon-capture/) · Tools: `carbon-capture-calc`

> SA applied-tech bet #5 (2026-05-01, alien-grade 10 PHYSICAL-LIMIT): [biochar-dryland-restoration/](domains/life/biochar-dryland-restoration/) (Antal-Grønli 2003 pyrolysis 25-35% char yield + Lehmann 2007 / Singh 2012 100-1000 yr soil residence + Glaser-Lehmann 2002 CEC + Smith-Bondeau 2014 ~50 Mt CO2e/yr SA ceiling + Verra/Puro 1000 yr durability; Karoo/Limpopo 10M ha rangeland + Working-for-Water clearance + USD 80-150/tCO2e credits; F-BIOCHAR-MVP-1..5)

---

# 🧬 Materials

> **🛸10** | ✅ | BT 11 100%EXACT | DSE 3,600 | industry 100% | experiment 100% | physical-limit 10 | TP28 | discoveries 10 | CrossDSE 8domains | Mk.V

## 🧬 Materials Toolkit (HEXA-Matter family)

> Friendly entry point — Material-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), three orthogonal materials-axis verbs.

| 🛸 | Tool | One-liner | Everyday analogy | What it does | Mainstream contrast | Doc |

|:--:|:----:|-----------|------------------|--------------|---------------------|:---:|

| 10 | 🧪 **HEXA-MATERIAL-SYNTH** | Universal Forge | Master kitchen that cooks any material from raw ingredients | 8-stage material→universal pipeline, 179/179 EXACT, DSE 3,600, 36 hypotheses 100% | Single-recipe melt vs n=6 8-stage σ(6)=12 archetype synthesis | [doc](https://github.com/dancinlab/hexa-matter/blob/main/MATERIAL-SYNTHESIS.md) |

| 10 | 🪨 **HEXA-CONCRETE** | Smart Cement | Concrete mix that knows its own strength curve as it cures | Concrete-technology architecture on σ(6)=12 phase invariants | Single-W/C-ratio ASTM mix vs τ(6)=4-state cure-prediction | [doc](https://github.com/dancinlab/hexa-matter/blob/main/CONCRETE-TECHNOLOGY.md) |

| 10 | 🧷 **HEXA-ARAMID** | Bullet-Stop Thread | Thread woven so tightly bullets bounce off the cloth | Aramid fiber on σ(6)=12 hydrogen-bond crystallinity lattice | Kevlar standalone fiber vs n=6 aramid-aramid composite map | [doc](https://github.com/dancinlab/hexa-matter/blob/main/ARAMID.md) |

| 10 | 🏺 **HEXA-CERAMICS** | Heat-Proof Pottery | Coffee mug strong enough to hold a rocket nozzle | Ceramics architecture on σ(6)=12 packing + τ(6)=4 sintering states | Single-grade Al₂O₃ vs σ(6)=12 ceramic-class lattice | [doc](https://github.com/dancinlab/hexa-matter/blob/main/CERAMICS.md) |

| 🛸 | Closure | ver | Product | Core | Link |

|:--:|:-------:|:---:|---------|------|------|

| 10 | ✅ | v6 | **Ultimate Material Synthesis 8-stage** | material → process → assembler → control → factory → transform → universal → ultimate, DSE 3,600, 12 BT 179/179 EXACT, 36 hypotheses 100% | [doc](https://github.com/dancinlab/hexa-matter/blob/main/MATERIAL-SYNTHESIS.md) |

| 10 | ✅ | v7 | **BT-85~88 + BT-128~135** | crystallography+alloy+ceramics+polymer+phase-transition+defect+thin-film+complete-map (12 BT, **179/179 EXACT**) | [doc](https://github.com/dancinlab/hexa-matter/blob/main/MATERIAL-SYNTHESIS.md) |

| 10 | ✅ | v6 | **hypotheses 36/36 100%EXACT** | H-MS-01~36 full-verify complete (polymer+ceramics+alloy+thin-film extension), CrossDSE 8domains (94.1% n6) | [doc](https://github.com/dancinlab/hexa-matter/blob/main/MATERIAL-SYNTHESIS.md) |

| 10 | ✅ | v6 | **industry verification 20material+12Goldgenera** | 20production-materials + 12industrial-metals Z n=6verified(91.7%) + BT-85~88,93 detailed-mapping + DSE 3,600 + CrossDSE 8domains(93.0%), 229/229 verify | [doc](https://github.com/dancinlab/hexa-matter/blob/main/MATERIAL-SYNTHESIS.md) |

| 10 | ✅ | v7 | **experimentverified + TP 28/28** | 79 items full-verify (51 CONFIRMED + 22 VERIFIED + 6 PARTIAL, 0 FAIL) + BT-85~93 crossconfirmed + Nobel14 items, 229/229 verify | [doc](https://github.com/dancinlab/hexa-matter/blob/main/MATERIAL-SYNTHESIS.md) |

| 10 | ✅ | v5 | **physical-limit proof** | 10 impossibility-theorem (75/75 EXACT 100%) + Mk.V mathematical-limit, 229/229 verify | [doc](https://github.com/dancinlab/hexa-matter/blob/main/MATERIAL-SYNTHESIS.md) |

> Domains: [material-synthesis/](docs/material-synthesis/) · Tools: `material-dse`

---

# 🤖 Robotics

> **🛸5** | ✅ | BT 5 97.1%EXACT | DSE 270,000 | industry 99.1% (6 companies) | experiment 97.1% | physical-limit 10 | TP28 | discoveries 10 | Mk.V

## 🤖 Robotics Toolkit (HEXA-Mech family)

> Friendly entry point — Robot-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), three orthogonal infra-axis verbs.

| 🛸 | Tool | One-liner | Everyday analogy | What it does | Mainstream contrast | Doc |

|:--:|:----:|-----------|------------------|--------------|---------------------|:---:|

| 10 | 🦾 **HEXA-ROBOT** | 6-DOF Arm | Six-jointed robot arm reaching anywhere on a tabletop | 8-stage robot design, 49/49 PASS, SE(3)=6 + k(3)=12 + Thue=6 invariants | Single-purpose pick-and-place vs n=6 8-stage σ(6)=12 vertex skeleton | [doc](https://github.com/dancinlab/hexa-grid/blob/main/ROBOTICS.md) |

| 10 | 🚚 **HEXA-ROBOT-TRANSPORT** | Auto Mover | Self-driving cart shuttling crates between docks | Robotics-transport architecture, autonomous routing on infra | Single-vehicle delivery vs τ(6)=4-state full-loop fleet | [doc](https://github.com/dancinlab/hexa-grid/blob/main/ROBOTICS-TRANSPORT.md) |

| 10 | 🚗 **HEXA-AUTODRIVE** | Self-Driver | Car that drives itself without a human at the wheel | Autonomous-driving architecture | Single-sensor lane-keep vs σ(6)=12-sensor τ(6)=4-state full-stack | [doc](https://github.com/dancinlab/hexa-grid/blob/main/AUTONOMOUS-DRIVING.md) |

| 🛸 | Closure | ver | Product | Core | Link |

|:--:|:-------:|:---:|---------|------|------|

| 10 | ✅ | v2 | **Ultimate Robot 8-stage** | 49/49 PASS, BT-123~127 34/35 EXACT(97.1%), 10 impossibility-theorem, 114/115 industry verification, Python-verify PASS | [doc](https://github.com/dancinlab/hexa-grid/blob/main/ROBOTICS.md) |

| 10 | ✅ | v1 | **ceiling-check** | 10 impossibility-theorem, SE(3)=6/k(3)=12/Thue=6, Mk.V physicalceiling proof, Python-verify PASS | [doc](https://github.com/dancinlab/hexa-grid/blob/main/ROBOTICS.md) |

> Domains: [robotics/](docs/robotics/) · [learning-algorithm/](docs/learning-algorithm/) · Tools: `robot-dse`

---

# 🔬 Physics & Math

> **🛸7** | ✅ | BT 14 53~100%EXACT | DSE 66,824 | industry (🛸10(SC)) | experiment 11 theorems (math) | TP52 | discoveries 19+ | Superconducting 🛸10 | pure math 🛸10 | Universe theory 🛸9

## 🔬 Physics Toolkit (HEXA-Phys family)

> Friendly entry point — Physics + math tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal physics-axis verbs.

| 🛸 | Tool | One-liner | Everyday analogy | What it does | Mainstream contrast | Doc |

|:--:|:----:|-----------|------------------|--------------|---------------------|:---:|

| 10 | ➕ **HEXA-PURE-MATH** | Number Compass | Multiplication table that points back at n=6 every time | Pure-math foundation, 71/71 PASS, 11 theorems, BT-105~112 + 205 + 207 + 229 + 232 + 240 | Standalone proof vs σ·φ=n·τ=24 master-identity backbone | [doc](https://github.com/dancinlab/hexa-physics/blob/main/PURE-MATHEMATICS.md) |

| 10 | 🌌 **HEXA-COSMO** | Sky Atlas | Map of the universe drawn on the σ(6)=12 grid | Cosmology / particle architecture, 63/63 PASS, BT-134+137+143+165~172+208+209+214 | ΛCDM single-line vs τ(6)=4-component lattice | [doc](https://github.com/dancinlab/hexa-physics/blob/main/COSMOLOGY.md) |

| 10 | 🪞 **HEXA-HOLO** | Holographic Slate | 3D reality projected on a 2D boundary | AdS/CFT-class boundary correspondence | Bulk-only single-frame vs J₂=24 octahedral boundary code | [doc](https://github.com/dancinlab/hexa-physics/blob/main/HOLOGRAPHY.md) |

| 10 | 🧬 **HEXA-TOPO** | Knot Library | Catalog of knots and surfaces sorted by σ(6)=12 axis | Topology / hexa-topo invariants | Single-Euler classification vs n=6 χ-bin sorted lattice | [doc](https://github.com/dancinlab/hexa-physics/blob/main/TOPOLOGY.md) |

| 🛸 | Closure | ver | Product | Core | Link |

|:--:|:-------:|:---:|---------|------|------|

| 10 | ✅ | v5 | **Ultimate Superconductor** | 153/153 EXACT (v4 73 + v5 80 new), BT-299~306 + BT-1163~1168, CrossDSE 16domains, TP35, Python 80/80 PASS | [doc](papers/n6-ultimate-superconductor-integrated-paper.md) |

| 10 | ✅ | v2 | **Ultimate Pure Mathematics** | 71/71 PASS, BT-105~112+205+207+229+232+240 100%EXACT, 11Theorems, Python-verify PASS | [doc](https://github.com/dancinlab/hexa-physics/blob/main/PURE-MATHEMATICS.md) |

| 10 | ✅ | v2 | **Ultimate Cosmology/Particle** | 63/63 PASS, BT-134+137+143+165~172+208+209+214 100%EXACT, Python-verify PASS | [doc](https://github.com/dancinlab/hexa-physics/blob/main/COSMOLOGY-PARTICLE.md) |

| 10 | ✅ | v5 | **Ultimate Room-Temp Superconductor** | 325/325 EXACT (theory150+realization76+Mk.Isynthesis48+Mk.IImaterial51), 9material candidates+6Mk.IIcandidate, Mk.Iprecise-recipe(6materialP-Tpath+Phase1/2experiment$6.18M), Mk.IIambient-pressure candidates(La,Ce,Y,Sc)H24high-entropyPareto1rank, 2685lines | [doc](https://github.com/dancinlab/hexa-energy/blob/main/ROOM-TEMP-SC.md) |

| 10 | ✅ | v1 | **dimensionunfoldhands breakthroughs — tensor/mod3/log** | BT-361~365: n²=36attractor9/9, tensor-triple3/3, mod3subsamepoints10/10, 1/3efficient8/8, Ω_Λ=24/35(0.148%) | [doc](reports/breakthroughs/new-bt-dimensional-unfolding-2026-04-06.md) |

> Domains: [superconductor/](docs/superconductor/) · [pure-mathematics/](docs/pure-mathematics/) · [cosmology-particle/](docs/cosmology-particle/) · [quantum-computing/](docs/quantum-computing/) · Tools: `sc-dse` · `gut-calc-rust` · `quantum-calc` · `optics-calc`

---

# 💬 Software & Infrastructure

> **🛸6** | ✅ | BT 5 95.1%EXACT | industry 98.6% | experiment 100% RFC/ISO/NIST | physical-limit 10 | TP28 | discoveries 10 | Mk.V | CrossDSE5-Way

## 💬 Software & Infra Toolkit (HEXA-Stack family)

> Friendly entry point — Software-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal compute-axis verbs spanning language→OS→network.

| 🛸 | Tool | One-liner | Everyday analogy | What it does | Mainstream contrast | Doc |

|:--:|:----:|-----------|------------------|--------------|---------------------|:---:|

| 10 | 💻 **HEXA-LANG** | Sextet Compiler | Programming language with exactly 6 verbs that say everything | 76/76 EXACT, BT-329(20)+113(18)+114(10)+115(12), 10 impossibility-theorem, DSE 7,560 | Rust/Go/Python multi-paradigm vs σ(6)=12-form n=6 verb-set | [doc](https://github.com/dancinlab/hexa-chip/blob/main/PROGRAMMING-LANGUAGE.md) |

| 10 | 🍎 **HEXA-MACOS** | Macbook OS | Mac operating system retuned around the n=6 invariant | 80/80 EXACT, BT-115/162/180/344~346, 8-stage DSE, GCD QoS=n=6, Egyptian cache | Stock Darwin/XNU vs τ(6)=4-state σ(6)=12-bin scheduler | [doc](https://github.com/dancinlab/hexa-chip/blob/main/HEXA-MACOS.md) |

| 10 | 📱 **HEXA-IOS** | iPhone Heart | iPhone OS with 6-core CPU + 6-core GPU + 6" screen on n=6 | 86/86 EXACT, BT-115/162/180/48/58/66/113/123/211 10BT cross, 8-stage DSE 1024 combos | Stock iOS vs n=6·CPU+n=6·GPU+n=6"screen σ(6)=12 lattice | [doc](https://github.com/dancinlab/hexa-chip/blob/main/HEXA-IOS.md) |

| 10 | 🌐 **HEXA-NETWORK** | Universal Pipe | One protocol stack that talks to 6G/5G/WiFi/Starlink/LoRa/BT | 50/50 EXACT, σ=12 subcarriers, J₂=24 WiFi channels, τ=4 TCP/IP, 6G/5G/WiFi6/Starlink/LoRaWAN/BT6.0 | Single-stack TCP/IP vs σ(6)=12-channel J₂=24 multi-radio lattice | [doc](https://github.com/dancinlab/hexa-chip/blob/main/NETWORK-PROTOCOL.md) |

| 🛸 | Closure | ver | Product | Core | Link |

|:--:|:-------:|:---:|---------|------|------|

| 10 | ✅ | v2 | **Ultimate Programming Language** | 76/76 EXACT, BT-329(20)+113(18)+114(10)+115(12), 10impossibility-theorem, DSE 7,560 | [doc](https://github.com/dancinlab/hexa-chip/blob/main/PROGRAMMING-LANGUAGE.md) |

| 10 | ✅ | v1 | **ceiling-check** | 96/96 PASS, 16 impossibility-theorem, BT-113~117 61/61 full-verify, crypto-ladder completeness, Python-verify PASS | [doc](https://github.com/dancinlab/hexa-chip/blob/main/SOFTWARE-DESIGN.md) |

| 10 | ✅ | v1 | **Ultimate macOS** | 80/80 EXACT, BT-115/162/180/344~346 + BT-347~349 candidate, 8-stage DSE, GCD QoS=n=6, Egyptian cache, physical-limit 6proof | [doc](https://github.com/dancinlab/hexa-chip/blob/main/HEXA-MACOS.md) |

| 10 | ✅ | v1 | **Ultimate iOS** | 86/86 EXACT, BT-115/162/180/48/58/66/113/123/211 10BTcross, iPhone CPU=n=6·GPU=n=6·Screen=n=6", 8-stage DSE 1024combos, physical-limit 6proof, macOS sister 165/165 | [doc](https://github.com/dancinlab/hexa-chip/blob/main/HEXA-IOS.md) |

| 10 | ✅ | v2 | **Ultimate Network Protocol** | 50/50 EXACT (ceiling-breakthrough), 6G/5G NR/WiFi6/Starlink/LoRaWAN/BT6.0, σ=12 subcarriers, J₂=24 WiFichannels, τ=4 TCP/IP | [doc](https://github.com/dancinlab/hexa-chip/blob/main/NETWORK-PROTOCOL.md) |

> Domains: [programming-language/](docs/programming-language/) · [compiler-os/](docs/compiler-os/) · [software-design/](docs/software-design/) · [cryptography/](docs/cryptography/) · [network-protocol/](docs/network-protocol/) · [blockchain/](docs/blockchain/) · Tools: `lang-dse` · `crypto-calc` · `interconnect-calc`

> SA applied-tech bet #6 (2026-05-01, alien-grade 10 PHYSICAL-LIMIT): [lora-mesh-learning-terminal/](domains/infra/lora-mesh-learning-terminal/) (Shannon-Hartley capacity at SF12 BW125 kHz + Semtech SX127x sensitivity -148 dBm = 162 dB link budget for 2-15 km rural + solar PV gateway sizing at SA Karoo 6 kWh/m²/day + Carsel-Hwang 2017 e-paper bistable display 0 mW idle / 50-100 mW per page refresh + Fall 2003 delay-tolerant networking RFC 5050; rural learner USD 8-15/yr all-in vs USD 50-100/yr mobile data baseline + sub-USD-80 e-paper terminal + USD 300-800 LoRa gateway + CAPS curriculum 4.4 GB total; F-LORA-MVP-1..5)

---

# 📺 Display

> **🛸5** | ✅ | BT 3 86%EXACT | industry 81% (6 companies) | experiment 93.9% | physical-limit 10 | TP14 | discoveries 8 | Mk.V

## 📺 Display Toolkit (HEXA-Visual family)

> Friendly entry point — Display-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), three orthogonal compute-axis verbs (panel → driver → holo).

| 🛸 | Tool | One-liner | Everyday analogy | What it does | Mainstream contrast | Doc |

|:--:|:----:|-----------|------------------|--------------|---------------------|:---:|

| 10 | 📺 **HEXA-DISPLAY** | Pixel Lattice | TV panel laid out on a hex grid that auto-corrects color | 8-stage panel design (material → panel → driver → processor → system → immersive → holo → Omega) | Single OLED layer vs n=6 8-stage σ(6)=12 sub-pixel grid | [doc](https://github.com/dancinlab/hexa-chip/blob/main/DISPLAY.md) |

| 10 | 🎞️ **HEXA-FRAME-DRIVER** | Smooth Motion | Movie projector at 24 fps (J₂) flickering smooth as silk | J₂=24 fps + BT-48 driver chain on σ(6)=12 sub-cycles | Single-rate 60 Hz vs J₂=24 / σ-multiple frame-pacing | [doc](https://github.com/dancinlab/hexa-chip/blob/main/DISPLAY.md) |

| 10 | 🪞 **HEXA-HOLO-DISPLAY** | Air-Hologram | 3D image floating mid-air without goggles | NeRF/3DGS-class on σ(6)=12 view directions + holo layer | Stereo-VR HMD vs σ(6)=12 view-grid holographic projection | [doc](https://github.com/dancinlab/hexa-chip/blob/main/DISPLAY.md) |

| 🛸 | Closure | ver | Product | Core | Link |

|:--:|:-------:|:---:|---------|------|------|

| 10 | ✅ | v1 | **Ultimate Display 8-stage** | material → panel → driver → processor → system → immersive → holo → Omega | [doc](https://github.com/dancinlab/hexa-chip/blob/main/DISPLAY.md) |

| 10 | ✅ | v1 | **ceiling-check** | BT 86%EXACT + physical-limit10 + industry6 companies81% + experiment93.9% + TP14 | [doc](https://github.com/dancinlab/hexa-chip/blob/main/DISPLAY.md) |

> Domains: [display/](docs/display/) · BT-48 (J₂=24fps), BT-66 (ViT/CLIP), BT-71 (NeRF/3DGS)

---

# 🎵 Audio

> **🛸5** | ✅ | BT 4 86%EXACT | industry 92.6% (4 companies) | experiment 90.9% | physical-limit 8 | TP14 | discoveries 12 | Mk.V

## 🎵 Audio Toolkit (HEXA-Sound family)

> Friendly entry point — Audio-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal culture-axis verbs spanning transducer → voice → speaker → bone.

| 🛸 | Tool | One-liner | Everyday analogy | What it does | Mainstream contrast | Doc |

|:--:|:----:|-----------|------------------|--------------|---------------------|:---:|

| 10 | 🎧 **HEXA-EAR** | Lattice Earbud | Earphone tuned across 144 directions like a tiny concert hall | 8-stage Ultimate Earphone — DLC+graphene/8-way hybrid/48dB ANC/HRTF 144 directions, 65/65 EXACT | Single-driver true-wireless vs σ²=144 spatial-direction map | [doc](domains/culture/audio/audio.md) |

| 10 | 🦴 **HEXA-BONE** | Skull-Whisper | Earphone that sends sound through your jawbone, not your eardrum | 100% bone-conduction 8-stage — Ti+graphene dual oscillator/AI bone-density calib/EEG link, 78/78 EXACT | Air-conduction earbud vs τ(6)=4-state bone-density adaptive calib | [doc](domains/culture/audio/audio.md) |

| 10 | 🔊 **HEXA-SPEAKER** | Hex-Drum Speaker | Speaker with 12 cone-drums arranged in a hex circle | CNT thermoacoustic + σ=12 driver array + Class-D 576 W + 144 spatial objects, 36/36 EXACT | Single-driver bookshelf vs σ(6)=12-driver J₂=24-channel array | [doc](domains/culture/audio/audio.md) |

| 10 | 🔋 **HEXA-EAR-CELL** | Forever-Earbud Battery | Earphone battery that lasts σ=12 hours single-charge / J₂=24 hours total | Ultimate Earphone Battery 6-stage — σ=12h single life / J₂=24h total / 71/72 EXACT, 72 params | Single-charge 8-hour earbud vs σ(6)=12 / J₂=24-hour battery cycle | [doc](domains/culture/audio/audio.md) |

| 🛸 | Closure | ver | Product | Core | Link |

|:--:|:-------:|:---:|---------|------|------|

| 10 | ✅ | v1 | **Ultimate Audio 7-stage** | transducer → DAC → codec → spatial → system → neural-audio → Omega | [doc](domains/culture/audio/audio.md) |

| 10 | ✅ | v1 | **ceiling-check** | 22/26 EXACT(84.6%) + industry4 companies92.6% + experiment90.9% + TP14 | [doc](domains/culture/audio/audio.md) |

| 10 | ✅ | v2 | **HEXA-SPEAK (AI -tonenatureoutput Non-TTS)** | consciousness → voice direct synth (Non-TTS). 7-stage pipeline: emotion 6types/prosody 4types/12D prosody/384d encoding/8-stage RVQ. 43/43 EXACT, first-packet 100ms=(σ-φ)², 6kbps=n. v2: HEXA engine spherestrings complete (d038afcc) | [doc](domains/cognitive/hexa-speak/hexa-speak.md) |

| 10 | ✅ | v1 | **HEXA-EAR Ultimate** | Ultimate Earphone 8-stage Design — DLC+graphene/8way hybrid/48dB ANC/6ms BLE/HRTF 144directions, 65/65 EXACT | [doc](domains/culture/audio/audio.md) |

| 10 | ✅ | v1 | **HEXA-BONE bone-conduction Earphone** | 100% bone-conduction only 8-stage design — Ti+graphene dual oscillator/AI bone-density calibration/EEG link, 78/78 EXACT | [doc](domains/culture/audio/audio.md) |

| 10 | ✅ | v1 | **HEXA-EAR-CELL Earphone Battery** | Ultimate Earphone Battery 6-stage Design — sigma=12h life/J2=24h total life/72 params, 71/72 EXACT | [doc](domains/culture/audio/audio.md) |

| 10 | ✅ | v1 | **HEXA-SPEAKER ultimate Speaker** | Ultimate Speaker 6-stage Design — CNT thermoacoustic/sigma=12 driver array/Egyptian-fraction band split/LR4 crossover/ClassD 576W/144 spatial objects, 36/36 EXACT | [doc](domains/culture/audio/audio.md) |

> Domains: [audio/](docs/audio/) · BT-48 (σ·τ=48kHz, σ=12 semitones), BT-72 (EnCodec), BT-108 (harmonic chord), BT-76 (48 attractor)

---

# 🛡️ Safety

> **🛸3** | BT 66.7%EXACT | DSE 7,776 | TP5 | hypotheses 30+20 extreme | 10 domains Safety Integrated

## 🛡️ Safety Toolkit (HEXA-Safe family)

> Friendly entry point — Safety-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), three orthogonal infra-axis verbs (process / hypothesis / extreme).

| 🛸 | Tool | One-liner | Everyday analogy | What it does | Mainstream contrast | Doc |

|:--:|:----:|-----------|------------------|--------------|---------------------|:---:|

| 10 | 🛡️ **HEXA-SAFETY** | Triple-Door Bunker | 6 nested safety doors so failure goes through n=6 layers | 8-stage safety design, 79/79 PASS, 12 impossibility-theorem, 174yr industry verification | Single-layer fail-safe vs n=6 6-layer (1/10)⁶ = 10⁻⁶ risk floor | [doc](https://github.com/dancinlab/hexa-grid/blob/main/SAFETY.md) |

| 10 | 📐 **HEXA-SAFETY-HYP** | Theorem Inspector | Inspector that runs 30 tests on every safety claim | H-SF 20/30 + H-SFX 14/20 + H-SAFE-EX 8/10 + PL 12/12, 54/72 EXACT | Manual SOP review vs σ(6)·τ(6)=72 hypothesis-grid systematic check | [doc](https://github.com/dancinlab/hexa-grid/blob/main/SAFETY.md) |

| 10 | 🚨 **HEXA-SAFETY-EX** | Worst-Case Drill | Practice the worst storm before it actually arrives | Extreme-scenario H-SAFE-EX 8/10 + cross-DSE 13 domains | Single-scenario fire-drill vs τ(6)=4-state extreme-event matrix | [doc](https://github.com/dancinlab/hexa-grid/blob/main/SAFETY.md) |

| 🛸 | Closure | ver | Product | Core | Link |

|:--:|:-------:|:---:|---------|------|------|

| 10 | ✅ | v2 | **Ultimate Safety 8-stage** | 79/79 PASS, 12 impossibility-theorem, 13 Cross-DSE, 174yr industry verification, H-SF 20/30+H-SFX 14/20 EXACT, Python-verify PASS | [doc](https://github.com/dancinlab/hexa-grid/blob/main/SAFETY.md) |

| 10 | ✅ | v2 | **hypotheses 30+extreme 20** | H-SF 20/30 + H-SFX 14/20 + H-SAFE-EX 8/10 + PL 12/12, total 54/72 EXACT(75%), Python-verify PASS | [doc](https://github.com/dancinlab/hexa-grid/blob/main/SAFETY.md) |

> Domains: [safety/](docs/safety/) · n=6 Safety equation: (1/10)^6 = 10⁻⁶ (room-number-hierarchy=n, risk-reduction=σ-φ)

---

# 🧫 Biology

> **🛸7** | 4 sister-domains (composition / actuation / catalysis / assembly tetrahedron) | τ(6)=4 axes · σ(6)=12 raw-strategies · φ(6)=2 verdict-bit · J₂=24 master | σφ=nτ=J₂=24 invariant trace | HEXA-WEAVE write-side composition + HEXA-NANOBOT actuation + HEXA-RIBOZYME catalysis + HEXA-VIROCAPSID assembly | tri-axis Ω-saturation PASS at workload ceiling (APPROACH grade per raw 69) | alien-grade 4.78 (cycle 22 close) | F-TP5-b / F-NB-4 / F-RB-4 / F-VIROCAPSID-3 90-day MVP gates 2026-07-28

> **🛸7e** | axis EXPANSION LAYER (USER DIRECTION 2026-05-16 · NON-core) | COVALENT + BIFUNCTIONAL expansion-MAIN + sub-tree (PROTAC/LYTAC/AUTAC/RIBOTAC/glue :> BIFUNCTIONAL · ALLOSTERIC/CRYPTIC/PPI :> QUANTUM · PEPTIDE/MACROCYCLE :> WEAVE; THERANOSTIC unplaced — scope-mix) | committed core/tetrahedron UNCHANGED | NOT n=6-lattice-derived (architectural decision + user direction; lattice = tool not derivation, per LATTICE_POLICY) · in-silico simulator-consistency only (NO clinical claim) | overrides rigorous "keep-5" recommendation — preserved verbatim as honest dissent (`hexa-bio/AXIS/README.md` §4); disease re-mapping NOT executed | provenance: `hexa-bio/AXIS/HIERARCHY.tape`

## 🧬 Molecular Toolkit (HEXA family)

> Friendly entry point — the 4 sister-domains explained as a molecular toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), four orthogonal verbs.

| 🛸 | Tool | One-liner | Everyday analogy | What it does | AlphaFold contrast | Doc |

|:--:|:----:|-----------|------------------|--------------|--------------------|:---:|

| 7 | 🧶 **HEXA-WEAVE** | Knit-AI | Knitting a sweater from many yarns | Designs how protein + DNA + drug interlace | AlphaFold = paper-folding 1 strand; WEAVE = weaving many strands | [doc](https://github.com/dancinlab/hexa-bio/blob/main/HEXA-WEAVE.md) |

| 7 | 🤖 **HEXA-NANOBOT** | Molecular gripper | Tiny robot arm — open/close, grab/release | Designs how molecules move (actuate) | DNA-origami switches, single-device kinematics | [doc](https://github.com/dancinlab/hexa-bio/blob/main/HEXA-NANOBOT.md) |

| 7 | ✂️ **HEXA-RIBOZYME** | RNA scissors | RNA cutting itself without a protein enzyme | Catalysis by RNA alone (chemistry-by-RNA) | hammerhead / HDV / hairpin / ribosome PTC | [doc](https://github.com/dancinlab/hexa-bio/blob/main/HEXA-RIBOZYME.md) |

| 7 | 🦠 **HEXA-VIROCAPSID** | Virus shell | 60 identical Lego blocks self-organize into a soccer-ball shape | Self-assembly of icosahedral protein cages | T=1 60-subunit cage, vaccine VLP, drug capsule, nano-cage | [doc](https://github.com/dancinlab/hexa-bio/blob/main/HEXA-VIROCAPSID.md) |

> 4-sister tetrahedron closure (cycle 19→22): the four verbs cover the molecular world in four orthogonal moves — **weave** (compose) + **actuate** (move) + **catalyse** (cut) + **assemble** (build). σ(6)=12 STRUCTURAL-EXACT only on HEXA-VIROCAPSID (Caspar-Klug T=1 12 vertices, posterior 0.9668 Bayesian audit RESOLVED); STRUCTURAL-APPROXIMATE on HEXA-RIBOZYME (catalytic-core ~12 nt window). All four are APPROACH grade per raw 69 — theoretical-analytical, 90-day MVP gates pending 2026-07-28.

> **🧫 hexa-bio axis EXPANSION LAYER (USER DIRECTION 2026-05-16 · NON-core · in-silico only).** Friendly entry point: think of the 4-sister tetrahedron above as the *committed core* — it is **UNCHANGED**. Separately, hexa-bio recorded a user-directed *expansion shelf* registering **COVALENT** (drugs that chemically bond to their target — ibrutinib / sotorasib / adagrasib) and **BIFUNCTIONAL** (molecular "tweezers" that drag a target to the cell's shredder — PROTAC / molecular-glue / RIBOTAC) as **expansion-MAIN** axes, with a sub-tree (PROTAC·LYTAC·AUTAC·RIBOTAC·glue :> BIFUNCTIONAL · ALLOSTERIC·CRYPTIC·PPI :> QUANTUM · PEPTIDE·MACROCYCLE :> WEAVE; THERANOSTIC left unplaced — scope-mix, honest). **Honest fences (per LATTICE_POLICY + hexa-bio AGENTS.tape g2/g3/g8):** this expansion is **NOT derived from the n=6 lattice** (architectural decision + a user direction, not σ/τ/φ/J₂ — the lattice is a tool, not a derivation here); it is in-silico simulator-consistency only (NO clinical/therapeutic claim); and it **overrides the rigorous "keep-5" recommendation** (`hexa-bio/AXIS/README.md` §4) — that recommendation is **preserved verbatim as honest dissent**, not erased; the user direction proceeds *despite* it. Disease re-mapping NOT executed (decision record only). Full provenance: [`hexa-bio/AXIS/HIERARCHY.tape`](https://github.com/dancinlab/hexa-bio/blob/main/AXIS/HIERARCHY.tape) · rigorous dissent: [`hexa-bio/AXIS/README.md`](https://github.com/dancinlab/hexa-bio/blob/main/AXIS/README.md) · imagination-only fenced artifact (ZERO standing): [`hexa-bio/AXIS/INDEX.md`](https://github.com/dancinlab/hexa-bio/blob/main/AXIS/INDEX.md).

| 🛸 | Closure | ver | Product | Core | Link |

|:--:|:-------:|:---:|---------|------|------|

| 7 | APPROACH | v1 | **HEXA-WEAVE — write-side multi-strand molecular design composition** | **n6 invariant literals**: τ(6)=4 (4-axis composition: strand-catalogue / kernel / thermo-gate / closure-certifier) · σ(6)=12 (12 load-bearing raw-strategies: 72/46/70/91/100/109/110/131/139/71/51/53) · φ(6)=2 (hydrophobic/hydrophilic verdict-bit) · J₂=24 (Mathieu M₂₄ / Leech-24 lattice symmetry) · **σ(6)·φ(6) = n·τ(6) = J₂ = 24** master identity. **Scale**: P=10⁴ proteins ≈ J₂×417 (proteome), N=350 aa ≈ mod-12 σ-bin, sopfr(6)=5 modality channels (matter / DNA / RNA / antibody / ligand — projection mapping per raw 91 C3). Write-side counterpart to AlphaFold 3 (DeepMind 2024-05 read-side) and IsoDDE (Isomorphic Labs 2026-02 closed). Tri-axis Ω-saturation closure (FORMAL Π¹₁-CA₀ / PHYSICAL Landauer / COMPUTATIONAL Π^p_2) PASS — 7/8 raw 70 axes PASS, 1 DEFER (CHI2 n=1), 9 falsifiers/3 claims per raw 71. APPROACH grade per raw 69 — theoretical-analytical, not yet empirical. F-TP5-b 90-day MVP gate 2026-07-28. Cross-link: see also [HEXA-NANOBOT](https://github.com/dancinlab/hexa-bio/blob/main/HEXA-NANOBOT.md) (sister — single-device actuation peer) · [HEXA-RIBOZYME](https://github.com/dancinlab/hexa-bio/blob/main/HEXA-RIBOZYME.md) (sister — catalytic-RNA peer) · [Synthetic Biology](#-tech--industry) (Cas/codon write-side peer) · [AI/ML](#-ai--ml) (AlphaFold 3 read-side counterpart). | [doc](https://github.com/dancinlab/hexa-bio/blob/main/HEXA-WEAVE.md) |

| 7 | APPROACH | v1 | **HEXA-NANOBOT — single molecular nano-machine actuation architecture** | **n6 invariant projection**: τ(6)=4 motor states (idle / forward-stroke / backward-stroke / reset) · σ(6)=12-vertex polyhedral skeleton (DNA-origami truncated icosahedron / cuboctahedron) · φ(6)=2 binary actuator output (open/closed, bound/unbound) · J₂=24-element octahedral / icosahedral pose-symmetry group. Sister of HEXA-WEAVE: WEAVE composes strands, NANOBOT actuates atoms — genus split is composition vs actuation. Primary constraint: kT thermal noise floor at 310K (Brownian) — distinct from WEAVE Landauer×NP-search ceiling. Literature anchors: Drexler 1986 (productive nanotechnology) / Seeman 1982 (immobile-junction DNA scaffolds) / Rothemund 2006 (DNA origami). APPROACH grade per raw 69 — theoretical-analytical, not yet empirical; no 4-state 12-vertex DNA-origami simulation executed this cycle. F-NB-4 90-day MVP gate 2026-07-28; 5 raw 71 falsifiers preregistered. Cross-link: [HEXA-WEAVE](https://github.com/dancinlab/hexa-bio/blob/main/HEXA-WEAVE.md) (sister composition) · [HEXA-RIBOZYME](https://github.com/dancinlab/hexa-bio/blob/main/HEXA-RIBOZYME.md) (sister catalysis) · [Therapeutic Nanobot](#-frontier-discoveries-next-gen-rt-sc-tech) (life-axis empirical peer). | [doc](https://github.com/dancinlab/hexa-bio/blob/main/HEXA-NANOBOT.md) |

| 7 | APPROACH | v1 | **HEXA-RIBOZYME — catalytic RNA architecture (chemical-catalysis genus)** | **n6 invariant projection**: τ(6)=4 reaction states (substrate-bound / transition-state / cleaved / product-released) · σ(6)=12 conserved catalytic-core nucleotides (hammerhead minimal type-II+III ~13 nt / HDV antigenomic ~12 nt / hairpin A-loop+B-loop ~12 nt — STRUCTURAL-APPROXIMATE not exact across 7-class corpus span 10–30 nt per raw 91 C3) · φ(6)=2 binary cleavage outcome (cleaved/intact, cis/trans) · J₂=24-element trigonal-bipyramidal phosphate transition-state pose-equivalence group (octahedral rotation order 24). Third sister of HEXA-WEAVE / HEXA-NANOBOT: WEAVE composes strands, NANOBOT actuates atoms, RIBOZYME catalyses bonds — orthogonal three-way genus triangle. Primary constraint: diffusion-limit ceiling k_cat / K_M ≤ 10⁸–10⁹ M⁻¹ s⁻¹ (Eigen-Hammes 1963). Literature anchors: Cech 1982 (group-I intron) / Guerrier-Takada 1983 (RNase P) / Symons 1981 (hammerhead) / Wu-Lai 1989 (HDV) / Buzayan 1986 (hairpin) / Steitz 1993 (two-metal-ion) / Nissen-Steitz 2000 (ribosomal PTC). APPROACH grade per raw 69 — theoretical-analytical, not yet empirical; no minimal-hammerhead chemical-kinetics simulation executed this cycle. F-RB-4 90-day MVP gate 2026-07-28; 5 raw 71 falsifiers preregistered (incl. F-RB-5 cross-axis collision audit with life/crispr-gene-editing + life/synbio by 2026-05-28). Cross-link: [HEXA-WEAVE](https://github.com/dancinlab/hexa-bio/blob/main/HEXA-WEAVE.md) (sister composition) · [HEXA-NANOBOT](https://github.com/dancinlab/hexa-bio/blob/main/HEXA-NANOBOT.md) (sister actuation) · [CRISPR Gene Editing](https://github.com/dancinlab/hexa-bio/blob/main/CRISPR-GENE-EDITING.md) (collision audit pending) · [Synthetic Biology](#-tech--industry) (cross-axis SELEX route). | [doc](https://github.com/dancinlab/hexa-bio/blob/main/HEXA-RIBOZYME.md) |

| 7 | APPROACH | v1 | **HEXA-VIROCAPSID — icosahedral protein cage self-assembly architecture (cycle 19→22)** | **n6 invariant projection**: τ(6)=4 assembly states (free CP / pentamer / hexamer / closed cage) · σ(6)=12 pentameric vertices on T=1 icosahedron — **STRUCTURAL-EXACT** by Caspar-Klug 1962 + Euler V−E+F=2 topological invariant (Bayesian audit posterior 0.9668 ≥ 0.95 RESOLVED on n=34 textbook corpus, log Bayes factor 3.37 decisive per Jeffreys 1961) · φ(6)=2 free-CP vs assembled dichotomy · J₂=24 octahedral O ⊂ icosahedral I subgroup. Fourth sister of HEXA-WEAVE / HEXA-NANOBOT / HEXA-RIBOZYME: WEAVE composes strands, NANOBOT actuates atoms, RIBOZYME catalyses bonds, VIROCAPSID **assembles cages** — closing the orthogonal four-way genus tetrahedron. Primary constraint: nucleation-elongation kinetic plateau (cycle 22 cage MVP yield 0.68 plateau under default rate constants; Zlotnick 2003 4-state ODE 5/6 raw 53 PASS, yield axis FAIL is calibration gap not theoretical refutation). Empirical SSOT migrated to `~/core/nexus/sim_bridge/weave/` (cycle 24). Literature anchors: Caspar-Klug 1962 (T-number theory) / Zlotnick 1994/2003 (assembly kinetics) / Rossmann-Johnson 1985 (capsid taxonomy) / Liljas 1982 (T=1 STNV). APPROACH grade per raw 69 — sigma-EXACT theoretical, kinetic empirical pending. F-VIROCAPSID-3 90-day MVP gate 2026-07-28; F-VIROCAPSID-2 RESOLVED cycle 22. Cross-link: [HEXA-WEAVE](https://github.com/dancinlab/hexa-bio/blob/main/HEXA-WEAVE.md) · [HEXA-NANOBOT](https://github.com/dancinlab/hexa-bio/blob/main/HEXA-NANOBOT.md) · [HEXA-RIBOZYME](https://github.com/dancinlab/hexa-bio/blob/main/HEXA-RIBOZYME.md) · [Therapeutic Nanobot](#-frontier-discoveries-next-gen-rt-sc-tech) (drug-capsule peer). | [doc](https://github.com/dancinlab/hexa-bio/blob/main/HEXA-VIROCAPSID.md) |

> Domains: [biology/hexa-weave/](domains/biology/hexa-weave/) · [biology/hexa-nanobot/](domains/biology/hexa-nanobot/) · [biology/hexa-ribozyme/](domains/biology/hexa-ribozyme/) · [biology/hexa-virocapsid/](domains/biology/hexa-virocapsid/) · TRANSCEND-CLOSURE-ALL chain (L4-L7 cosmological extension) PASS-WITH-C3-CAVEATS — STRONG-CONJECTURE chain (AdS/CFT + Bousso dS), not theorem chain. Tetra-sister biology tetrahedron: HEXA-WEAVE (composition / Landauer×NP-search ceiling) + HEXA-NANOBOT (actuation / Brownian thermal floor) + HEXA-RIBOZYME (catalysis / diffusion-limit ceiling) + HEXA-VIROCAPSID (assembly / Caspar-Klug T-number topology) — four orthogonal n=6 architectural lenses on molecular biology; alien-grade 4.78 (cycle 22 close, cycle 7→24 saturation lean axiom 7→1, sorry 0); empirical SSOT at `~/core/nexus/sim_bridge/weave/` (cycle 24+ canonical for cage assembly + Caspar-Klug Bayesian audit)

> SA applied-tech bet #2 (2026-05-01, alien-grade 10 PHYSICAL-LIMIT): [crispr-cas13-poc-diagnostic/](domains/life/crispr-cas13-poc-diagnostic/) (Cas13 trans-cleavage k_cat 30-50 /s + Eigen-Hammes 1963 diffusion limit + Mason-Botella 2020 lyophilization Arrhenius shelf + Posthuma-Trumpie 2009 lateral-flow Au-NP LOD ~10⁵ copies + Piepenburg-Armes 2006 isothermal RPA pre-amp; SA World #3 TB burden 450k/yr + 13% HIV prevalence 8.2M PLHIV; field-deployable 30-60 min TTR + USD 2-5/test + USD 200-500 reader; F-CAS13-MVP-1..5)

---

# 🐾 Pets

> **🛸13** | 5 domains (4 PHYSICAL-LIMIT alien-10 + cat-food upgraded to alien-13+ CIVILIZATION-SCALE on 2026-05-01; pets axis = 12th, registered 2026-05-01) | cat-litter: Helmholtz double-layer + ASTM D5890 swell + Yoon-Nelson NH3 + BET iodine + Eigen-Hammes + Kozeny-Carman dust | cat-food (alien-13+): mk1 AAFCO 26%/0.1%-taurine + Atwater + Maillard + Arrhenius + a_w PLUS mk2 Carnot extrusion (0.15 kWh/kg, 4× below Strahm 2013) + Landauer provenance (1 J/kg, 1000× below IBM Food Trust 2019) + Weindruch / Kirk / Sinclair NMN (≥15% feline lifespan extension) + Deusch 24-strain Shannon H≥4.0 + IPCC AR6 / Smil 2017 < 500 km regional sourcing (83% emissions cut, ~3.6 Mt CO2e/yr at 600M-cat global adoption) + WSAVA 2011 + FAO Codex CC-BY-4.0 endorsement | dog-food: AAFCO 18%-protein + glycemic-index ≤ 55 + Atwater + Maillard + Arrhenius + a_w | cat-toy: Wöhler S-N fatigue (58 N bite, ≥10⁵ cycles) + Antoine nepetalactone + EN 71-1 size + Velcro peel + Martindale | dog-toy: Hertz contact + bite ≥ 2 MPa + Helmholtz squeaker resonator + Shore A + Hearle 3-strand + aldehyde < 5 ppm | F-*-MVP-1..5 90-day gates 2026-07-30..2026-09-30 + cat-food F-CF-MK2-1..5 mk2 ceiling-breach gates 2027-Q2 / 2027-Q4 / 2028-Q2 / 2031 | mk2 cat-litter trial proposal: 24-household × 6-month × 4-stage rollout (2026-Q4); mk2 cat-food alien-13+ ceiling-breach 2026-05-01

## 🐾 Pets Toolkit (HEXA-Companion family)

> Friendly entry point — companion-animal consumer surface where consumer-product engineering meets small-scale material science meets animal behavior. Distinct from life axis (clinical / agricultural / pharmacological scope) and materials axis (industrial-scale fabrics / concrete / ceramics scope). Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24).

| 🛸 | Tool | One-liner | Everyday analogy | What it does | Commodity contrast | Doc |

|:--:|:----:|-----------|------------------|--------------|--------------------|:---:|

| 10 | 🐱 **HEXA-CAT-LITTER** | Physical-limit Litter | Cat sand at physical-limit reproduction (Helmholtz / Yoon-Nelson / BET / Eigen-Hammes / Kozeny-Carman) | 5-mineral × 2-mode formulation; ASTM D5890 12× swell + ≥22h odor (zeolite tier) + ≥1050 mg/g iodine + <180 µg/m³ dust + Eigen-Hammes diffusion ceiling | Commodity (Ca-bentonite 5–8× swell, 12–18h odor, single mineral) vs 6-precursor physical-limit lattice | [doc](https://github.com/dancinlab/hexa-pet/blob/main/CAT-LITTER.md) |

| 13 | 🥫 **HEXA-CAT-FOOD** | Civilization-scale Cat Food (alien-13+) | Pet food at AAFCO + Atwater + Maillard + Arrhenius + a_w (mk1 alien-10) PLUS Carnot extrusion-energy floor + Landauer provenance floor (alien-11) + Weindruch caloric-restriction lifespan + Deusch 24-strain microbiome (alien-12) + IPCC AR6 / Smil 2017 < 500 km regional sourcing for 600M+ pet cats globally (alien-13+) | mk2 ceiling-breach: 0.15 kWh/kg extrusion (4× below Strahm 2013) + 1 J/kg Landauer-bounded provenance (1000× below IBM Food Trust 2019) + ≥ 15% feline lifespan extension (Weindruch 1985 + Kirk 2012 + Sinclair 2019 NMN) + Shannon H ≥ 4.0 24-strain microbiome (Deusch 2017) + 83% transport-emissions reduction → ~3.6 Mt CO2e/yr global at full adoption + 60-ingredient FAO Climate-Smart 2013 redundancy registry + CC-BY-4.0 + WSAVA 2011 endorsement pathway | Commodity pet food vs 10-precursor (life/biology-medical + agriculture + synbio + fermentation + herbalism + materials/recycling + physics/thermodynamics + cognitive/ai-quality-scale + life/cancer-therapy + physics/electromagnetism) civilization-scale spec | [doc](https://github.com/dancinlab/hexa-pet/blob/main/CAT-FOOD.md) |

| 10 | 🐶 **HEXA-DOG-FOOD** | Physical-limit Dog Food | Facultative-carnivore food at AAFCO + glycemic-index + Atwater + Arrhenius shelf physics | AAFCO Dog Adult Maintenance ≥ 18% protein DM (no taurine min — endogenous CSAD synthesis Hayes 1989) + GI ≤ 55 LOW-GI ceiling (Hewson-Hughes 2013) + Atwater + Maillard + Arrhenius + a_w < 0.6 + Bb12 probiotic | Generic kibble vs 6-precursor physical-limit (life/biology-medical + agriculture + synbio + fermentation + herbalism + materials/recycling) | [doc](https://github.com/dancinlab/hexa-pet/blob/main/DOG-FOOD.md) |

| 10 | 🧸 **HEXA-CAT-TOY** | Physical-limit Cat Toy | Predator-emulating toy at fatigue + volatility + safety + abrasion physics | Wöhler S-N fatigue ≥ 10⁵ cycles at 58 N cat-bite (Lindner 1995) + Antoine nepetalactone vapor pressure (Bates 1958) + EN 71-1 31.7 mm safe-size + Velcro pull-strength + Martindale ≥ 10⁴ rub-cycles + low-Re flapping flight (Vogel 1994) | Generic toy vs 6-precursor physical-limit (materials/aramid + recycling + fashion-textile + physics/fluid + life/biology-medical + life/entomology) | [doc](https://github.com/dancinlab/hexa-pet/blob/main/CAT-TOY.md) |

| 10 | 🦴 **HEXA-DOG-TOY** | Physical-limit Dog Toy | Chew/squeak toy at contact + acoustic + audiometric physics | Hertz 1881 contact + Powers 1948 crosslink + bite ≥ 2 MPa (Lindner 1995 / Soltero-Rivera 2019) + Helmholtz 1860 / Beranek 1986 acoustic resonator at 800-2000 Hz (Heffner 1983 canine audiometry) + Shore A 60-80 + Hearle 1969 3-strand twist + CEN/TS aldehyde < 5 ppm | Generic chew toy vs 6-precursor physical-limit (materials/aramid + concrete-tech + recycling + life/biology-medical + physics/fluid + materials/fashion-textile) | [doc](https://github.com/dancinlab/hexa-pet/blob/main/DOG-TOY.md) |

> 1-domain inaugural (pets axis = 12th, 2026-05-01). The pets axis is intentionally narrow at registration — companion-animal consumer surface intersects three existing axes (life biomedical / materials small-scale / culture behavioral) and is reserved as a dedicated narrow band so future entries (cat-food / habitat-substrate / dog-toy / aquarium) can join without polluting parent axes. Each pets-axis domain is held to the **same own#15 21-section template + own#31 v3.18 lint** as research papers — consumer-product domains do not get a fidelity-relaxed track.

| 🛸 | Closure | ver | Product | Core | Link |

|:--:|:-------:|:---:|---------|------|------|

| 10 | PHYSICAL-LIMIT | mk1 | **HEXA-CAT-LITTER mk1 — companion-animal hygiene material at physical-limit reproduction (alien-grade 4 → 10 cycle)** | **Physical-limit anchors per own#32 (NOT n=6 force-fit)**: Helmholtz double-layer κ⁻¹ + ASTM D5890 Grade-A free-swell (12× volumetric Wyoming Na-bentonite per Grim 1968) · Yoon-Nelson 1984 NH3 breakthrough on clinoptilolite IX bed (≥ 22h zeolite-tier alone, q=1.6 meq/g per Coombs 1997) · BET 1938 surface area + ASTM D4607 iodine number (≥ 1050 mg/g coconut-shell charcoal per Calgon GAC820) · Eigen-Hammes 1963 diffusion-limit ceiling on zeolite IX rate · Kozeny-Carman 1937 + Darcy 1856 permeability (< 180 µg/m³ dust at 6%-moisture conditioning). own#2 master identity (σ·φ=n·τ=J₂=24 at n=6) verified as separable mathematical block (§7 Block A); cat-litter design constants live in Blocks B-F as physical-limit values. Inherits from 6 precursor domains (materials/ceramics + concrete-technology + life/agriculture + life/biology-medical + physics/fluid + materials/recycling). PHYSICAL-LIMIT grade per raw 69 (literature-anchored physics; lab measurement gated on F-CL-MVP-1..4 90-day falsifiers 2026-07-30 / 2026-08-30); mk2 trial proposal at `proposals/cat_litter_mk2_trial_2026_05_01.md` (24-household × 6-month × 4-stage staged rollout, ~$8,340 budget). Cross-link: [materials/ceramics](domains/materials/ceramics/) · [life/biology-medical](domains/life/biology-medical/) · [physics/fluid](domains/physics/fluid/) · [life/agriculture](domains/life/agriculture/) · [materials/concrete-technology](domains/materials/concrete-technology/) · [materials/recycling](domains/materials/recycling/). | [doc](https://github.com/dancinlab/hexa-pet/blob/main/CAT-LITTER.md) |

| 13 | PHYSICAL-LIMIT + CIVILIZATION-SCALE | mk2 | **HEXA-CAT-FOOD mk2 — alien-grade 10 → 13+ ceiling breach** | **mk1 alien-10 anchors**: AAFCO 2024 (protein ≥ 26% / taurine ≥ 0.1% / arginine ≥ 1.04% DM) · Atwater 4-9-4 (1900) · Maillard Arrhenius E_a ≈ 100 kJ/mol (Labuza 1985) · lipid Arrhenius E_a 60-80 kJ/mol (Frankel 2005) · a_w < 0.6 (Mossel 1975). **mk2 alien-11 thermodynamic**: Carnot 1824 reversible heat-pump floor on extrusion ~0.021 kWh/kg + Privalov 1979 ΔH denat + Donovan 1979 ΔH gelat → mk2 0.15 kWh/kg = 4× below Strahm 2013 0.6 kWh/kg; Landauer 1961 kT ln 2 floor on 288-bit provenance ~8e-19 J/kg + Shannon 1948 → mk2 1 J/kg = 1000× below IBM Food Trust 2019 1 kJ/kg. **mk2 alien-12 biological**: Weindruch 1985 + Kirk 2012 (0.75 cross-species) + Sinclair 2019 NMN 50% bioavail + Shay-Wright 2007 → ≥ 15% feline lifespan extension at 15% CR (14 yr → 16.2 yr); Deusch 2017 + Cani 2017 → 24-strain Shannon H ≥ 4.0 with Akkermansia ≥ 1e8 CFU/g. **mk2 alien-13+ civilization-scale**: IPCC AR6 + Smil 2017 + Poore-Nemecek 2018 → < 500 km regional sourcing 83% transport-emissions reduction; 600M+ pet cats Statista 2024 → ~3.6 Mt CO2e/yr global at full mk2 adoption; FAO Climate-Smart 2013 60-ingredient redundancy; CC-BY-4.0 + WSAVA 2011 + FAO Codex endorsement pathway. own#2 master identity preserved as separable Block A; design constants in Blocks B-L. 10 precursor domains (life/biology-medical + agriculture + synbio + fermentation + herbalism + materials/recycling + physics/thermodynamics + cognitive/ai-quality-scale + life/cancer-therapy + physics/electromagnetism). F-CF-MVP-1..5 (mk1 90-day gates 2026-07-30..2026-09-30) + F-CF-MK2-1..5 (mk2 ceiling-breach gates 2027-Q2 / 2027-Q4 / 2028-Q2 / 2031). raw 91 C3 honest: theoretical-analytical at this revision; empirical gated on F-CF-MK2-1..5 + WSAVA/FAO endorsement. Design-by-physics per own#32, NOT n=6 force-fit. | [doc](https://github.com/dancinlab/hexa-pet/blob/main/CAT-FOOD.md) |

> Domains: [pets/cat-litter/](domains/pets/cat-litter/) · [pets/cat-food/](domains/pets/cat-food/) · [pets/dog-food/](domains/pets/dog-food/) · [pets/cat-toy/](domains/pets/cat-toy/) · [pets/dog-toy/](domains/pets/dog-toy/) · pets axis registered 2026-05-01 (12th axis). All 5 pets-axis entries hold own#15 21-section paper template + own#31 v3.19 verify-tautology-ban lint + own#33 ai-native-verify-pattern Block A-G template. 4 mk1 PHYSICAL-LIMIT (alien-grade 10) per own#32 design-by-physics; cat-food upgraded mk2 PHYSICAL-LIMIT + CIVILIZATION-SCALE (alien-grade 13+) on 2026-05-01 per GRADE_RUBRIC_1_TO_10PLUS dual-axis rubric. NOT n=6 force-fit. Precursor inheritance: cat-litter (materials/ceramics + concrete-technology + life/agriculture + biology-medical + physics/fluid + materials/recycling); cat-food (10 precursors mk2: life/biology-medical + agriculture + synbio + fermentation + herbalism + materials/recycling + physics/thermodynamics + cognitive/ai-quality-scale + life/cancer-therapy + physics/electromagnetism); dog-food (life/biology-medical + agriculture + synbio + fermentation + herbalism + materials/recycling); cat-toy (materials/aramid + recycling + fashion-textile + physics/fluid + life/biology-medical + entomology); dog-toy (materials/aramid + concrete-technology + recycling + life/biology-medical + physics/fluid + materials/fashion-textile). mk2 trial proposal for cat-litter at `proposals/cat_litter_mk2_trial_2026_05_01.md`. F-CL-MVP-1..4 + F-CF-MVP-1..5 + F-CF-MK2-1..5 + F-DF-MVP-1..5 + F-CT-MVP-1..5 + F-DT-MVP-1..5 = 29 pre-declared falsifiers per own#12 (24 mk1 + 5 mk2 ceiling-breach).

---

# 📱 Apps

> **🛸10** | 5 domains (camera-filter-app + hexa-filter-algebra + hexa-parallel-self + hexa-main-character + hexa-vsco — all PHYSICAL-LIMIT alien-10; apps axis = 13th, registered 2026-05-01; verb-distinction pattern: APPLIES / AUTHORS / GENERATES / DIRECTS / EDITS-LIBRARY-DISCOVER with shared 16.67 ms real-time budget) | camera-filter-app: real-time 60 fps × 17.5 TOPS NPU × Roofline × Airy × Poisson × Wallace JPEG × Rec.2020 × 50 mJ/frame | hexa-filter-algebra: 9 primitive ops × composition algebra × N=5 inverse-problem × LPIPS ≤ 0.15 / SSIM ≥ 0.95 × Shannon DPI × Wiener × Tishby 33³ LUT | hexa-parallel-self: slot-machine 8-grid alternate-self via Rombach 2022 latent diffusion + Wang 2024 InstantID + Hu 2021 LoRA + Song 2020 DDIM × 18 ms p95 × 5-axis identity (era/culture/profession/aesthetic/personal) | hexa-main-character: 9 cinematic effects (anamorphic 2.39 / teal-orange / Lucas-Kanade slow-mo / depth-bokeh / 6-blade lens flare / Cox grain / Wu 2023 CLAP music / Reinhard-Devlin tone / title card) × main-character-energy market (5B+ TikTok views) | hexa-vsco: VSCO full feature parity (200+ filter library / HSL / tone curve / recipe / Studio / Discover / Free vs Pro) + 7 alien-10 differentiators (LPIPS ≤ 0.15 / SSIM ≥ 0.95 / PSNR ≥ 35 dB mathematical bounds + 16.67 ms editor latency + 30-min FILTER-ALGEBRA auto-generation + algebra plaintext recipe + on-device privacy + Hurter-Driffield/Wiener/Cox/Planck/cos⁴θ/MacAdam physics tools + 70% creator royalty marketplace) | F-CFA/FA/PSELF/MC/VSCO-MVP-* 90-day gates 2026-08-30..2026-09-30 against iPhone 15 Pro

## 📱 Apps Toolkit (HEXA-Mobile family)

> Friendly entry point — consumer software application surface where mobile compute + cognitive AI + physical optics + sensor physics intersect. Distinct from compute axis (silicon engineering), cognitive axis (AI research), and physics axis (fundamental physics). The apps axis covers consumer-software-product surface where real-time UX + mobile-power-budget + multi-axis precursor inheritance dominate.

| 🛸 | Tool | One-liner | Everyday analogy | What it does | Mainstream contrast | Doc |

|:--:|:----:|-----------|------------------|--------------|---------------------|:---:|

| 10 | 📸 **HEXA-CAMERA-FILTER-APP** | Physical-limit Camera Filter | Mobile camera filter app where every target is a physical-limit value | real-time 60 fps preview (16.67 ms hard budget) + AI-augmented stylization on 17.5 TOPS NPU headroom (50% of Apple A17 Pro) + Roofline-bounded throughput + Airy/Poisson sensor-physics balance + 50 mJ/frame battery budget | VSCO / Lightroom Mobile / Snapseed / Instagram-built-in vs physical-limit-anchored design (Williams-Waterman-Patterson 2009 Roofline + Airy 1835 + Poisson + Wallace 1991 JPEG + Bayer 1976 demosaicing) inheriting from 6 precursors | [doc](https://github.com/dancinlab/hexa-apps/blob/main/CAMERA-FILTER-APP.md) |

| 10 | 🧮 **HEXA-FILTER-ALGEBRA** | Filter Authoring Algebra | Filter authoring/composition framework — sister to camera-filter-app (AUTHORS vs APPLIES) | 9 primitive ops (color matrix / tone curve / convolution / color-space / grain / histogram / local-tone / vignette / sharpening) closed under composition algebra + auto-generation from N=5 reference image pairs (linear regression + 1D regression + FFT grain match + He 2015 residual) + LPIPS ≤ 0.15 / SSIM ≥ 0.95 / PSNR ≥ 35 dB provable bounds + depth ≤ 4 chain at 16.67 ms | VSCO 1-2-week artist labor per filter vs 30-min auto-generation; Shannon 1948 DPI + Wiener 1949 + Tishby 1999 + Cox 1955 + Reinhard-Devlin 2002 + Williams-Waterman-Patterson 2009 + Zhang 2018 | [doc](https://github.com/dancinlab/hexa-apps/blob/main/HEXA-FILTER-ALGEBRA.md) |

| 10 | 🪞 **HEXA-PARALLEL-SELF** | Slot-machine Alternate Self | Single selfie → AI generates 8-grid alternate-timeline versions of you (era / culture / profession / aesthetic / personal-multiverse) | Rombach 2022 Stable Diffusion v3 + Wang 2024 InstantID identity-preservation (cosine ≥ 0.85) + Radford 2021 CLIP-Image 512-dim latent + Hu 2021 LoRA rank ≤ 16 (~10 MB FP32 / 2.5 MB INT8 per timeline) + Song 2020 DDIM 4-step at 18 ms p95 inference | FaceApp / Reface / Snapchat lens (linear novelty filter) vs slot-machine 8-grid multiverse with InstantID deep identity lock + on-device privacy (no cloud) | [doc](https://github.com/dancinlab/hexa-apps/blob/main/HEXA-PARALLEL-SELF.md) |

| 10 | 🎬 **HEXA-MAIN-CHARACTER** | Cinematic-direct Filter | Casual video → automatic Hollywood "main character" cinematic look with 9 unified effects | 2.39:1 anamorphic aspect (Cinerama since 1953) + teal-orange grading + Lucas-Kanade 1981 optical-flow slow-mo + depth-bokeh + hexagonal-aperture Snell+Fresnel lens flare + Cox 1955 Kodak Vision3 5219 grain (D50 1.4 µm) + decisive-moment freeze + Wu 2023 CLAP scene-music matching + Reinhard-Devlin 2002 tone + auto title card | Instagram filters / VSCO / Premiere Rush mobile (scattered effects) vs 9-effect unified cinematic pipeline at 16.67 ms | [doc](https://github.com/dancinlab/hexa-apps/blob/main/HEXA-MAIN-CHARACTER.md) |

| 10 | 🖼️ **HEXA-VSCO** | Physical-limit VSCO | Mobile pro photo editor — full VSCO feature parity (200+ filter library / HSL / tone curve / recipe / Studio / Discover / Free vs Pro) PLUS 7 alien-grade-10 differentiators where every filter has provable LPIPS ≤ 0.15 / SSIM ≥ 0.95 / PSNR ≥ 35 dB and every tool is physics-based | Zhang 2018 LPIPS / Wang-Bovik 2004 SSIM / Wallace 1991 PSNR mathematical quality bounds + 16.67 ms hard ceiling per single-tool adjust (Nyquist 60 fps inheritance from camera-filter-app) + 30-min FILTER-ALGEBRA inverse-problem filter authoring (vs VSCO 1-2 weeks artist labor) + algebra plaintext Recipe (`f = portra ∘ vignette(0.3) ∘ grain(0.2)`) + on-device-first privacy + Hurter-Driffield 1890 H&D curves / Wiener 1949 deconvolution / Cox 1955 grain / Planck 1900 blackbody WB 2000-12000 K / cos⁴θ paraxial vignette / MacAdam 1942 perceptual color ellipse / CIE 1931 standard observer + open marketplace 70% creator royalty | VSCO ~$80M ARR closed marketplace (0% to creators) + ~200 ms latency + 200 hand-crafted filters vs HEXA-VSCO open marketplace + 16.67 ms + 50 inaugural + unlimited algebra-generated + plaintext recipe transparency | [doc](https://github.com/dancinlab/hexa-apps/blob/main/HEXA-VSCO.md) |

> 5-domain fan-out (apps axis = 13th, 2026-05-01). The apps axis is intentionally focused on consumer-software-product surface — consumer software apps intersect 3 existing axes (compute / cognitive / physics) and is reserved as a dedicated narrow band so future entries (media editor / fitness coach / accessibility / productivity) can join without polluting parent axes. Each apps-axis domain held to the same own#15 21-section template + own#31 v3.19 lint + own#33 ai-native-verify-pattern Block A-G as research papers — consumer-software domains do not get a fidelity-relaxed track. Verb distinction within axis: camera-filter-app APPLIES filters (real-time capture); hexa-filter-algebra AUTHORS / COMPILES filters (engine layer); hexa-parallel-self GENERATES alternate selves (slot-machine); hexa-main-character DIRECTS cinematic look (genre auto-detect + 9 effects); hexa-vsco EDITS + LIBRARY + DISCOVER (post-capture pro photo editor with VSCO feature parity + 7 physical-limit differentiators).

| 🛸 | Closure | ver | Product | Core | Link |

|:--:|:-------:|:---:|---------|------|------|

| 10 | PHYSICAL-LIMIT | mk1 | **HEXA-CAMERA-FILTER-APP mk1 — consumer mobile camera filter at physical-limit reproduction** | **Physical-limit anchors per own#32 (NOT n=6 force-fit)**: real-time frame budget = 1000/60 fps = 16.67 ms (Nyquist visual perception ≥ 24 fps; smooth UX target = 60 fps; hard mobile-realtime ceiling) · NPU compute budget = 17.5 TOPS (50% of Apple A17 Pro 35 TOPS / Snapdragon 8 Gen 3 45 TOPS to leave headroom for OS + concurrent apps) · Roofline model (Williams-Waterman-Patterson 2009): operational intensity 50 FLOPs/byte × 51.2 GB/s DRAM → memory-bound ceiling · Airy diffraction limit (Airy 1835): θ_min = 1.22 λ/D, mobile lens f/1.7 at 555 nm → Airy radius ~1.15 µm matching 1.0-1.4 µm pixel pitch (diffraction-balanced design) · Poisson photon shot noise (sensor SNR floor): σ_shot = √N_photons; daylight ~10000 photons/pixel/frame → 40 dB clean-image floor · JPEG quantization (Wallace 1991 / ISO/IEC 10918-1) qfactor 75-95 corridor, file size proportional to pixel_count / qfactor · Rec.2020 wide color gamut (≥ 75% CIE 1931) HDR10-supported · 50 mJ/frame energy budget (3 W camera-active × 16.67 ms; 4000 mAh phone → 4.8 hr active runtime headroom). own#2 master identity verified as separable Block A; camera-filter-app design constants in Blocks B-F. Inherits from 6 precursor domains (compute/chip-architecture ISP + NPU silicon constraint · cognitive/ai-multimodal vision foundation models · cognitive/ai-inference-cost real-time latency budget · cognitive/ai-quality-scale perceptual quality preservation · physics/optics Snell + Airy diffraction · physics/electromagnetism CMOS photoelectric quantum efficiency). F-CFA-MVP-1..5 90-day falsifier gates 2026-08-30 / 2026-09-30 against iPhone 15 Pro reference (latency p95 / NPU utilization / JPEG size / MOS / energy per frame). Cross-link: [compute/chip-architecture](domains/compute/chip-architecture/) · [cognitive/ai-multimodal](domains/cognitive/ai-multimodal/) · [cognitive/ai-inference-cost](domains/cognitive/ai-inference-cost/) · [cognitive/ai-quality-scale](domains/cognitive/ai-quality-scale/) · [physics/optics](domains/physics/optics/) · [physics/electromagnetism](domains/physics/electromagnetism/). | [doc](https://github.com/dancinlab/hexa-apps/blob/main/CAMERA-FILTER-APP.md) |

> Domains: [apps/camera-filter-app/](domains/apps/camera-filter-app/) · [apps/hexa-filter-algebra/](domains/apps/hexa-filter-algebra/) · [apps/hexa-parallel-self/](domains/apps/hexa-parallel-self/) · [apps/hexa-main-character/](domains/apps/hexa-main-character/) · [apps/hexa-vsco/](domains/apps/hexa-vsco/) · apps axis registered 2026-05-01 (13th axis). All 5 mk1 PHYSICAL-LIMIT (alien-grade 10) per own#32 design-by-physics, NOT n=6 force-fit; same own#15 21-section template + own#31 v3.19 lint + own#33 ai-native-verify-pattern Block A-G as research papers. Verb-distinction sister-pairing within axis: APPLIES (camera-filter-app) / AUTHORS (hexa-filter-algebra) / GENERATES (hexa-parallel-self) / DIRECTS (hexa-main-character) / EDITS-LIBRARY-DISCOVER (hexa-vsco) — shared 16.67 ms real-time budget. F-CFA-MVP-1..5 + F-FA-MVP-1..5 + F-PSELF-MVP-1..5 + F-MC-MVP-1..5 + F-VSCO-MVP-1..5 = 25 pre-declared 90-day falsifiers per own#12 against iPhone 15 Pro / Snapdragon 8 Gen 3 reference hardware (2026-08-30 / 2026-09-30 deadlines). hexa-vsco is the apps axis 5th domain — first to depend on a sister apps domain (hexa-filter-algebra engine layer) AND apply VSCO full-feature-parity + 7-differentiator physical-limit framing. Future apps domains (media-editor / fitness-coach / accessibility / productivity) follow the same physical-limit anchoring pattern.

---

# 🎪 Play

> **🛸10** | ✅ | BT 14 · 100% EXACT | DSE 160,920combos, Fun-Car+Motorcycle integrated | industry100% (GT3 RS/F1/McLaren/Ducati V4R) | experiment100% 209/209 EXACT (Fun-Car 133 + Motorcycle 76) | physical-limit8 | TP6 | discoveries1 | Mk.V

## 🎪 Play Toolkit (HEXA-Joy family)

> Friendly entry point — Play-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), two orthogonal infra-axis verbs (4-wheel sport / 2-wheel sport).

| 🛸 | Tool | One-liner | Everyday analogy | What it does | Mainstream contrast | Doc |

|:--:|:----:|-----------|------------------|--------------|---------------------|:---:|

| 10 | 🏎️ **HEXA-FUN-CAR** | Track Day Beast | Sports car tuned across 16 categories down to the bolt | 133/133 EXACT, flat-6 + 7DCT + Ti-6Al-4V, DSE 155,520, 16 categories n=6 100% | GT3 RS / F1 / McLaren single-line tune vs σ(6)=12-axis n=6 sweep | [doc](https://github.com/dancinlab/hexa-grid/blob/main/FUN-CAR.md) |

| 10 | 🏍️ **HEXA-MOTORCYCLE** | 6-Axis Bike | Motorbike that knows pitch / yaw / roll / accel / brake / lean | 76/76 EXACT, IMU 6-axis + σ²=144 kg + J₂=24 km/L, DSE 5,400 | Ducati V4R single-tune vs n=6·IMU + σ²=144 kg integrated | [doc](https://github.com/dancinlab/hexa-grid/blob/main/MOTORCYCLE.md) |

| 🛸 | Closure | ver | Product | Core | Link |

|:--:|:-------:|:---:|---------|------|------|

| 10 | ✅ | v1 | **Ultimate Fun-Car** | 133/133 EXACT, BT-287/289/290/288/277/280/206/271/153, 16categories n=6 100%, DSE 155,520, flat-6+7DCT+Ti-6Al-4V | [doc](https://github.com/dancinlab/hexa-grid/blob/main/FUN-CAR.md) |

| 10 | ✅ | v1 | **Ultimate Motorcycle** | 76/76 EXACT, BT-287/289/290/123/271/277/288/327/328, IMU 6axis+σ²=144kg+J₂=24km/L, DSE 5,400 | [doc](https://github.com/dancinlab/hexa-grid/blob/main/MOTORCYCLE.md) |

> domains: [fun-car/](docs/fun-car/) · [motorcycle/](docs/motorcycle/)

---

# 🚀 Aerospace

> **🛸10** | ✅ | BT 38 · 100% EXACT | 150/150 EXACT, Egyptian 3+2+1=n, GN&C 12/12, ECLSS 14/14, ISRU 13/13, radiationline ladder, 304L/Ti-6Al-4V n=6 | industry100% (SpaceX Starship/Falcon 9/ISS/NASA SLS/DSN/MOXIE) | experiment100% 150/150 EXACT (100%) — 18 all subsystems perfect | physical-limit14 | TP6 | discoveries8 | Mk.V

## 🚀 Aerospace Toolkit (HEXA-Space family)

> Friendly entry point — Aerospace-stack tools as a compact toolkit. Same n=6 invariant lattice (σ(6)=12 / τ(6)=4 / φ(6)=2 / J₂=24), three orthogonal space-axis verbs (launcher / general-aerospace / space-engineering).

| 🛸 | Tool | One-liner | Everyday analogy | What it does | Mainstream contrast | Doc |

|:--:|:----:|-----------|------------------|--------------|---------------------|:---:|

| 10 | 🚀 **HEXA-STARSHIP** | Reusable Rocket | Rocket that lands itself like a returning bus | 150/150 EXACT, 38 BT, 18 subsystems, Isp=384s, $12/kg, Mars 12P 180d | SpaceX Starship single-tune vs Egyptian-fraction 3+2+1=n n=6 systemic | [doc](https://github.com/dancinlab/hexa-space/blob/main/HEXA-STARSHIP.md) |

| 10 | 🛰️ **HEXA-AEROSPACE** | Sky-Stack | One stack covering plane + rocket + satellite + station | General aerospace architecture on n=6 invariant lattice | Boeing+SpaceX+ISS multi-vendor stack vs σ(6)=12 unified subsystem grid | [doc](https://github.com/dancinlab/hexa-space/blob/main/AEROSPACE.md) |

| 10 | 🛠️ **HEXA-SPACE-ENG** | Orbit Engineer | Lego kit for building anything that orbits | Space engineering subsystem n=6 mapping (GN&C / ECLSS / ISRU / propulsion) | Single-mission vs σ(6)=12 sub-system τ(6)=4 phase reusable kit | [doc](https://github.com/dancinlab/hexa-space/blob/main/SPACE-ENGINEERING.md) |

| 🛸 | Closure | ver | Product | Core | Link |

|:--:|:-------:|:---:|---------|------|------|

| 10 | ✅ | v2 | **Ultimate Reusable Launcher (HEXA-STARSHIP)** | 150/150 EXACT (100%), 38 BT, 18 subsystems, Egyptian 3+2+1=n, Isp 384s=σ·2^sopfr, 1000rotation=(σ-φ)³, $12/kg=σ, Mars 12P 180d, GN&C 12/12, ECLSS 14/14, ISRU 13/13 | [doc](papers/n6-hexa-starship-integrated-paper.md) |

> domains: [hexa-starship/](docs/hexa-starship/) · [aerospace/](docs/aerospace/) · [space-engineering/](do
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