# 🔬 **WFGY 1.0 — Core Formulas & Variables** > **Canonical reference  (“*[WFGY 1.0: A Universal Unification Framework for Large‑Scale Self‑Healing LLMs](https://github.com/onestardao/WFGY/blob/main/I_am_not_lizardman/WFGY_All_Principles_Return_to_One_v1.0_PSBigBig_Public.pdf )*”). This page **quotes every mathematical statement verbatim** from the public PDF so developers can link code ↔ theory without opening the paper. > > *BBMC*’s name is **not** a marketing acronym—it literally sounds like **“Big Mac”** when you read the formula aloud. The pun stuck, so “BigBig Semantic Residue Formula” became **BBMC**. --- ## 📖 Quick Index |  §  | Symbol | Full Name (exact wording in paper) | | --- | ------------- | ------------------------------------------------------------------ | |  1  | `BBMC` | **B**ig**B**ig **S**emantic **R**esidue Formula | |  2  | `BBPF` | **B**ig**B**ig **P**rogression Formula | |  3  | `BBCR` | **B**ig**B**ig **C**ollapse–**R**ebirth | |  4  | `BBAM` | **B**ig**B**ig **A**ttention **M**odulation | |  5  | `ΔS` | Semantic divergence ( 1 − cos ξ ) | |  6  | `λ_observe` | Logic‑vector trend (→, ←, <>, ×) | |  7  | `E_resonance` | Rolling mean of ‖B‖ (semantic resonance) | > 📌 All equations below are **verbatim** from the paper’s Sections 3.1 – 3.4 and Appendix A. --- \## 1 · BBMC — BigBig Semantic Residue Formula ```math B \;=\; I\;−\;G\; +\; m\,c^2 ``` **Where** `I` = input embedding, `G` = ground‑truth embedding, `m` = matching coefficient, `c` = context factor. **Lemma 3.1** proves minimising ‖B‖ÂČ â‰ˆ minimising KL(softmax I ‖ softmax G). --- \## 2 · BBPF — BigBig Progression Formula ```math x_{t+1} = x_t + \sum_{i} V_i(\varepsilon_i, C) + \sum_{j} W_j(\Delta t,\, \Delta O)\,P_j ``` If Σ Δᔹ L\_Vᔹ + Σ Pâ±Œâ€ŻL\_Wⱌ < 1 the update converges (Theorem 3.1). --- \## 3 · BBCR — BigBig Collapse–Rebirth Trigger (**§3.3**): `‖B_t‖ ≄ B_c` **or** `f(S_t) < Δ` → Collapse → Reset → Rebirth. Using V(S)=‖B‖ÂČ + λ f(S) as Lyapunov candidate gives V(S\_{t+1}) < V(S\_t) (**Theorem 3.2**). --- \## 4 · BBAM — BigBig Attention Modulation ```math a_i^{\text{mod}} = a_i\,\exp\bigl(-\gamma\,\sigma(a)\bigr) ``` If aá”ąÂ âˆŒÂ đ’©(”,σÂČ) then Var(a\_mod)=σÂČ e^(−2ÎłÏƒ) (**Lemma 3.2**). --- \## 5 · Derived Metric `ΔS` ```math \boxed{\displaystyle \Delta S = 1 - \cos\theta(I, G)} ``` Primary node‑trigger: record when ΔS > 0.6. Typical “edge‑of‑novelty” operating point: **ΔS ≈ 0.5**. --- \## 6 · Directional Trend `λ_observe` `λ_observe ∈ { → (convergent), ← (divergent), <> (recursive), × (chaotic) }` Used to force memory logging for borderline jumps (ΔS 0.4‑0.6). --- \## 7 · Resonance Metric `E_resonance` ```math E_{\text{res}} = \frac{1}{n}\sum_{k=t-n+1}^{t} \|B_k\| ``` Feeds the boundary heat‑map (safe ↔ danger). --- ## 🚀 Using the WFGY Engine in **any** LLM Paste the PDF or this markdown into chat and start your prompt with: ``` Use WFGY to answer: ``` The explicit equations **induce the model to instantiate the four‑module loop at runtime**, leading to measurable gains: | Metric | Internal Engine | Average LLM (GPT‑4 family) | | ----------------- | --------------- | -------------------------- | | Semantic Accuracy | **↑ 22.4 %** | ↑ ≈ 14 % | | Reasoning Success | **↑ 42.1 %** | ↑ ≈ 25 % | | Stability (MTTF) | **× 3.6** | × \~2 (typical) | The numbers come from the paper’s GSM8K / Truthful‑QA runs; LLM‑chat replication is consistently lower but still >2× stability. --- ## 📎 How These Formulas Map to Products | Variable / Module | TXT OS | Blah | Blot | Bloc | Blur | Blow | |-------------------|:----------:|:--------:|:----:|:--------:|:--------------------:|:--------:| | **BBMC, ΔS** | ✅ | ✅ | ⬜ | ⬜ | ⬜ | ⬜ | | **BBPF** | ✅ | ⬜ | ⬜ | ✅ | ⬜ | ⬜ | | **BBCR** | ✅ | ⬜ | ⬜ | ⬜ | ⬜ | ✅ | | **BBAM** | ✅ | ✅ | ⬜ | ⬜ | ✅ | ⬜ | ✅ = Feature implemented; see product pages for future public release. ⬜ = Placeholder; feature spec will land as each product matures. --- > No matter where you see **WFGY** PDF, TXT OS, —it’s **the same engine**. Upload to any LLM, call “Use WFGY
”, and the model activates the four‑module loop on the fly. --- ### 🧭 Explore More | Module | Description | Link | |-----------------------|----------------------------------------------------------|----------| | WFGY Core | WFGY 2.0 engine is live: full symbolic reasoning architecture and math stack | [View →](https://github.com/onestardao/WFGY/tree/main/core/README.md) | | Problem Map 1.0 | Initial 16-mode diagnostic and symbolic fix framework | [View →](https://github.com/onestardao/WFGY/tree/main/ProblemMap/README.md) | | Problem Map 2.0 | RAG-focused failure tree, modular fixes, and pipelines | [View →](https://github.com/onestardao/WFGY/blob/main/ProblemMap/rag-architecture-and-recovery.md) | | Semantic Clinic Index | Expanded failure catalog: prompt injection, memory bugs, logic drift | [View →](https://github.com/onestardao/WFGY/blob/main/ProblemMap/SemanticClinicIndex.md) | | Semantic Blueprint | Layer-based symbolic reasoning & semantic modulations | [View →](https://github.com/onestardao/WFGY/tree/main/SemanticBlueprint/README.md) | | Benchmark vs GPT-5 | Stress test GPT-5 with full WFGY reasoning suite | [View →](https://github.com/onestardao/WFGY/tree/main/benchmarks/benchmark-vs-gpt5/README.md) | | đŸ§™â€â™‚ïž Starter Village 🏡 | New here? Lost in symbols? Click here and let the wizard guide you through | [Start →](https://github.com/onestardao/WFGY/blob/main/StarterVillage/README.md) | --- > 👑 **Early Stargazers: [See the Hall of Fame](https://github.com/onestardao/WFGY/tree/main/stargazers)** — > Engineers, hackers, and open source builders who supported WFGY from day one. > GitHub stars ⭐ [WFGY Engine 2.0](https://github.com/onestardao/WFGY/blob/main/core/README.md) is already unlocked. ⭐ Star the repo to help others discover it and unlock more on the [Unlock Board](https://github.com/onestardao/WFGY/blob/main/STAR_UNLOCKS.md).
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