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1794299a6c
Systematic native_decide → dec_trivial/rfl migration across all Lean modules to comply with AGENTS.md rule 5 (no native_decide unless only option): - CoreFormalism: BraidEigensolid, BraidField, ChentsovFinite, HachimojiBase, HachimojiBridging, HachimojiCodec, HachimojiLUT, HachimojiManifoldAxiom, Q16_16Numerics - BindingSite: BindingSiteCodec, BindingSiteEntropy, BindingSiteHachimoji - SilverSight: ProductSchema, ProductWireFormat, PolyFactorIdentity, Schema, WireFormat - PVGS_DQ_Bridge: all three files (native_decide->dec_trivial) - UniversalEncoding/ChiralitySpace Additional changes: - gemma4_mcp.py: upgraded to two-tier routing (local Gemma4 + FreeLLMAPI proxy) - ChentsovFinite: added traceability map and Chentsov (1972) citation - HachimojiBase: renamed Σ→Sig, Π→Pi to avoid non-ASCII issues - Import path fixes for Mathlib 4.30.0-rc2 compatibility - Doc updates: PURE_FORMULAS, SOS_CERTIFICATE, fundamental math derivations - Build log: 2026-06-26 session findings - BRKGLASS_NR_BRACKET_PROPOSAL: updated to REAL-DATA VALIDATED status - New docs: FOUNDATIONAL_GUIDANCE, PURE_EQUATION_MAP, CHENTSOV_FINITE_MATH, BREAKGLASS_FUSION_REVIEW_SPEC, COLD_REVIEWER_FORMULA - New python: phi pipeline (equation_dna_encoder, ast_parse, charclass, consistency, embed, output), nr_bracket_validation with receipt Build: lake build SilverSightRRC — passes on all committed modules. Excluded: HachimojiN8Bridge, HachimojiCharClass (missing CoreFormalism.HachimojiManifoldAxiom olean — WIP)
91 lines
2.2 KiB
Markdown
91 lines
2.2 KiB
Markdown
# SilverSight — Pure Mathematical Formulas
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No English. No code. Minimum notation only.
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---
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## 1. Sidon
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$$A \subset \mathbb{Z},\quad a+b=c+d \implies \{a,b\}=\{c,d\}$$
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$$A_8 = \{2^i\}_{i=0}^7$$
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$$h(N) = \max|A|,\quad A \subseteq \{1,\ldots,N\} \text{ Sidon}$$
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$$h(N) \leq \lfloor\sqrt{2N}\rfloor + 1$$
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$$S_p = \{x \in \mathbb{F}_{p^3}^\times / \mathbb{F}_p^\times : \text{Tr}(x)=0\},\quad |S_p|=p+1,\quad p \text{ prime}$$
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**Fisher note:** \(\Delta_7\) denotes the **open** simplex \(\{p \in \mathbb{R}^8 : p_i > 0,\; \sum p_i = 1\}\). All Fisher metric formulas require this domain (\(p_i > 0\)).
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---
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## 2. Braid
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$$C \in \{0,\tfrac{1}{4},\tfrac{1}{2},\tfrac{3}{4}\}^{8\times 8}$$
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$$\varepsilon_{ij} = C_{ij}(\phi_i - \phi_j)$$
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$$\text{crossStep}(s) = s \iff s \in \text{Eigensolid}$$
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---
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## 3. Spectral
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$$\text{active}(s) = \{i : s_i \neq 0\}$$
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$$\text{gap}(s) = \bigwedge_{i,j \in \text{active}(s)} (i=j \lor |i-j|>1)$$
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$$\text{merge}(s,e)_i = \min(1, s_i+e_i)$$
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$$\text{res}(s,e) = |\{i : s_i \neq 0 \land e_i \neq 0\}|$$
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$$\text{cross}(s,e) = \bigwedge_{i} \neg(s_i \neq 0 \land e_{i+1} \neq 0) \land \neg(e_i \neq 0 \land s_{i+1} \neq 0)$$
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$$\text{gap}(s) \land \text{gap}(e) \land \text{res}(s,e)=0 \land \text{cross}(s,e) \implies \text{gap}(\text{merge}(s,e))$$
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---
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## 4. Byte
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$$\text{byteGap}(n) = (n \land (n \gg 1)) = 0$$
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$$\text{pack}(s) = \sum_{i=0}^{7} [s_i \neq 0] \cdot 2^i$$
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$$\text{byteGap}(\text{pack}(s)) = \text{gap}(s)$$
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---
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## 5. Chiral
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$$q = q_r + \varepsilon q_d,\quad \varepsilon^2 = 0$$
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$$\chi = \frac{|q_r|^2}{|q_r|^2 + |q_d|^2},\quad |q_r|^2 + |q_d|^2 > 0$$
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$$\chi > \frac{1}{2} \implies \text{compressive}$$
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$$\chi < \frac{1}{2} \implies \text{anti-compressive}$$
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$$\chi = \frac{1}{2} \implies \text{critical balance}$$
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---
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## 6. Q16_16
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$$\text{Q16}(x) = \text{clamp}(-2^{31}, \lfloor x \cdot 2^{16} \rfloor, 2^{31}-1)$$
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$$\text{Q16}(1) = 65536$$
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$$\text{Q16}(0) = 0$$
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$$a \oplus b = \text{clamp}(-2^{31}, a+b, 2^{31}-1)$$
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$$a \otimes b = \text{clamp}(-2^{31}, \lfloor ab/2^{16} \rfloor, 2^{31}-1)$$
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---
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## 7. Verification Protocol
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$$\text{define} \to \text{compute} \to \text{verify} \to \text{claim}$$
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$$\text{verify} = \text{false} \implies \text{formula wrong}$$
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