mirror of
https://github.com/zooai/proofs.git
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zooqueenandHanzo Dev
d3bff5e2dc
The lean/ proof library (88 files) had ~180 type-check errors across ~45 files plus 31 proof-by-assumption axiom cheats. It now type-checks cleanly under Lean 4.14.0 + Mathlib, with every theorem genuinely proven from definitions. Errors fixed: - Stale Mathlib imports: Data.Nat.Basic / Data.Int.Basic were removed this rev -> Data.Nat.Defs / Data.Int.Defs (57 files). - Shared AI/Agent/Governance/Contract/DeFi/Ecology draft files: same proof-rot as the zoo-labs sibling library (now reconciled): omega missing in-scope bounds, dead tactics after simp, simp over-reduction, doc-comment placement, reserved-word binders, deriving Repr on Finset-bearing structs, noncomputable defs over opaque primitives. - Consensus/Liveness: collapsed a 74-error cascade (undefined shared state model inlined from Safety.lean; the |>. pipe-projection vs comparison parse trap on 14 lines rewritten to explicit dot projection). - Crypto (BLS/FROST/Corona/Hybrid/threshold/FHE), Consensus, Protocol, Warp, Trust, GPU, Compute, Network, DeFi: brought structure invariants into scope for omega, Nat-division bounds via Nat.div_le_of_le_mul / Nat.div_mul_le_self, noncomputable over opaque crypto ops, deriving Inhabited for index access. Integrity: - Removed all 31 `theorem X := X_ax` cheats (axiom asserting the identical statement) and proved each from definitions; removed the UNSOUND content_addressed axiom (hash-injectivity over a struct with free fields). - Quorum-intersection theorems (BFT/Quasar/Flare/Warp/BLS/GPU/Bridge): the draft hypothesis 3f<n is insufficient (n unbounded above makes them false); tightened to the optimal-resilience invariant n=3f+1 / 2t>n. Statement intent preserved. - Net axiom change: -35 / +1 (the one addition, honesty_static, is a fixed-validator-set modeling assumption matching sibling files). - Remaining axioms are trusted-base only: opaque crypto primitives (groups, pairings, hardness, hashes, FHE encrypt/decrypt, BLS soundness, forward secrecy, Fisher-Yates uniformity) and protocol modeling assumptions. No sorry/admit/native_decide. Verified all theorems trace to [propext, Classical.choice, Quot.sound] plus those primitives. Co-authored-by: Hanzo Dev <[email protected]>
70 lines
2.1 KiB
Lean4
70 lines
2.1 KiB
Lean4
/-
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Authors: Antje Worring, Zach Kelling
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Embedding Correctness (7680-dimensional)
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Vector embeddings for semantic search and RAG.
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Zoo uses 7680-dimensional embeddings for maximum resolution.
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Maps to:
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- zoo/papers/embedding-7680.tex: embedding specification
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- hanzo/engine: embedding inference
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- zoo/node: embedding storage
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Properties:
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- Dimensionality: 7680 dimensions (highest resolution)
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- Normalization: unit-length vectors for cosine similarity
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- Determinism: same input → same embedding
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- Batching: batch embeddings preserve individual results
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Author: Zach Kelling
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-/
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import Mathlib.Data.Nat.Defs
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import Mathlib.Data.List.Basic
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import Mathlib.Tactic
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namespace AI.Embedding
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def standardDim : Nat := 7680
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structure EmbeddingVector where
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dim : Nat
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hash : Nat -- content hash of the vector
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normalized : Bool -- unit length for cosine sim
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axiom embed : Nat → EmbeddingVector
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axiom embed_deterministic : ∀ (input : Nat), embed input = embed input
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/-- DIMENSIONALITY: Standard embedding is 7680-dim -/
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axiom embed_dim : ∀ (input : Nat), (embed input).dim = standardDim
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theorem dim_is_7680 : standardDim = 7680 := rfl
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/-- NORMALIZATION: Embeddings are unit-length -/
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axiom embed_normalized : ∀ (input : Nat), (embed input).normalized = true
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/-- DETERMINISM: Same input always produces same vector -/
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theorem deterministic (input : Nat) :
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embed input = embed input := rfl
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/-- BATCH: Batch embedding = individual embeddings -/
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noncomputable def batchEmbed (inputs : List Nat) : List EmbeddingVector :=
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inputs.map embed
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theorem batch_length (inputs : List Nat) :
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(batchEmbed inputs).length = inputs.length := by
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simp [batchEmbed]
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theorem batch_preserves (inputs : List Nat) (i : Fin inputs.length) :
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(batchEmbed inputs)[i]'(by simp [batchEmbed, i.isLt]) = embed inputs[i] := by
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simp [batchEmbed, List.getElem_map]
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/-- 7680 > 1536 (OpenAI ada-002) -/
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theorem higher_resolution : standardDim > 1536 := by simp [standardDim]
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/-- 7680 > 3072 (OpenAI text-embedding-3-large) -/
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theorem higher_than_openai : standardDim > 3072 := by simp [standardDim]
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end AI.Embedding
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