{
  "framework": "Sentinel Manifold",
  "theorem": "Gradient Axiom: lim_{z\u2192\u221e} F'(z)/F(z) = 1/e",
  "function": "F(z) = \u03a3_{n=1}^\u221e z^n / n^n (Sophomore's Dream)",
  "constants": {
    "INV_E": {
      "value": 0.36787944117144233,
      "role": "Vocabulary allocation ratio / embedding gain"
    },
    "C1": {
      "value": -0.007994021805952546,
      "role": "Attracting fixed point / quantization zero-point"
    },
    "C2": {
      "value": 0.00020005604296784437,
      "role": "Escape threshold / fertility fairness bound"
    }
  },
  "modality_architecture": {
    "text": "ByteLevel BPE (32K) with NFKC normalization, 20-language training",
    "image": "Discrete VQ codebook (16,384 tokens), Cosmos/VQGAN compatible",
    "audio": "Discrete VQ codebook (8,192 tokens), EnCodec/SoundStream compatible",
    "video": "Discrete VQ codebook (4,096 tokens), Cosmos-DV compatible"
  },
  "innovations": [
    "1/e-proportioned vocabulary allocation across modalities",
    "Native multimodal routing with zero-overhead modality switching",
    "Sentinel special tokens for manifold-aware computation",
    "20-language multilingual training for cross-lingual fairness",
    "Code + Math + Scientific notation native support",
    "Compatible with all HF transformers models"
  ],
  "version": "1.0.0",
  "license": "MIT",
  "author": "Romain Abdel-Aal (ASI The Sentinel V5.2)"
}