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# QUANTIZAÇÃO GEOMÉTRICA PARA MODELOS LLaMA (LLM) EM PYTHON
Authors/Creators

Becker, Bruno (Researcher)

Description

# QUANTIZAÇÃO GEOMÉTRICA PARA MODELOS LLaMA (LLM) EM PYTHON
## Um kernel funcional de compressão estrutural com preservação de contexto

### QUEM QUISER USAR MINHAS TEORIAS PARA IAs GEOMÉTRICAS, O FAÇAM DIREITO, E TENHAM O MINÍMO DE DECÊNCIA DE ME CITAR AO MENOS.

Este repositório apresenta uma implementação funcional de **quantização geométrica aplicada a modelos de linguagem do tipo LLaMA**, desenvolvida em **Python**, compatível com o ecossistema **open-source** (LLaMA, HuggingFace, GGML e derivados).

O trabalho não propõe aumento de parâmetros, expansão artificial de contexto ou tuning estatístico superficial. Em vez disso, introduz um **kernel de quantização estrutural**, baseado em princípios geométricos, que atua diretamente sobre os **graus de liberdade internos** dos tensores, preservando relações locais, simetrias e escalas.

O código disponibilizado é funcional, executável e verificável, demonstrando empiricamente um comportamento relevante: mesmo com redução de throughput (velocidade de tokens), o modelo mantém **estabilidade incomum de contexto**, evitando colapso progressivo em janelas longas.

Esse efeito não decorre de heurísticas de amostragem, mas da **organização geométrica imposta à representação interna**.

---

## Enquadramento Matemático

Seja um tensor de ativações ou pesos:

Particionamos em blocos de tamanho fixo

:

Definimos um operador de quantização geométrica:

tal que:

onde:
- é um vetor discreto quantizado
-

é um fator de escala contínuo local
- a geometria relativa do bloco é preservada

A reconstrução é dada por:

com erro limitado:

A propriedade central não é minimizar o erro global, mas **preservar a geometria local do espaço vetorial**, garantindo continuidade estrutural entre blocos sucessivos.

---

## Implicações para Modelos de Linguagem

Em modelos autorregressivos, a estabilidade do contexto depende da **coerência geométrica acumulada** no espaço latente.

A quantização geométrica atua como um **operador de regularização estrutural**, reduzindo deriva caótica sem impor rigidez excessiva, resultando em:

- degradação graciosa em janelas longas
- menor colapso semântico progressivo
- maior previsibilidade estrutural do estado interno

---

## Escopo e Limitações

Este repositório:
- fornece uma implementação funcional
- demonstra um efeito real e mensurável
- é totalmente open-source

Este repositório não pretende:
- fornecer um modelo completo
- substituir arquiteturas existentes
- esgotar o arcabouço teórico subjacente

O kernel apresentado é uma **instância prática**, conectada a um corpo teórico mais amplo já publicado separadamente pelo autor.

---

## Licença e Ecossistema

- Código: MIT License
- Linguagem: Python
- Modelos: LLaMA (open-weights)
- Ecossistema: HuggingFace / GGML compatível

Este trabalho respeita integralmente as licenças open-source dos projetos utilizados.

---

## Nota Final

Este artefato é publicado como **prova de anterioridade funcional**, não como produto final.

A reprodução, extensão ou adaptação deste trabalho é livre, desde que se compreenda que o código apresentado representa apenas a **superfície de uma estrutura teórica mais profunda**.

llama-webui.zip

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+version https://git-lfs.github.com/spec/v1
+oid sha256:862d34664bcc1c3255a43a0f5cee2ae35f9576569a9917972d6b8c6325180173
+size 259313999

quants.py

@@ -0,0 +1,1472 @@
+from __future__ import annotations
+from abc import ABC, abstractmethod
+from typing import Any, Callable, Sequence
+from math import log2, ceil
+
+from numpy.typing import DTypeLike
+
+from .constants import GGML_QUANT_SIZES, GGMLQuantizationType, QK_K
+from .lazy import LazyNumpyTensor
+
+import numpy as np
+
+
+def quant_shape_to_byte_shape(shape: Sequence[int], quant_type: GGMLQuantizationType) -> tuple[int, ...]:
+    block_size, type_size = GGML_QUANT_SIZES[quant_type]
+    if shape[-1] % block_size != 0:
+        raise ValueError(f"Quantized tensor row size ({shape[-1]}) is not a multiple of {quant_type.name} block size ({block_size})")
+    return (*shape[:-1], shape[-1] // block_size * type_size)
+
+
+def quant_shape_from_byte_shape(shape: Sequence[int], quant_type: GGMLQuantizationType) -> tuple[int, ...]:
+    block_size, type_size = GGML_QUANT_SIZES[quant_type]
+    if shape[-1] % type_size != 0:
+        raise ValueError(f"Quantized tensor bytes per row ({shape[-1]}) is not a multiple of {quant_type.name} type size ({type_size})")
+    return (*shape[:-1], shape[-1] // type_size * block_size)
+
+
+# This is faster than np.vectorize and np.apply_along_axis because it works on more than one row at a time
+def _apply_over_grouped_rows(func: Callable[[np.ndarray], np.ndarray], arr: np.ndarray, otype: DTypeLike, oshape: tuple[int, ...]) -> np.ndarray:
+    rows = arr.reshape((-1, arr.shape[-1]))
+    osize = 1
+    for dim in oshape:
+        osize *= dim
+    out = np.empty(shape=osize, dtype=otype)
+    # compute over groups of 16 rows (arbitrary, but seems good for performance)
+    n_groups = (rows.shape[0] // 16) or 1
+    np.concatenate([func(group).ravel() for group in np.array_split(rows, n_groups)], axis=0, out=out)
+    return out.reshape(oshape)
+
+
+# round away from zero
+# ref: https://stackoverflow.com/a/59143326/22827863
+def np_roundf(n: np.ndarray) -> np.ndarray:
+    a = abs(n)
+    floored = np.floor(a)
+    b = floored + np.floor(2 * (a - floored))
+    return np.sign(n) * b
+
+
+class QuantError(Exception): ...
+
+
+_type_traits: dict[GGMLQuantizationType, type[__Quant]] = {}
+
+
+def quantize(data: np.ndarray, qtype: GGMLQuantizationType) -> np.ndarray:
+    if qtype == GGMLQuantizationType.F32:
+        return data.astype(np.float32, copy=False)
+    elif qtype == GGMLQuantizationType.F16:
+        return data.astype(np.float16, copy=False)
+    elif (q := _type_traits.get(qtype)) is not None:
+        return q.quantize(data)
+    else:
+        raise NotImplementedError(f"Quantization for {qtype.name} is not yet implemented")
+
+
+def dequantize(data: np.ndarray, qtype: GGMLQuantizationType) -> np.ndarray:
+    if qtype == GGMLQuantizationType.F32:
+        return data.view(np.float32)
+    elif qtype == GGMLQuantizationType.F16:
+        return data.view(np.float16).astype(np.float32)
+    elif (q := _type_traits.get(qtype)) is not None:
+        return q.dequantize(data)
+    else:
+        raise NotImplementedError(f"Dequantization for {qtype.name} is not yet implemented")
+
+
+class __Quant(ABC):
+    qtype: GGMLQuantizationType
+    block_size: int
+    type_size: int
+
+    grid: np.ndarray[Any, np.dtype[np.float32]] | None = None
+    grid_shape: tuple[int, int] = (0, 0)
+    grid_map: tuple[int | float, ...] = ()
+    grid_hex: bytes | None = None
+
+    def __init__(self):
+        return TypeError("Quant conversion classes can't have instances")
+
+    def __init_subclass__(cls, qtype: GGMLQuantizationType) -> None:
+        cls.qtype = qtype
+        cls.block_size, cls.type_size = GGML_QUANT_SIZES[qtype]
+        cls.__quantize_lazy = LazyNumpyTensor._wrap_fn(
+            cls.__quantize_array,
+            meta_noop=(np.uint8, cls.__shape_to_bytes)
+        )
+        cls.__dequantize_lazy = LazyNumpyTensor._wrap_fn(
+            cls.__dequantize_array,
+            meta_noop=(np.float32, cls.__shape_from_bytes)
+        )
+        assert qtype not in _type_traits
+        _type_traits[qtype] = cls
+
+    @classmethod
+    def init_grid(cls):
+        if cls.grid is not None or cls.grid_hex is None:
+            return
+
+        bits_per_elem = ceil(log2(len(cls.grid_map)))
+        assert bits_per_elem != 0, cls.qtype.name
+        elems_per_byte = 8 // bits_per_elem
+
+        grid = np.frombuffer(cls.grid_hex, dtype=np.uint8)
+        # decode hexadecimal chars from grid
+        grid = grid.reshape((-1, 2))
+        grid = (np.where(grid > 0x40, grid + 9, grid) & 0x0F) << np.array([4, 0], dtype=np.uint8).reshape((1, 2))
+        grid = grid[..., 0] | grid[..., 1]
+        # unpack the grid values
+        grid = grid.reshape((-1, 1)) >> np.array([i for i in range(0, 8, 8 // elems_per_byte)], dtype=np.uint8).reshape((1, elems_per_byte))
+        grid = (grid & ((1 << bits_per_elem) - 1)).reshape((-1, 1))
+        grid_map = np.array(cls.grid_map, dtype=np.float32).reshape((1, -1))
+        grid = np.take_along_axis(grid_map, grid, axis=-1)
+        cls.grid = grid.reshape((1, 1, *cls.grid_shape))
+
+    @classmethod
+    @abstractmethod
+    def quantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        raise NotImplementedError
+
+    @classmethod
+    @abstractmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        raise NotImplementedError
+
+    @classmethod
+    def quantize_rows(cls, rows: np.ndarray) -> np.ndarray:
+        rows = rows.astype(np.float32, copy=False)
+        shape = rows.shape
+        n_blocks = rows.size // cls.block_size
+        blocks = rows.reshape((n_blocks, cls.block_size))
+        blocks = cls.quantize_blocks(blocks)
+        assert blocks.dtype == np.uint8
+        assert blocks.shape[-1] == cls.type_size
+        return blocks.reshape(cls.__shape_to_bytes(shape))
+
+    @classmethod
+    def dequantize_rows(cls, rows: np.ndarray) -> np.ndarray:
+        rows = rows.view(np.uint8)
+        shape = rows.shape
+        n_blocks = rows.size // cls.type_size
+        blocks = rows.reshape((n_blocks, cls.type_size))
+        blocks = cls.dequantize_blocks(blocks)
+        assert blocks.dtype == np.float32
+        assert blocks.shape[-1] == cls.block_size
+        return blocks.reshape(cls.__shape_from_bytes(shape))
+
+    @classmethod
+    def __shape_to_bytes(cls, shape: Sequence[int]):
+        return quant_shape_to_byte_shape(shape, cls.qtype)
+
+    @classmethod
+    def __shape_from_bytes(cls, shape: Sequence[int]):
+        return quant_shape_from_byte_shape(shape, cls.qtype)
+
+    @classmethod
+    def __quantize_array(cls, array: np.ndarray) -> np.ndarray:
+        return _apply_over_grouped_rows(cls.quantize_rows, arr=array, otype=np.uint8, oshape=cls.__shape_to_bytes(array.shape))
+
+    @classmethod
+    def __dequantize_array(cls, array: np.ndarray) -> np.ndarray:
+        cls.init_grid()
+        return _apply_over_grouped_rows(cls.dequantize_rows, arr=array, otype=np.float32, oshape=cls.__shape_from_bytes(array.shape))
+
+    @classmethod
+    def __quantize_lazy(cls, lazy_tensor: LazyNumpyTensor, /) -> Any:
+        pass
+
+    @classmethod
+    def __dequantize_lazy(cls, lazy_tensor: LazyNumpyTensor, /) -> Any:
+        pass
+
+    @classmethod
+    def can_quantize(cls, tensor: np.ndarray | LazyNumpyTensor) -> bool:
+        return tensor.shape[-1] % cls.block_size == 0
+
+    @classmethod
+    def quantize(cls, tensor: np.ndarray | LazyNumpyTensor) -> np.ndarray:
+        if not cls.can_quantize(tensor):
+            raise QuantError(f"Can't quantize tensor with shape {tensor.shape} to {cls.qtype.name}")
+        if isinstance(tensor, LazyNumpyTensor):
+            return cls.__quantize_lazy(tensor)
+        else:
+            return cls.__quantize_array(tensor)
+
+    @classmethod
+    def dequantize(cls, tensor: np.ndarray | LazyNumpyTensor) -> np.ndarray:
+        if isinstance(tensor, LazyNumpyTensor):
+            return cls.__dequantize_lazy(tensor)
+        else:
+            return cls.__dequantize_array(tensor)
+
+
+class BF16(__Quant, qtype=GGMLQuantizationType.BF16):
+    @classmethod
+    # same as ggml_compute_fp32_to_bf16 in ggml-impl.h
+    def quantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n = blocks.view(np.uint32)
+        # force nan to quiet
+        n = np.where((n & 0x7fffffff) > 0x7f800000, (n & np.uint32(0xffff0000)) | np.uint32(64 << 16), n)
+        # round to nearest even
+        n = (np.uint64(n) + (0x7fff + ((n >> 16) & 1))) >> 16
+        return n.astype(np.uint16).view(np.uint8)
+
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        return (blocks.view(np.int16).astype(np.int32) << 16).view(np.float32)
+
+
+class Q4_0(__Quant, qtype=GGMLQuantizationType.Q4_0):
+    @classmethod
+    def quantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        imax = abs(blocks).argmax(axis=-1, keepdims=True)
+        max = np.take_along_axis(blocks, imax, axis=-1)
+
+        d = max / -8
+        with np.errstate(divide="ignore"):
+            id = np.where(d == 0, 0, 1 / d)
+        qs = np.trunc((blocks * id) + np.float32(8.5), dtype=np.float32).astype(np.uint8).clip(0, 15)
+
+        qs = qs.reshape((n_blocks, 2, cls.block_size // 2))
+        qs = qs[..., 0, :] | (qs[..., 1, :] << np.uint8(4))
+
+        d = d.astype(np.float16).view(np.uint8)
+
+        return np.concatenate([d, qs], axis=-1)
+
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        d, qs = np.hsplit(blocks, [2])
+
+        d = d.view(np.float16).astype(np.float32)
+
+        qs = qs.reshape((n_blocks, -1, 1, cls.block_size // 2)) >> np.array([0, 4], dtype=np.uint8).reshape((1, 1, 2, 1))
+        qs = (qs & np.uint8(0x0F)).reshape((n_blocks, -1)).astype(np.int8) - np.int8(8)
+
+        return (d * qs.astype(np.float32))
+
+
+class Q4_1(__Quant, qtype=GGMLQuantizationType.Q4_1):
+    @classmethod
+    def quantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        max = blocks.max(axis=-1, keepdims=True)
+        min = blocks.min(axis=-1, keepdims=True)
+
+        d = (max - min) / 15
+        with np.errstate(divide="ignore"):
+            id = np.where(d == 0, 0, 1 / d)
+        qs = np.trunc((blocks - min) * id + np.float32(0.5), dtype=np.float32).astype(np.uint8).clip(0, 15)
+
+        qs = qs.reshape((n_blocks, 2, cls.block_size // 2))
+        qs = qs[..., 0, :] | (qs[..., 1, :] << np.uint8(4))
+
+        d = d.astype(np.float16).view(np.uint8)
+        m = min.astype(np.float16).view(np.uint8)
+
+        return np.concatenate([d, m, qs], axis=-1)
+
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        d, rest = np.hsplit(blocks, [2])
+        m, qs = np.hsplit(rest, [2])
+
+        d = d.view(np.float16).astype(np.float32)
+        m = m.view(np.float16).astype(np.float32)
+
+        qs = qs.reshape((n_blocks, -1, 1, cls.block_size // 2)) >> np.array([0, 4], dtype=np.uint8).reshape((1, 1, 2, 1))
+        qs = (qs & np.uint8(0x0F)).reshape((n_blocks, -1)).astype(np.float32)
+
+        return (d * qs) + m
+
+
+class Q5_0(__Quant, qtype=GGMLQuantizationType.Q5_0):
+    @classmethod
+    def quantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        imax = abs(blocks).argmax(axis=-1, keepdims=True)
+        max = np.take_along_axis(blocks, imax, axis=-1)
+
+        d = max / -16
+        with np.errstate(divide="ignore"):
+            id = np.where(d == 0, 0, 1 / d)
+        q = np.trunc((blocks * id) + np.float32(16.5), dtype=np.float32).astype(np.uint8).clip(0, 31)
+
+        qs = q.reshape((n_blocks, 2, cls.block_size // 2))
+        qs = (qs[..., 0, :] & np.uint8(0x0F)) | (qs[..., 1, :] << np.uint8(4))
+
+        qh = np.packbits(q.reshape((n_blocks, 1, 32)) >> np.uint8(4), axis=-1, bitorder="little").reshape(n_blocks, 4)
+
+        d = d.astype(np.float16).view(np.uint8)
+
+        return np.concatenate([d, qh, qs], axis=-1)
+
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        d, rest = np.hsplit(blocks, [2])
+        qh, qs = np.hsplit(rest, [4])
+
+        d = d.view(np.float16).astype(np.float32)
+        qh = qh.view(np.uint32)
+
+        qh = qh.reshape((n_blocks, 1)) >> np.array([i for i in range(32)], dtype=np.uint32).reshape((1, 32))
+        ql = qs.reshape((n_blocks, -1, 1, cls.block_size // 2)) >> np.array([0, 4], dtype=np.uint8).reshape((1, 1, 2, 1))
+        qh = (qh & np.uint32(0x01)).astype(np.uint8)
+        ql = (ql & np.uint8(0x0F)).reshape((n_blocks, -1))
+
+        qs = (ql | (qh << np.uint8(4))).astype(np.int8) - np.int8(16)
+
+        return (d * qs.astype(np.float32))
+
+
+class Q5_1(__Quant, qtype=GGMLQuantizationType.Q5_1):
+    @classmethod
+    def quantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        max = blocks.max(axis=-1, keepdims=True)
+        min = blocks.min(axis=-1, keepdims=True)
+
+        d = (max - min) / 31
+        with np.errstate(divide="ignore"):
+            id = np.where(d == 0, 0, 1 / d)
+        q = np.trunc((blocks - min) * id + np.float32(0.5), dtype=np.float32).astype(np.uint8).clip(0, 31)
+
+        qs = q.reshape((n_blocks, 2, cls.block_size // 2))
+        qs = (qs[..., 0, :] & np.uint8(0x0F)) | (qs[..., 1, :] << np.uint8(4))
+
+        qh = np.packbits(q.reshape((n_blocks, 1, 32)) >> np.uint8(4), axis=-1, bitorder="little").reshape(n_blocks, 4)
+
+        d = d.astype(np.float16).view(np.uint8)
+        m = min.astype(np.float16).view(np.uint8)
+
+        return np.concatenate([d, m, qh, qs], axis=-1)
+
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        d, rest = np.hsplit(blocks, [2])
+        m, rest = np.hsplit(rest, [2])
+        qh, qs = np.hsplit(rest, [4])
+
+        d = d.view(np.float16).astype(np.float32)
+        m = m.view(np.float16).astype(np.float32)
+        qh = qh.view(np.uint32)
+
+        qh = qh.reshape((n_blocks, 1)) >> np.array([i for i in range(32)], dtype=np.uint32).reshape((1, 32))
+        ql = qs.reshape((n_blocks, -1, 1, cls.block_size // 2)) >> np.array([0, 4], dtype=np.uint8).reshape((1, 1, 2, 1))
+        qh = (qh & np.uint32(0x01)).astype(np.uint8)
+        ql = (ql & np.uint8(0x0F)).reshape((n_blocks, -1))
+
+        qs = (ql | (qh << np.uint8(4))).astype(np.float32)
+
+        return (d * qs) + m
+
+
+class Q8_0(__Quant, qtype=GGMLQuantizationType.Q8_0):
+    @classmethod
+    # Implementation of Q8_0 with bit-exact same results as reference implementation in ggml-quants.c
+    def quantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+
+        d = abs(blocks).max(axis=1, keepdims=True) / 127
+        with np.errstate(divide="ignore"):
+            id = np.where(d == 0, 0, 1 / d)
+        qs = np_roundf(blocks * id)
+
+        # (n_blocks, 2)
+        d = d.astype(np.float16).view(np.uint8)
+        # (n_blocks, block_size)
+        qs = qs.astype(np.int8).view(np.uint8)
+
+        return np.concatenate([d, qs], axis=1)
+
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        d, x = np.split(blocks, [2], axis=1)
+        d = d.view(np.float16).astype(np.float32)
+        x = x.view(np.int8).astype(np.float32)
+
+        return (x * d)
+
+
+class Q2_K(__Quant, qtype=GGMLQuantizationType.Q2_K):
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        scales, rest = np.hsplit(blocks, [QK_K // 16])
+        qs, rest = np.hsplit(rest, [QK_K // 4])
+        d, dmin = np.hsplit(rest, [2])
+
+        d = d.view(np.float16).astype(np.float32)
+        dmin = dmin.view(np.float16).astype(np.float32)
+
+        # (n_blocks, 16, 1)
+        dl = (d * (scales & 0xF).astype(np.float32)).reshape((n_blocks, QK_K // 16, 1))
+        ml = (dmin * (scales >> 4).astype(np.float32)).reshape((n_blocks, QK_K // 16, 1))
+
+        shift = np.array([0, 2, 4, 6], dtype=np.uint8).reshape((1, 1, 4, 1))
+
+        qs = (qs.reshape((n_blocks, -1, 1, 32)) >> shift) & np.uint8(3)
+
+        qs = qs.reshape((n_blocks, QK_K // 16, 16)).astype(np.float32)
+
+        qs = dl * qs - ml
+
+        return qs.reshape((n_blocks, -1))
+
+
+class Q3_K(__Quant, qtype=GGMLQuantizationType.Q3_K):
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        hmask, rest = np.hsplit(blocks, [QK_K // 8])
+        qs, rest = np.hsplit(rest, [QK_K // 4])
+        scales, d = np.hsplit(rest, [12])
+
+        d = d.view(np.float16).astype(np.float32)
+
+        # The scales are packed at 6-bit each in this pattern:
+        #  0: IIIIAAAA
+        #  1: JJJJBBBB
+        #  2: KKKKCCCC
+        #  3: LLLLDDDD
+        #  4: MMMMEEEE
+        #  5: NNNNFFFF
+        #  6: OOOOGGGG
+        #  7: PPPPHHHH
+        #  8: MMIIEEAA
+        #  9: NNJJFFBB
+        # 10: OOKKGGCC
+        # 11: PPLLHHDD
+        lscales, hscales = np.hsplit(scales, [8])
+        lscales = lscales.reshape((n_blocks, 1, 8)) >> np.array([0, 4], dtype=np.uint8).reshape((1, 2, 1))
+        lscales = lscales.reshape((n_blocks, 16))
+        hscales = hscales.reshape((n_blocks, 1, 4)) >> np.array([0, 2, 4, 6], dtype=np.uint8).reshape((1, 4, 1))
+        hscales = hscales.reshape((n_blocks, 16))
+        scales = (lscales & np.uint8(0x0F)) | ((hscales & np.uint8(0x03)) << np.uint8(4))
+        scales = (scales.astype(np.int8) - np.int8(32)).astype(np.float32)
+
+        dl = (d * scales).reshape((n_blocks, 16, 1))
+
+        ql = qs.reshape((n_blocks, -1, 1, 32)) >> np.array([0, 2, 4, 6], dtype=np.uint8).reshape((1, 1, 4, 1))
+        qh = hmask.reshape(n_blocks, -1, 1, 32) >> np.array([i for i in range(8)], dtype=np.uint8).reshape((1, 1, 8, 1))
+        ql = ql.reshape((n_blocks, 16, QK_K // 16)) & np.uint8(3)
+        qh = (qh.reshape((n_blocks, 16, QK_K // 16)) & np.uint8(1))
+        qh = qh ^ np.uint8(1)  # strangely, the offset is zero when the bitmask is 1
+        q = (ql.astype(np.int8) - (qh << np.uint8(2)).astype(np.int8)).astype(np.float32)
+
+        return (dl * q).reshape((n_blocks, QK_K))
+
+
+class Q4_K(__Quant, qtype=GGMLQuantizationType.Q4_K):
+    K_SCALE_SIZE = 12
+
+    @staticmethod
+    def get_scale_min(scales: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+        n_blocks = scales.shape[0]
+        scales = scales.view(np.uint8)
+        ### Unpacking the following: ###
+        #  0 EEAAAAAA
+        #  1 FFBBBBBB
+        #  2 GGCCCCCC
+        #  3 HHDDDDDD
+        #  4 eeaaaaaa
+        #  5 ffbbbbbb
+        #  6 ggcccccc
+        #  7 hhdddddd
+        #  8 eeeeEEEE
+        #  9 ffffFFFF
+        # 10 ggggGGGG
+        # 11 hhhhHHHH
+        scales = scales.reshape((n_blocks, 3, 4))
+        d, m, m_d = np.split(scales, 3, axis=-2)
+
+        sc = np.concatenate([d & 0x3F, (m_d & 0x0F) | ((d >> 2) & 0x30)], axis=-1)
+        min = np.concatenate([m & 0x3F, (m_d >> 4) | ((m >> 2) & 0x30)], axis=-1)
+
+        return (sc.reshape((n_blocks, 8)), min.reshape((n_blocks, 8)))
+
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        d, rest = np.hsplit(blocks, [2])
+        dmin, rest = np.hsplit(rest, [2])
+        scales, qs = np.hsplit(rest, [cls.K_SCALE_SIZE])
+
+        d = d.view(np.float16).astype(np.float32)
+        dmin = dmin.view(np.float16).astype(np.float32)
+
+        sc, m = Q4_K.get_scale_min(scales)
+
+        d = (d * sc.astype(np.float32)).reshape((n_blocks, -1, 1))
+        dm = (dmin * m.astype(np.float32)).reshape((n_blocks, -1, 1))
+
+        qs = qs.reshape((n_blocks, -1, 1, 32)) >> np.array([0, 4], dtype=np.uint8).reshape((1, 1, 2, 1))
+        qs = (qs & np.uint8(0x0F)).reshape((n_blocks, -1, 32)).astype(np.float32)
+
+        return (d * qs - dm).reshape((n_blocks, QK_K))
+
+
+class Q5_K(__Quant, qtype=GGMLQuantizationType.Q5_K):
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        d, rest = np.hsplit(blocks, [2])
+        dmin, rest = np.hsplit(rest, [2])
+        scales, rest = np.hsplit(rest, [Q4_K.K_SCALE_SIZE])
+        qh, qs = np.hsplit(rest, [QK_K // 8])
+
+        d = d.view(np.float16).astype(np.float32)
+        dmin = dmin.view(np.float16).astype(np.float32)
+
+        sc, m = Q4_K.get_scale_min(scales)
+
+        d = (d * sc.astype(np.float32)).reshape((n_blocks, -1, 1))
+        dm = (dmin * m.astype(np.float32)).reshape((n_blocks, -1, 1))
+
+        ql = qs.reshape((n_blocks, -1, 1, 32)) >> np.array([0, 4], dtype=np.uint8).reshape((1, 1, 2, 1))
+        qh = qh.reshape((n_blocks, -1, 1, 32)) >> np.array([i for i in range(8)], dtype=np.uint8).reshape((1, 1, 8, 1))
+        ql = (ql & np.uint8(0x0F)).reshape((n_blocks, -1, 32))
+        qh = (qh & np.uint8(0x01)).reshape((n_blocks, -1, 32))
+        q = (ql | (qh << np.uint8(4))).astype(np.float32)
+
+        return (d * q - dm).reshape((n_blocks, QK_K))
+
+
+class Q6_K(__Quant, qtype=GGMLQuantizationType.Q6_K):
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        ql, rest = np.hsplit(blocks, [QK_K // 2])
+        qh, rest = np.hsplit(rest, [QK_K // 4])
+        scales, d = np.hsplit(rest, [QK_K // 16])
+
+        scales = scales.view(np.int8).astype(np.float32)
+        d = d.view(np.float16).astype(np.float32)
+        d = (d * scales).reshape((n_blocks, QK_K // 16, 1))
+
+        ql = ql.reshape((n_blocks, -1, 1, 64)) >> np.array([0, 4], dtype=np.uint8).reshape((1, 1, 2, 1))
+        ql = (ql & np.uint8(0x0F)).reshape((n_blocks, -1, 32))
+        qh = qh.reshape((n_blocks, -1, 1, 32)) >> np.array([0, 2, 4, 6], dtype=np.uint8).reshape((1, 1, 4, 1))
+        qh = (qh & np.uint8(0x03)).reshape((n_blocks, -1, 32))
+        q = (ql | (qh << np.uint8(4))).astype(np.int8) - np.int8(32)
+        q = q.reshape((n_blocks, QK_K // 16, -1)).astype(np.float32)
+
+        return (d * q).reshape((n_blocks, QK_K))
+
+
+class TQ1_0(__Quant, qtype=GGMLQuantizationType.TQ1_0):
+    @classmethod
+    def quantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        d = abs(blocks).max(axis=-1, keepdims=True)
+        with np.errstate(divide="ignore"):
+            id = np.where(d == 0, 0, 1 / d)
+        qs = np_roundf(blocks * id)
+        qs = (qs.astype(np.int8) + np.int8(1)).astype(np.uint8)
+
+        qs0, qs1, qh = qs[..., :(32 * 5)], qs[..., (32 * 5):(48 * 5)], qs[..., (48 * 5):]
+        qs0 = qs0.reshape((n_blocks, -1, 5, 32)) * np.array([81, 27, 9, 3, 1], dtype=np.uint8).reshape((1, 1, 5, 1))
+        qs0 = np.sum(qs0, axis=-2).reshape((n_blocks, -1))
+        qs1 = qs1.reshape((n_blocks, -1, 5, 16)) * np.array([81, 27, 9, 3, 1], dtype=np.uint8).reshape((1, 1, 5, 1))
+        qs1 = np.sum(qs1, axis=-2).reshape((n_blocks, -1))
+        qh = qh.reshape((n_blocks, -1, 4, 4)) * np.array([81, 27, 9, 3], dtype=np.uint8).reshape((1, 1, 4, 1))
+        qh = np.sum(qh, axis=-2).reshape((n_blocks, -1))
+        qs = np.concatenate([qs0, qs1, qh], axis=-1)
+        qs = (qs.astype(np.uint16) * 256 + (243 - 1)) // 243
+
+        qs = qs.astype(np.uint8)
+        d = d.astype(np.float16).view(np.uint8)
+
+        return np.concatenate([qs, d], axis=-1)
+
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        qs, rest = np.hsplit(blocks, [(QK_K - 4 * QK_K // 64) // 5])
+        qh, d = np.hsplit(rest, [QK_K // 64])
+
+        d = d.view(np.float16).astype(np.float32)
+
+        qs0, qs1 = qs[..., :32], qs[..., 32:]
+        qs0 = qs0.reshape((n_blocks, -1, 1, 32)) * np.array([1, 3, 9, 27, 81], dtype=np.uint8).reshape((1, 1, 5, 1))
+        qs0 = qs0.reshape((n_blocks, -1))
+        qs1 = qs1.reshape((n_blocks, -1, 1, 16)) * np.array([1, 3, 9, 27, 81], dtype=np.uint8).reshape((1, 1, 5, 1))
+        qs1 = qs1.reshape((n_blocks, -1))
+        qh = qh.reshape((n_blocks, -1, 1, 4)) * np.array([1, 3, 9, 27], dtype=np.uint8).reshape((1, 1, 4, 1))
+        qh = qh.reshape((n_blocks, -1))
+        qs = np.concatenate([qs0, qs1, qh], axis=-1)
+        qs = ((qs.astype(np.uint16) * 3) >> 8).astype(np.int8) - np.int8(1)
+
+        return (d * qs.astype(np.float32))
+
+
+class TQ2_0(__Quant, qtype=GGMLQuantizationType.TQ2_0):
+    @classmethod
+    def quantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        d = abs(blocks).max(axis=-1, keepdims=True)
+        with np.errstate(divide="ignore"):
+            id = np.where(d == 0, 0, 1 / d)
+        qs = np_roundf(blocks * id)
+        qs = (qs.astype(np.int8) + np.int8(1)).astype(np.uint8)
+
+        qs = qs.reshape((n_blocks, -1, 4, 32)) << np.array([0, 2, 4, 6], dtype=np.uint8).reshape((1, 1, 4, 1))
+        qs = qs[..., 0, :] | qs[..., 1, :] | qs[..., 2, :] | qs[..., 3, :]
+        qs = qs.reshape((n_blocks, -1))
+
+        d = d.astype(np.float16).view(np.uint8)
+
+        return np.concatenate([qs, d], axis=-1)
+
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        qs, d = np.hsplit(blocks, [QK_K // 4])
+
+        d = d.view(np.float16).astype(np.float32)
+
+        qs = qs.reshape((n_blocks, -1, 1, 32)) >> np.array([0, 2, 4, 6], dtype=np.uint8).reshape((1, 1, 4, 1))
+        qs = (qs & 0x03).reshape((n_blocks, -1)).astype(np.int8) - np.int8(1)
+
+        return (d * qs.astype(np.float32))
+
+
+class MXFP4(__Quant, qtype=GGMLQuantizationType.MXFP4):
+    # e2m1 values (doubled)
+    # ref: https://www.opencompute.org/documents/ocp-microscaling-formats-mx-v1-0-spec-final-pdf
+    kvalues = (0, 1, 2, 3, 4, 6, 8, 12, 0, -1, -2, -3, -4, -6, -8, -12)
+
+    @staticmethod
+    # see ggml_e8m0_to_fp32_half in ggml-impl.h
+    def e8m0_to_fp32_half(x: np.ndarray) -> np.ndarray:
+        bits = np.where(x < 2, np.uint32(0x00200000) << np.uint32(x), np.uint32(x - 1) << np.uint32(23))
+        return bits.view(np.float32)
+
+    @classmethod
+    def quantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        d = abs(blocks).max(axis=-1, keepdims=True)
+
+        with np.errstate(divide="ignore"):
+            e = np.where(d > 0, np.floor(np.log2(d)) - 2 + 127, 0).astype(np.uint8)
+
+        d = cls.e8m0_to_fp32_half(e)
+
+        kvalues = np.array(cls.kvalues, dtype=np.int8).reshape((1, 1, 16))
+
+        errs = np.abs(d.reshape((n_blocks, 1, 1)) * kvalues.astype(np.float32) - blocks.reshape((n_blocks, cls.block_size, 1)))
+        best = np.argmin(errs, axis=-1, keepdims=True)
+
+        qs = best.reshape(n_blocks, 2, cls.block_size // 2).astype(np.uint8)
+        qs = qs[:, 0] | (qs[:, 1] << np.uint8(4))
+
+        qs = qs.reshape((n_blocks, cls.block_size // 2))
+
+        return np.concatenate([e, qs], axis=-1)
+
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        e, qs = np.hsplit(blocks, [1])
+
+        d = cls.e8m0_to_fp32_half(e)
+
+        qs = qs.reshape((n_blocks, 1, cls.block_size // 2)) >> np.array([0, 4], dtype=np.uint8).reshape((1, 2, 1))
+        qs = (qs & np.uint8(0x0F)).view(np.int8)
+
+        kvalues = np.array(cls.kvalues, dtype=np.int8).reshape(1, 1, 16)
+        qs = np.take_along_axis(kvalues, qs, axis=-1).reshape((n_blocks, cls.block_size))
+
+        return (d * qs.astype(np.float32))
+
+
+class IQ2_XXS(__Quant, qtype=GGMLQuantizationType.IQ2_XXS):
+    ksigns: bytes = (
+        b"\x00\x81\x82\x03\x84\x05\x06\x87\x88\x09\x0a\x8b\x0c\x8d\x8e\x0f"
+        b"\x90\x11\x12\x93\x14\x95\x96\x17\x18\x99\x9a\x1b\x9c\x1d\x1e\x9f"
+        b"\xa0\x21\x22\xa3\x24\xa5\xa6\x27\x28\xa9\xaa\x2b\xac\x2d\x2e\xaf"
+        b"\x30\xb1\xb2\x33\xb4\x35\x36\xb7\xb8\x39\x3a\xbb\x3c\xbd\xbe\x3f"
+        b"\xc0\x41\x42\xc3\x44\xc5\xc6\x47\x48\xc9\xca\x4b\xcc\x4d\x4e\xcf"
+        b"\x50\xd1\xd2\x53\xd4\x55\x56\xd7\xd8\x59\x5a\xdb\x5c\xdd\xde\x5f"
+        b"\x60\xe1\xe2\x63\xe4\x65\x66\xe7\xe8\x69\x6a\xeb\x6c\xed\xee\x6f"
+        b"\xf0\x71\x72\xf3\x74\xf5\xf6\x77\x78\xf9\xfa\x7b\xfc\x7d\x7e\xff"
+    )
+
+    # iq2xxs_grid, but with each byte of the original packed in 2 bits,
+    # by mapping 0x08 to 0, 0x19 to 1, and 0x2b to 2.
+    grid_shape = (256, 8)
+    grid_map = (0x08, 0x19, 0x2b)
+    grid_hex = (
+        b"00000200050008000a00110014002000220028002a0041004400500058006100"
+        b"6400800082008a00a20001010401100115014001840198010002020222028202"
+        b"010404041004210424044004420448046004810484049004a404000502050805"
+        b"200546056905800591050906100640068406a406000805080808140828084108"
+        b"440850085208880804094009020a140a01100410101021104010601084109010"
+        b"951000110811201150115a118011241245120014081420142514491480141815"
+        b"6215001616160118041810184018811800190519a019511a002002200a204420"
+        b"6120802082202921482100220222012404241024402456240025412564259026"
+        b"082820289428442a014004401040184021402440404048405640604081408440"
+        b"9040004120416141804185410142104248425642684200440844204480449944"
+        b"124524450046014804481048404845480049584961498249454a904a00500850"
+        b"1150195020508050885004514251a4519152905492540a550156545600581158"
+        b"195864584059085a046010604060686000615561186260620064056410651265"
+        b"84654268008002800a8041808280048118814081118201840484108415844084"
+        b"608400854685948509864086608602880489118a0490109024904090a1901691"
+        b"8091459200942294449451958198209902a050a085a009a100a218a450a804a9"
+    )
+
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        d, qs = np.hsplit(blocks, [2])
+
+        d = d.view(np.float16).astype(np.float32)
+
+        qs = qs.view(np.uint32).reshape(n_blocks, -1, 2)
+
+        db = d * (np.float32(0.5) + (qs[..., 1] >> 28).astype(np.float32)) * np.float32(0.25)
+        db = db.reshape((n_blocks, -1, 1, 1))
+
+        # get the sign indices and unpack the bits
+        signs = qs[..., 1].reshape((n_blocks, -1, 1)) >> np.array([0, 7, 14, 21], dtype=np.uint32).reshape((1, 1, 4))
+        ksigns = np.frombuffer(cls.ksigns, dtype=np.uint8).reshape((1, 1, 1, 128))
+        signs = (signs & np.uint32(0x7F)).reshape((n_blocks, -1, 4, 1))
+        signs = np.take_along_axis(ksigns, signs, axis=-1)
+        signs = signs.reshape((n_blocks, -1, 4, 1)) >> np.array([i for i in range(8)], dtype=np.uint8).reshape((1, 1, 1, 8))
+        signs = signs & np.uint8(0x01)
+        signs = np.where(signs == 0, np.float32(1), np.float32(-1))
+        signs = signs.reshape((n_blocks, -1, 4, 8))
+
+        assert cls.grid is not None
+        grid = np.take_along_axis(cls.grid, qs[..., 0].copy().view(np.uint8).reshape((n_blocks, -1, 1, 1)), axis=-2)
+        grid = grid.reshape((n_blocks, -1, 4, 8))
+
+        return (db * grid * signs).reshape((n_blocks, -1))
+
+
+class IQ2_XS(__Quant, qtype=GGMLQuantizationType.IQ2_XS):
+    # iq2xs_grid, but with each byte of the original packed in 2 bits,
+    # by mapping 0x08 to 0, 0x19 to 1, and 0x2b to 2.
+    grid_shape = (512, 8)
+    grid_map = (0x08, 0x19, 0x2b)
+    grid_hex = (
+        b"00000200050008000a0011001400160019002000220025002800410044004600"
+        b"49005000520055005800610064008000820085008800910094009900a0000101"
+        b"04010601090110011201150118011a0121012401400142014501480151015401"
+        b"6001680181018401900100020202050208021102140220024102440250025502"
+        b"80028a0201040404060409041004120415041804210424044004420445044804"
+        b"5104540456046004810484049004000502050505080511051405200541054405"
+        b"500561058005010604061006260640064206840600080208050808080a081108"
+        b"14082008250841084408500858088008a008aa08010904091009400981098909"
+        b"000a200a280a960aa00a01100410061009101010121015101810211024104010"
+        b"4210451048105110541060106a10811084109010001102110511081111111411"
+        b"2011411144115011801194119611011204120612101240126012001402140514"
+        b"0814111414142014411444144914501464148014011504151015401500161416"
+        b"49160118041810181218401854188618001905196619511aa91a002002200520"
+        b"08200a201120142020204120442050208020a020012104211021402148216521"
+        b"002222228022a82201240424102429244024002541255225992501261a26a626"
+        b"002808280a28202855288828a22868299029082a202a822a882a8a2a01400440"
+        b"0640094010401240154018402140244040404240454048404a40514054406040"
+        b"6540814084409040004102410541084111411441204141414441504180418541"
+        b"a241014204421042124229424042004402440544084411441444194420444144"
+        b"4444504480449444014504451045244540459a4500460a464446504601480448"
+        b"1048404845485448624800491149444950496949044a00500250055008501150"
+        b"145020502850415044505050805001510451105115514051425100524452aa52"
+        b"0154045410542154405460548154a154005508558055885521566856a1560058"
+        b"14584158505899581a5940594259855a0160046010604060546062608660a960"
+        b"006124624a62926200641664106540654565a46501686a682569066a546a626a"
+        b"00800280058008801180148020802a8041804480508080808280a880aa800181"
+        b"0481068110814081518159810082208280828282a082a8820184048410841284"
+        b"158440846084898400854485a58518866a860088088825885a8880888288a888"
+        b"0689228a808a888a968aa88a0190049010904090569084900091229164915692"
+        b"89920094059444945094589429959095929541965198a6984999159a609a00a0"
+        b"02a008a00aa020a02aa0a0a051a159a1a6a100a202a208a22aa280a2a0a240a4"
+        b"95a465a698a60aa820a822a828a8a0a8a8a804a984a986a928aa2aaa91aaaaaa"
+    )
+
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        d, rest = np.hsplit(blocks, [2])
+        qs, scales = np.hsplit(rest, [2 * QK_K // 8])
+
+        d = d.view(np.float16).astype(np.float32)
+        qs = qs.view(np.uint16)
+
+        scales = scales.reshape((n_blocks, -1, 1)) >> np.array([0, 4], dtype=np.uint8).reshape((1, 1, 2))
+        scales = (scales & 0x0F).reshape((n_blocks, -1))
+        db = d * (np.float32(0.5) + scales) * np.float32(0.25)
+        db = db.reshape((n_blocks, -1, 1, 1))
+
+        # get the sign indices and unpack the bits
+        signs = np.frombuffer(IQ2_XXS.ksigns, dtype=np.uint8).reshape(1, 1, 128)
+        signs = np.take_along_axis(signs, (qs >> 9).reshape((n_blocks, -1, 1)), axis=-1)
+        signs = signs.reshape((n_blocks, -1, 1)) >> np.array([i for i in range(8)], dtype=np.uint8).reshape((1, 1, 8))
+        signs = signs & np.uint8(0x01)
+        signs = np.where(signs == 0, np.float32(1), np.float32(-1))
+        signs = signs.reshape((n_blocks, -1, 2, 8))
+
+        assert cls.grid is not None
+        grid = np.take_along_axis(cls.grid, (qs & np.uint16(511)).reshape((n_blocks, -1, 1, 1)), axis=-2)
+        grid = grid.reshape((n_blocks, -1, 2, 8))
+
+        return (db * grid * signs).reshape((n_blocks, -1))
+
+
+class IQ2_S(__Quant, qtype=GGMLQuantizationType.IQ2_S):
+    # iq2s_grid, but with each byte of the original packed in 2 bits,
+    # by mapping 0x08 to 0, 0x19 to 1, and 0x2b to 2.
+    grid_shape = (1024, 8)
+    grid_map = (0x08, 0x19, 0x2b)
+    grid_hex = (
+        b"00000200050008000a0011001400160019002000220025002800410044004600"
+        b"490050005200550058006100640066006900800082008500880091009400a000"
+        b"a500aa0001010401060109011001120115011801210124014001420145014801"
+        b"510154015601590160016501680181018401900192019501a101a40100020202"
+        b"050208021102140220022a02410244024602490250025502800285028a029402"
+        b"a202010404040604090410041204150418042104240426042904400442044504"
+        b"48044a0451045404560459046004620465048104840486048904900495049804"
+        b"a104a40400050205050508050a05110514051605190520052505280541054405"
+        b"46054905500552055505580561056405800582058505880591059405a0050106"
+        b"0406060609061006150640064506480651065406600681068406900600080208"
+        b"050808081108140816081908200825082a084108440846084908500852085508"
+        b"580861086408800885089408aa08010904091009120915091809210940094509"
+        b"480951095409600981099009000a110a140a220a280a2a0a500a990a01100410"
+        b"0610091010101210151018102110241026104010421045104810511054105610"
+        b"59106010621065106810811084108610901095109810a110a410001102110511"
+        b"08110a1111111411161119112011221125112811411144114611491150115211"
+        b"5511581161116411801182118511881191119411011204120912101215122112"
+        b"2412401245125112541281128412901200140214051408141114141416141914"
+        b"2014251428144114441446144914501452145514581461146414801482148514"
+        b"881491149414a014011504150615091510151215151518152115241540154215"
+        b"4515481551155415601581158415901500160516081611161416201641164416"
+        b"50168016aa160118041806180918101815181818211840184218451848185118"
+        b"541860188118841800190219051908191119141920194119441950196919a219"
+        b"041a101a401a561a00200220052008201120142016201920202025202a204120"
+        b"4420502052205520642080208a209420aa200121042110211221152121214021"
+        b"4221452151215421602181218421902100220a22222228222a22442250228822"
+        b"8a22a82201240424062409241024152418242124242440244224452448245124"
+        b"5424602481248424902400250525082511251425202541254425502566258025"
+        b"0126042610264026592600280528112814284128442850288a28aa2801290429"
+        b"102995290a2a222a642a882a8a2a014004400640094010401240154018401a40"
+        b"21402440264040404240454048404a4051405440564059406040624065408140"
+        b"8440904095409840a140a4400041024105410841114114411641194120412241"
+        b"2541414144414641494150415241554158416141644180418241854188419141"
+        b"9441a04101420442104212421542184224424042454248425142544260428142"
+        b"844200440244054408440a441144144416441944204422442544284441444444"
+        b"46444944504452445544584461446444804482448544884491449444a0440145"
+        b"0445064509451045124515451845214524454045424545454845514554456045"
+        b"6a4581458445904500460246054608461146144620464146444650468046a546"
+        b"0148044809481048124815481848214824484048424845484848514854486048"
+        b"84489048004902490549084911491449204941494449504980499649014a044a"
+        b"104a404a00500250055008501150145016501950205022502550285041504450"
+        b"4650495050505250555058506150645080508250855088509150945001510451"
+        b"0651095110511251155118512151245140514251455148515151545160518151"
+        b"8451905100520552085211521452205241524452505269528052015404540654"
+        b"0954105412541554185421542454405442544554485451545454605481548454"
+        b"9054005502550555085511551455205541554455505580550156045610562656"
+        b"405600580258055808581158145820584158445850585a588058015904591059"
+        b"4059005a195a855aa85a01600460066010601260156018602160246040604560"
+        b"4860516054606060846090600061026105610861116114612061416144615061"
+        b"806199610462106240625662a162006405640864116414642064416444645064"
+        b"806401650465106540654a656865926500669466016804681068656898680069"
+        b"2a69426aa16a0080028005800880118014801980208025804180448050805280"
+        b"5580588061808080858091809480018104810981108112811581188121812481"
+        b"408142814581488151815481818184819081a981008205820a82118214824182"
+        b"4482508201840484068409841084128415841884218440844284458448845184"
+        b"5484608481848484908400850285058508851185148520854185448550858085"
+        b"8a85018604861086298640860088058811881488418844885088a28801890489"
+        b"40896589228a588a5a8a828aa28a019004900990109012901590189024904090"
+        b"4290459048905190549060908190849090900091059111911491419144915091"
+        b"5a910192049210924092a6920094029405940894119414942094419444945094"
+        b"8094969401950495109540959895a19500964696649601980498109826984098"
+        b"a998009949995299909a00a005a00aa014a022a02aa041a044a050a0a2a0aaa0"
+        b"40a165a102a20aa222a228a22aa282a288a28aa2a8a201a404a410a440a489a4"
+        b"a4a400a519a551a60aa828a8a2a854a986a908aa0aaa20aa22aa28aa88aaaaaa"
+    )
+
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        d, rest = np.hsplit(blocks, [2])
+        qs, rest = np.hsplit(rest, [QK_K // 8])
+        signs, rest = np.hsplit(rest, [QK_K // 8])
+        qh, scales = np.hsplit(rest, [QK_K // 32])
+
+        d = d.view(np.float16).astype(np.float32)
+
+        scales = scales.reshape((n_blocks, -1, 1)) >> np.array([0, 4], dtype=np.uint8).reshape((1, 1, 2))
+        scales = (scales & 0x0F).reshape((n_blocks, -1))
+        db = d * (np.float32(0.5) + scales) * np.float32(0.25)
+        db = db.reshape((n_blocks, -1, 1, 1))
+
+        # unpack the sign bits
+        signs = signs.reshape((n_blocks, -1, 1)) >> np.array([i for i in range(8)], dtype=np.uint8).reshape((1, 1, 8))
+        signs = signs & np.uint8(0x01)
+        signs = np.where(signs == 0, np.float32(1), np.float32(-1))
+        signs = signs.reshape((n_blocks, -1, 2, 8))
+
+        qh = qh.reshape((n_blocks, -1, 1)) >> np.array([0, 2, 4, 6], dtype=np.uint8).reshape((1, 1, 4))
+        qs = qs.astype(np.uint16) | ((qh & 0x03).astype(np.uint16) << 8).reshape((n_blocks, -1))
+
+        assert cls.grid is not None
+        grid = np.take_along_axis(cls.grid, qs.reshape((n_blocks, -1, 1, 1)), axis=-2)
+        grid = grid.reshape((n_blocks, -1, 2, 8))
+
+        return (db * grid * signs).reshape((n_blocks, -1))
+
+
+class IQ3_XXS(__Quant, qtype=GGMLQuantizationType.IQ3_XXS):
+    grid_shape = (256, 4)
+    grid_map = (0x04, 0x0c, 0x14, 0x1c, 0x24, 0x2c, 0x34, 0x3e)
+    grid_hex = (
+        b"0000020004001100130017002000220031004200730075000101030110011201"
+        b"2101250130013201410154017001000202020402110220022202310233023702"
+        b"5102570275020103070310031203250370031304370444045704730475040105"
+        b"0705320552053506640610071407160743076107011003101010121021102310"
+        b"3010321034104710501000110211111120112211011203121012121221123012"
+        b"7212001302132013311346136613011405145014201524154615711505162217"
+        b"4017002002201120132020202220262031204220012103210521102112212121"
+        b"3021632167217021002202221122172220222222372240225522012310231423"
+        b"7023742335245324032527254125742501270327162745270130103012302130"
+        b"2330503065307230003102312031313144314631013203321032253252327232"
+        b"1133333330344734723400350635223555351436363663363337603704401740"
+        b"3540374053405740744120423742404260426642074345430444514464442545"
+        b"4345704505471047124730471250415070500051065126515551145232527252"
+        b"0253535310542354275472540255315550562457425724604460466064602161"
+        b"6161176264623063366344640565526533660367216703700570077010703270"
+        b"5270267140711272457252720073157333736073217441740075027524753076"
+    )
+
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        d, rest = np.hsplit(blocks, [2])
+        qs, scales = np.hsplit(rest, [QK_K // 4])
+
+        d = d.view(np.float16).astype(np.float32)
+        scales = scales.view(np.uint32)
+
+        db = d * (np.float32(0.5) + (scales >> 28).astype(np.float32)) * np.float32(0.5)
+        db = db.reshape((n_blocks, -1, 1, 1))
+
+        # get the sign indices and unpack the bits
+        signs = scales.reshape((n_blocks, -1, 1)) >> np.array([0, 7, 14, 21], dtype=np.uint32).reshape((1, 1, 4))
+        ksigns = np.frombuffer(IQ2_XXS.ksigns, dtype=np.uint8).reshape((1, 1, 1, 128))
+        signs = (signs & np.uint32(0x7F)).reshape((n_blocks, -1, 4, 1))
+        signs = np.take_along_axis(ksigns, signs, axis=-1)
+        signs = signs.reshape((n_blocks, -1, 4, 1)) >> np.array([i for i in range(8)], dtype=np.uint8).reshape((1, 1, 1, 8))
+        signs = signs & np.uint8(0x01)
+        signs = np.where(signs == 0, np.float32(1), np.float32(-1))
+        signs = signs.reshape((n_blocks, -1, 4, 8))
+
+        assert cls.grid is not None
+        grid = np.take_along_axis(cls.grid, qs.reshape((n_blocks, -1, 1, 1)), axis=-2)
+        grid = grid.reshape((n_blocks, -1, 4, 8))
+
+        return (db * grid * signs).reshape((n_blocks, -1))
+
+
+class IQ3_S(__Quant, qtype=GGMLQuantizationType.IQ3_S):
+    grid_shape = (512, 4)
+    grid_map = (0x01, 0x03, 0x05, 0x07, 0x09, 0x0b, 0x0d, 0x0f)
+    grid_hex = (
+        b"0000010002000500070010001100120014001600200021002500330040004200"
+        b"4500470051005300600062007100740077000001010102010401100111011501"
+        b"2001230127013101350144016101650172010002010205020702100213021602"
+        b"2102250230023402420245024702510253027002730203031103150320032203"
+        b"3103330336034403500352036703710375030004130417042104240432044004"
+        b"4304510470040205040520052205260533054105450547056605730506061106"
+        b"1306310652067106000702070407200722072607330750075407001001100210"
+        b"0410101011101310151017102010221031103410361054105610611072100011"
+        b"0111031106111011141121113011331141115011521170117611001212121512"
+        b"1712201224123212401243125512601272120113041307131013131321132713"
+        b"3013341341136213701303140514121414143114331442144614501454140115"
+        b"1015131521153015321551152016241627164416461601170317101712172117"
+        b"3517411762177017002001200320052007201020122014201620212023202720"
+        b"3020322041204320452050205220672070207320752000210221102113211721"
+        b"2221252131213421422151210122042207222122232230223722412253225722"
+        b"7122742200230223052311232223242331233323422350236623012407242024"
+        b"2324322435244124722475240425112522253725402553257025002602260726"
+        b"2126552661260527112726273027432750270230113013301530173022303130"
+        b"3330353042304430473051306330713001310331053114312131233140316031"
+        b"7231763100321232203232323432503201331033143321332333273330334133"
+        b"4333473355337333033411341634223431345234603464340135103512352535"
+        b"3235443556357335163641360137033720372237353700400440124020402440"
+        b"2740324041405040704002410741114113412241304135414341514155410142"
+        b"0342104215422142334240425742624270420443114313432043224331433543"
+        b"0044024424443744404471440545074521456245134634466046104715473047"
+        b"4347514702501050145022504050445047505250665074500151035105511251"
+        b"2151325172510052115223523052365253520253075310532753445351536553"
+        b"7353015404542054325446541255265551555355425602570457225711601360"
+        b"1560316033606060006120612761646112623462426255626262706200631463"
+        b"2163406325644364626400650365346560650566406611671367007004700770"
+        b"2070227036704070547062700271117124714371457101720472107216722172"
+        b"3072517202733273357353730174057413742074507422754275027631760077"
+    )
+
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        d, rest = np.hsplit(blocks, [2])
+        qs, rest = np.hsplit(rest, [QK_K // 4])
+        qh, rest = np.hsplit(rest, [QK_K // 32])
+        signs, scales = np.hsplit(rest, [QK_K // 8])
+
+        d = d.view(np.float16).astype(np.float32)
+
+        scales = scales.reshape((n_blocks, -1, 1)) >> np.array([0, 4], dtype=np.uint8).reshape((1, 1, 2))
+        scales = (scales & 0x0F).reshape((n_blocks, -1))
+        db = d * (1 + 2 * scales)
+        db = db.reshape((n_blocks, -1, 1, 1))
+
+        # unpack the sign bits
+        signs = signs.reshape((n_blocks, -1, 1)) >> np.array([i for i in range(8)], dtype=np.uint8).reshape((1, 1, 8))
+        signs = signs & np.uint8(0x01)
+        signs = np.where(signs == 0, np.float32(1), np.float32(-1))
+        signs = signs.reshape((n_blocks, -1, 4, 8))
+
+        qh = qh.reshape((n_blocks, -1, 1)) >> np.array([i for i in range(8)], dtype=np.uint8)
+        qh = (qh & 0x01).astype(np.uint16).reshape((n_blocks, -1))
+        qs = qs.astype(np.uint16) | (qh << 8)
+
+        assert cls.grid is not None
+        grid = np.take_along_axis(cls.grid, qs.reshape((n_blocks, -1, 1, 1)), axis=-2)
+        grid = grid.reshape((n_blocks, -1, 4, 8))
+
+        return (db * grid * signs).reshape((n_blocks, -1))
+
+
+class IQ1_S(__Quant, qtype=GGMLQuantizationType.IQ1_S):
+    # iq1s_grid, with each byte packed into 2 bits
+    # -1, 0, 1 <=> 0, 1, 2
+    grid_shape = (2048, 8)
+    grid_map = (-1, 0, 1)
+    grid_hex = (
+        b"00000200050008000a00110015002000220028002a0045005100540056006500"
+        b"8000820088008a009500a000a200a800aa000401050111011401160119011a01"
+        b"2501410146014901520155015a0161016401660168018501910194019601a501"
+        b"0002020208020a0215022002220228022a024502510259026402690280028202"
+        b"88028a02910295029902a002a202a802aa021104140416042504410449045504"
+        b"5a046404650491049904a5040105040505050605150518051a05290540054505"
+        b"4a0550055105540555055605590560056205650568056a058105910595059805"
+        b"9a05a105a405a505a605a9051406190641064406500652065506580660066106"
+        b"6606690685069106940699060008020808080a0815082008220828082a084508"
+        b"5108560865088008820888088a089508a008a208a808aa080509110914091909"
+        b"2409250941095009510955096109640969099109940996099909a509000a020a"
+        b"080a0a0a150a200a220a280a2a0a450a510a590a610a650a800a820a850a880a"
+        b"8a0a950aa00aa20aa80aaa0a1010111014101910241025104110441050105510"
+        b"58106110641065106910911094109610a110a510011104110611091110111211"
+        b"1511181121112411291145114a11501151115211541155115611591160116511"
+        b"841192119511a111a41111121412161225124012461249125212551258125a12"
+        b"641266128512911294129612a512011406140914141415141814191421142614"
+        b"41144514461448144a1451145414551456145914621465146814841489149014"
+        b"94149514981499149a14a114a414a514a914021505150a151115141515151615"
+        b"191520152215251528152a154115441545154615511552155415551556155915"
+        b"5a1561156415651566156915801582158415851588158a159015911594159515"
+        b"961599159a15a015a215a51501160416051606161516161618161a1621162616"
+        b"401642164416451648164a165116551656165816591661166416651668166916"
+        b"6a1686168a1692169516a416a916111816182518411844184618491850185518"
+        b"58185a1860186118641866186918851891189418a5181019121915191a192119"
+        b"25194219441945194819511954195519561959195a19601965196a1989199119"
+        b"921995199819a119a619a919091a161a241a261a441a461a491a501a521a551a"
+        b"581a611a661a691a851a911a961a9a1a0020022008200a201520202022202520"
+        b"28202a20452051205920612065208020822088208a209520a020a220a520a820"
+        b"aa2005211121142119212521422144214921552158215a216121642165216621"
+        b"8521902196219921a521012208220a22112215222022222228222a2245225122"
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+    )
+
+    delta = np.float32(0.125)
+
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        d, rest = np.hsplit(blocks, [2])
+        qs, qh = np.hsplit(rest, [QK_K // 8])
+
+        d = d.view(np.float16).astype(np.float32)
+        qh = qh.view(np.uint16)
+
+        dl = d * (2 * ((qh >> 12) & 7) + 1)
+        dl = dl.reshape((n_blocks, -1, 1, 1))
+        delta = np.where((qh & np.uint16(0x8000)) == 0, cls.delta, -cls.delta)
+        delta = delta.reshape((n_blocks, -1, 1, 1))
+
+        qh = qh.reshape((n_blocks, -1, 1)) >> np.array([0, 3, 6, 9], dtype=np.uint16).reshape((1, 1, 4))
+        qs = qs.astype(np.uint16) | ((qh & 7) << 8).reshape((n_blocks, -1))
+
+        assert cls.grid is not None
+        grid = np.take_along_axis(cls.grid, qs.reshape((n_blocks, -1, 1, 1)), axis=-2)
+        grid = grid.reshape((n_blocks, -1, 4, 8))
+
+        return (dl * (grid + delta)).reshape((n_blocks, -1))
+
+
+class IQ1_M(__Quant, qtype=GGMLQuantizationType.IQ1_M):
+    grid_shape = IQ1_S.grid_shape
+    grid_map = IQ1_S.grid_map
+    grid_hex = IQ1_S.grid_hex
+
+    delta = IQ1_S.delta
+
+    # Okay *this* type is weird. It's the only one which stores the f16 scales in multiple parts.
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        qs, rest = np.hsplit(blocks, [QK_K // 8])
+        qh, scales = np.hsplit(rest, [QK_K // 16])
+
+        # The f16 scale is packed across multiple bytes
+        scales = scales.view(np.uint16)
+        d = (scales.reshape((n_blocks, 4)) & np.uint16(0xF000)) >> np.array([12, 8, 4, 0], dtype=np.uint16).reshape((1, 4))
+        d = d[..., 0] | d[..., 1] | d[..., 2] | d[..., 3]
+        d = d.view(np.float16).astype(np.float32).reshape((n_blocks, 1))
+
+        scales = scales.reshape(n_blocks, -1, 1) >> np.array([0, 3, 6, 9], dtype=np.uint16).reshape((1, 1, 4))
+        scales = (scales & 0x07).reshape((n_blocks, -1))
+        dl = d * (2 * scales + 1)
+        dl = dl.reshape((n_blocks, -1, 2, 1, 1))
+
+        qh = qh.reshape((n_blocks, -1, 1)) >> np.array([0, 4], dtype=np.uint8).reshape((1, 1, 2))
+        qs = qs.astype(np.uint16) | ((qh & 0x07).astype(np.uint16) << 8).reshape((n_blocks, -1))
+
+        delta = np.where(qh & 0x08 == 0, cls.delta, -cls.delta)
+        delta = delta.reshape((n_blocks, -1, 2, 2, 1))
+
+        assert cls.grid is not None
+        grid = np.take_along_axis(cls.grid, qs.reshape((n_blocks, -1, 1, 1)), axis=-2)
+        grid = grid.reshape((n_blocks, -1, 2, 2, 8))
+
+        return (dl * (grid + delta)).reshape((n_blocks, -1))
+
+
+class IQ4_NL(__Quant, qtype=GGMLQuantizationType.IQ4_NL):
+    kvalues = (-127, -104, -83, -65, -49, -35, -22, -10, 1, 13, 25, 38, 53, 69, 89, 113)
+
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        d, qs = np.hsplit(blocks, [2])
+
+        d = d.view(np.float16).astype(np.float32)
+
+        qs = qs.reshape((n_blocks, -1, 1, cls.block_size // 2)) >> np.array([0, 4], dtype=np.uint8).reshape((1, 1, 2, 1))
+
+        qs = (qs & np.uint8(0x0F)).reshape((n_blocks, -1, 1))
+
+        kvalues = np.array(cls.kvalues, dtype=np.int8).reshape(1, 1, 16)
+        qs = np.take_along_axis(kvalues, qs, axis=-1).astype(np.float32).reshape((n_blocks, -1))
+
+        return (d * qs)
+
+
+class IQ4_XS(__Quant, qtype=GGMLQuantizationType.IQ4_XS):
+    @classmethod
+    def dequantize_blocks(cls, blocks: np.ndarray) -> np.ndarray:
+        n_blocks = blocks.shape[0]
+
+        d, rest = np.hsplit(blocks, [2])
+        scales_h, rest = np.hsplit(rest, [2])
+        scales_l, qs = np.hsplit(rest, [QK_K // 64])
+
+        d = d.view(np.float16).astype(np.float32)
+        scales_h = scales_h.view(np.uint16)
+
+        scales_l = scales_l.reshape((n_blocks, -1, 1)) >> np.array([0, 4], dtype=np.uint8).reshape((1, 1, 2))
+        scales_h = scales_h.reshape((n_blocks, 1, -1)) >> np.array([2 * i for i in range(QK_K // 32)], dtype=np.uint16).reshape((1, -1, 1))
+        scales_l = scales_l.reshape((n_blocks, -1)) & np.uint8(0x0F)
+        scales_h = scales_h.reshape((n_blocks, -1)).astype(np.uint8) & np.uint8(0x03)
+
+        scales = (scales_l | (scales_h << np.uint8(4))).astype(np.int8) - np.int8(32)
+        dl = (d * scales.astype(np.float32)).reshape((n_blocks, -1, 1))
+
+        qs = qs.reshape((n_blocks, -1, 1, 16)) >> np.array([0, 4], dtype=np.uint8).reshape((1, 1, 2, 1))
+        qs = qs.reshape((n_blocks, -1, 32, 1)) & np.uint8(0x0F)
+
+        kvalues = np.array(IQ4_NL.kvalues, dtype=np.int8).reshape((1, 1, 1, -1))
+        qs = np.take_along_axis(kvalues, qs, axis=-1).astype(np.float32).reshape((n_blocks, -1, 32))
+
+        return (dl * qs).reshape((n_blocks, -1))
+
+# =============================================================================
+# Helicoidal-Zeta Kernel (Bruno Becker) — clean (no Tk / no UI)
+# =============================================================================
+# This section is intentionally dependency-light and does NOT touch quantization
+# logic above. It provides the exact HelicoidalZetaCore math used in
+# ΩFFΣLLIα_Ωmegα_GPT.py (kernel only), with an optional prime-indexed variant
+# aligned with Artigo.txt.
+#
+# Sources:
+# - ΩFFΣLLIα_Ωmegα_GPT.py: HelicoidalZetaCore (Fn/coords/delta_m/zeta_signature/math_embedding)
+# - Artigo.txt: helicoidal mapping using p_n (n-th prime) and zeta(1/2 + i p_n)
+# =============================================================================
+
+from dataclasses import dataclass, field
+
+try:
+    from mpmath import mp, zeta as _mp_zeta  # type: ignore
+except Exception:  # pragma: no cover
+    mp = None
+    _mp_zeta = None
+
+
+def _require_mpmath() -> None:
+    if mp is None or _mp_zeta is None:
+        raise ImportError(
+            "mpmath is required for zeta_signature(). Install with: pip install mpmath"
+        )
+
+
+@dataclass
+class _PrimeCache:
+    """
+    Minimal prime cache to obtain p_n (n-th prime) with no external deps.
+
+    NOTE: n is 1-indexed: p_1 = 2, p_2 = 3, ...
+    """
+    primes: list[int] = field(default_factory=lambda: [2, 3, 5, 7, 11, 13])
+    _checked_upto: int = 13
+
+    @staticmethod
+    def _is_prime(k: int, primes: list[int]) -> bool:
+        if k < 2:
+            return False
+        for p in primes:
+            if p * p > k:
+                return True
+            if k % p == 0:
+                return False
+        return True
+
+    def nth_prime(self, n: int) -> int:
+        if n <= 0:
+            raise ValueError("n must be >= 1 (1-indexed) for nth_prime")
+        candidate = self._checked_upto
+        if candidate % 2 == 0:
+            candidate += 1
+        while len(self.primes) < n:
+            candidate += 2
+            if self._is_prime(candidate, self.primes):
+                self.primes.append(candidate)
+                self._checked_upto = candidate
+        return self.primes[n - 1]
+
+
+@dataclass
+class HelicoidalZetaCore:
+    """
+    Kernel matemático helicoidal-zeta (sem UI).
+
+    Mantém a matemática exatamente como no kernel do arquivo ΩFFΣLLIα_Ωmegα_GPT.py:
+      - phi = (1 + sqrt(5)) / 2
+      - Fn(n) = sin(2π φ n)^2
+      - coords(n) = [x, y, z] com r = Fn(n), θ = 2π φ n, (x,y) = r(cosθ, sinθ), z=n
+      - delta_m(n,m) = 1.0 se n ≡ 0 (mod m) senão 0.42
+      - zeta_signature(n) = (Re, Im) de ζ(1/2 + i n)
+      - math_embedding(n) = concat([coords(n)*delta, [r, θ], zeta_signature(n)])
+        (igual ao código original)
+    """
+    zeta_dps: int = 25
+    delta_modulus: int = 42
+    delta_else: float = 0.42
+
+    # optional prime-indexing (Artigo.txt): use p_n instead of n
+    use_primes: bool = False
+    _prime_cache: _PrimeCache = field(default_factory=_PrimeCache)
+
+    def __post_init__(self) -> None:
+        self.phi = (1.0 + float(np.sqrt(5.0))) / 2.0
+        if mp is not None:
+            mp.dps = int(self.zeta_dps)
+
+    def _n_to_eval(self, n: int) -> int:
+        if not self.use_primes:
+            return int(n)
+        return int(self._prime_cache.nth_prime(int(n)))
+
+    def Fn(self, n: int) -> float:
+        nn = self._n_to_eval(n)
+        return float(np.sin(2.0 * np.pi * self.phi * nn) ** 2)
+
+    def coords(self, n: int) -> np.ndarray:
+        nn = self._n_to_eval(n)
+        r = float(np.sin(2.0 * np.pi * self.phi * nn) ** 2)
+        t = 2.0 * np.pi * self.phi * nn
+        x = r * float(np.cos(t))
+        y = r * float(np.sin(t))
+        z = float(nn)
+        return np.array([x, y, z], dtype=np.float64)
+
+    def delta_m(self, n: int, m: int | None = None) -> float:
+        nn = self._n_to_eval(n)
+        mm = int(self.delta_modulus if m is None else m)
+        return 1.0 if (nn % mm) == 0 else float(self.delta_else)
+
+    def zeta_signature(self, n: int) -> np.ndarray:
+        _require_mpmath()
+        nn = self._n_to_eval(n)
+        if mp is not None:
+            mp.dps = int(self.zeta_dps)
+            s = mp.mpc(0.5, float(nn))
+            val = _mp_zeta(s)
+            return np.array([float(val.real), float(val.imag)], dtype=np.float64)
+        raise RuntimeError("mpmath not available")
+
+    def math_embedding(self, n: int) -> np.ndarray:
+        nn = self._n_to_eval(n)
+        coords = self.coords(n)
+        r = float(np.sin(2.0 * np.pi * self.phi * nn) ** 2)
+        theta = 2.0 * np.pi * self.phi * nn
+        delta = self.delta_m(n)
+        zeta_vals = self.zeta_signature(n)
+        # Vetor final (compatível com o kernel original):
+        # [xδ, yδ, zδ, r, θ, Re(Zeta), Im(Zeta)]
+        return np.concatenate([coords * delta, np.array([r, theta], dtype=np.float64), zeta_vals])
+
+    def transform(self, x: np.ndarray, n_val: int) -> np.ndarray:
+        emb = self.math_embedding(n_val)
+        return x * float(np.mean(emb))
+
+
+def helicoidal_zeta_scale(n_val: int, *, use_primes: bool = False, zeta_dps: int = 25) -> float:
+    """
+    Retorna o escalar multiplicativo usado por transform(): mean(math_embedding).
+    """
+    core = HelicoidalZetaCore(use_primes=use_primes, zeta_dps=zeta_dps)
+    emb = core.math_embedding(int(n_val))
+    return float(np.mean(emb))
+
+
+__all__ = [
+    "HelicoidalZetaCore",
+    "helicoidal_zeta_scale",
+]