> For the complete documentation index, see [llms.txt](https://clarity-7.gitbook.io/clarity-docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://clarity-7.gitbook.io/clarity-docs/clarity-moniversive-invariant-static-mis/core-protocol-specs/gitbook-moniversive-mis-core-specs.md).

# gitbook.moniversive.mis — tensors, Q64.64, invariant state

> Generated 2026-07-29T03:15:30Z · mathematical tensors · **Q64.64** fixed-point · invariant state frameworks

**Core Protocol Specs (`gitbook.moniversive.mis`):** mathematical tensor definitions, **Q64.64** fixed-point math rules, and invariant state frameworks.

Document id: **`gitbook.moniversive.mis`** — language GitBook core protocol layer (not chain product docs). SSOT companions: `CLRTY_SUBSTRATE/boot/clrty1_static_ml_invariants.json` · `moniversive/framework/mis_ml.mis` · surfaces under `languages/mis-ml/surfaces/`. Indexed as **`gitbook.moniversive.mis`** in `mis_code_index.json`.

## 1. Mathematical tensor definitions

| Construct                   | Definition                                           | MIS module / surface                                                                                                                       |
| --------------------------- | ---------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------ |
| `mis_tensor[dtype, shape]`  | Static rank & shape at compile time; no dynamic rank | [mis\_tensor](/clarity-docs/clarity-moniversive-invariant-static-mis/framework-.mis/mis_tensor.md) · `MisMl.assert_mis_tensor`             |
| `WeightTensorDescriptor`    | Bit-packed dims, strides, alignment (band 601–615)   | `DeterministicWeightOps.clrty`                                                                                                             |
| `GradientAccumulatorBuffer` | 64-byte aligned lane sums (band 201–215)             | Static ML catalog                                                                                                                          |
| `mis_array[T, N]`           | Bounded storage · `vector_map` / GEMM kernels        | [collections-concurrency](/clarity-docs/clarity-moniversive-invariant-static-mis/language-and-coding-breakdown/collections-concurrency.md) |
| Spectral / norm tensors     | $\sigma\_{max}$ lock · L2 clip · RMSNorm             | bands 761–775 · 876–975 `fn_*`                                                                                                             |

**Layout rules**

* Row-major unless pack manifest says otherwise; stride multiples of **64 bytes** for SIMD (catalog `VectorPaddingAlignment`, `CachePrefetchInstruction`).
* Quantized activations: per-channel scales with fixed-point restore on matmul (see Q formats below).

## 2. Q64.64 fixed-point math rules

**Q64.64** — 64-bit signed integer + 64-bit fractional field (128-bit logical value in registers / wide accumulators). Used for **protocol-grade** accumulations where IEEE float is forbidden.

| Rule             | Specification                                                                                                                             |
| ---------------- | ----------------------------------------------------------------------------------------------------------------------------------------- |
| Representation   | `value_q6464 = (int64 << 64) \| frac64` (logical); physical storage may be pair of `i64` or `u128` with defined endianness in kernel pack |
| Add / sub        | Same-scale only; overflow → **saturating** or **trap** per `HardwareExceptionTrap` (band 761–775)                                         |
| Mul              | Widening multiply to **128-bit** product; round with **deterministic** mode (ties-to-even unless pack locks RN)                           |
| Shift / quantize | `VectorShiftRightRound`: scale wide accumulators down to **Q32.32** or **Q8.24** lanes with explicit rounding bit                         |
| Compare          | Branchless masks (`mis.select`, `VectorBitwiseSelect`) — no hidden float compare                                                          |
| Literal policy   | No runtime float literals in hot kernels; use `fixed_point_literal` outcomes where declared                                               |

**Related formats (same protocol family)**

| Format         | Use                                                                                |
| -------------- | ---------------------------------------------------------------------------------- |
| **Q8.24**      | Gradients, weights, DSP primitives (`fixed_point_q8_24` invariants on ML surfaces) |
| **Q32.32**     | Intermediate dot-product lanes before down-quant                                   |
| **INT8 / FP8** | Storage tensors after `DeterministicQuantRound` / E4M3 unpack kernels              |

```bash
bin/misc languages/mis-ml/surfaces/NativeDspPrimitives.clrty --check --compact-letters
bin/misc languages/mis-ml/surfaces/HardwareVectorMath.clrty --check --compact-letters
```

## 3. Invariant state frameworks

State is **predicate-first**: transitions must satisfy named invariants before commit (replaces ad-hoc `require` / exceptions).

| Layer               | Framework                               | Examples                                                                                                                                         |
| ------------------- | --------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------ |
| Module              | `invariant` + `outcome` in **`.mis`**   | `letter_hash_bound`, `settlement_chain`, `mis_tensor_bound`                                                                                      |
| Static ML catalog   | 1025 named invariants                   | [static ML bands](/clarity-docs/clarity-moniversive-invariant-static-mis/catalog-generated/static-ml-invariant-bands.md)                         |
| Cross-shard         | 746–760                                 | `CrossShardStateRoot`, `GlobalSolvencyCrossCheck`                                                                                                |
| On-chain style sets | `mis_set` opcodes / supply caps         | [definitions-variables-sets](/clarity-docs/clarity-moniversive-invariant-static-mis/language-and-coding-breakdown/definitions-variables-sets.md) |
| EVM analogue        | `invariant` ≈ `require` at compile time | [evm-to-mis](/clarity-docs/clarity-moniversive-invariant-static-mis/architecture-static-ml/evm-to-mis.md)                                        |

**State transition pattern**

1. Load static bounds (`mis.load` / register file).
2. Prove guards (`mis.invariant` / `invariant` in `.mis`).
3. Branchless update (`mis.select` / bitwise masks).
4. Atomic commit (`mis.store` + barrier); shard/global roots per cross-shard band.

## Commands & index

```bash
make gitbook-moniversive-build
bin/misc moniversive/framework/mis_ml.mis --check --compact-letters
```

Resolve symbols: **`mis_code_index.json`** · RPC **`clrty_getMisCodeIndex`**. Kernel repo: [moniversive\_invariant\_static\_ML](https://github.com/clarity-fintech/moniversive_invariant_static_ML).

See also: [math/invariant-primer.md](/clarity-docs/clarity-moniversive-invariant-static-mis/math/invariant-primer.md) · [operational rulebook](/clarity-docs/clarity-moniversive-invariant-static-mis/architecture-static-ml/operational-rulebook.md) · [full language breakdown](/clarity-docs/clarity-moniversive-invariant-static-mis/language-and-coding-breakdown/full-language-breakdown.md).


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