# sym-int8: mirror symmetry and int8 bps offsets

## Method

**Chosen: adaptive100, 10,024 bytes total; report-set loss -0.008644684, SE 0.007750660, n=2048.** The 12 KB and mean-loss <0.2 targets are met on the replica. Negative loss means the decoded policy scored higher.

Credit: Taylor (gtmcknight), solved policy and replica, commit `4812a6382311624e1506aca131ca35c378f930d9`. Read [README](https://raw.githubusercontent.com/gtmcknight/amm-sim/4812a6382311624e1506aca131ca35c378f930d9/research/solved/README.md) first. Source policy tables are [pol_mid.json](https://raw.githubusercontent.com/gtmcknight/amm-sim/4812a6382311624e1506aca131ca35c378f930d9/research/solved/pol_mid.json); SHA-256 `efbb5ee102db4d312f64565d9bf7232b6becbe02b624164f744a402bbbf2983b`, 780,061 bytes. All experimental numbers below are local measurements using those pinned files, not claims of Rust-engine performance.

### Original policy inventory

Values are quote offsets from estimated fair price, in bps. The six policy tables contain 71,262 values. Rows in every table are `w=(i-160)*5` bps, i=0..320, from -800 to +800. A is ask; B is bid. The policy accesses these six arrays through [DPPolicy](https://raw.githubusercontent.com/gtmcknight/amm-sim/4812a6382311624e1506aca131ca35c378f930d9/research/solved/evalpol.py).

| Table | Shape (w × R) | Minimum bps | Maximum bps | R axis |
|---|---|---:|---:|---|
| A0 | 321 × 13 | -24.262 | 800 | -30..30 by 5 bps |
| B0 | 321 × 13 | -24.262 | 800 | -30..30 by 5 bps |
| A1 | 321 × 49 | -31.323 | 800 | 5 × W2L below |
| B1 | 321 × 49 | -31.323 | 800 | 5 × W2L below |
| A2 | 321 × 49 | -31.333 | 800 | 5 × W2L below |
| B2 | 321 × 49 | -31.333 | 800 | 5 × W2L below |

`W2L = [-160,-130,-100,-80,-60,-50,-40,-30,-25,-20,-17,-14,-12,-11,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,11,12,14,17,20,25,30,40,50,60,80,100,130,160]`.

The nonuniform R grids span -800..800 bps; successive bps steps are 5 times successive differences in this list (5, 10, 15, 25, 50, 100, or 150 bps, depending on location). No R columns are removed. `VD0` and `VD1` are value-function arrays, not policy quote tables. They are omitted from the decoder output; all six fee arrays and every non-array grid/solve metadata field are restored in the original JSON schema accepted by `real.py`.

### Gate P and symmetry, before compression

Unmodified `python3 -I gates.py` reproduced [the pinned gates](https://raw.githubusercontent.com/gtmcknight/amm-sim/4812a6382311624e1506aca131ca35c378f930d9/research/solved/gates.py) before creating the encoding:

```text
seed   perfect-info      gaussian+plain    gaussian+qm       lattice+qm
10000  448.261189  443.455598  443.522608  443.663520
10001  576.779199  571.463409  571.623551  571.977293
10002  531.886497  525.168028  525.865859  526.411631
```

Exhaustive comparison `abs(Ap[i][j] - Bp[320-i][nc-1-j])` across every cell gave maximum **0.000 bps** in each phase (and globally). Both axes are sign-symmetric, including W2L. Store A only, reconstruct B by reversing both axes. This halves the full policy table set without approximation.

For every retained A row, base = Python `round((min(row)+max(row))/2)` bps; signed residual = `clip(round(value-base), -128, 127)` at **1 bps per unit**. `round` uses ties to even. The largest within-row spans before sampling are 47.699, 160, and 150 bps in phases 0, 1, and 2, so **zero residuals clip in every candidate**. The base is signed int16 bps. Fill missing w rows by linear interpolation of decoded retained rows, then mirror to form B. Original bilinear lookup and all Gaussian filter logic stay unchanged.

## Encoding

One representation only: one-sided symmetric tables, integer row bases, signed int8 bps residuals; row subsampling is the tuned parameter. No entropy coding, low-rank model, or second codec.

All integers are little-endian; residuals use two's complement. No padding. Exact chosen layout:

| Byte offsets, inclusive | Content |
|---|---|
| 0..3 | ASCII `SI81` |
| 4..5 | uint16 JSON header length H=377 |
| 6..7 | uint16 retained row count K=81 |
| 8..384 | H bytes UTF-8 compact JSON containing original scalar metadata and W2L |
| 385..546 | K uint16 original w-row indices, sorted ascending |
| 547..1761 | phase 0: 81 records of 15 bytes each |
| 1762..5892 | phase 1: 81 records of 51 bytes each |
| 5893..10023 | phase 2: 81 records of 51 bytes each |

Each record is `[int16 base][int8 residual column 0]...[int8 residual column nc-1]`, nc=13 for phase 0, 49 otherwise. Records follow retained row order; column order is the original R grid. For phase start S and retained row index k, base address is `S+k*(nc+2)`; residual (k,j) is at `S+k*(nc+2)+2+j`. Offset value is `sign16(base)+sign8(residual)` bps. Header magic is versioned; K comes from the header, not the magic's digits.

Total = 8 prefix + 377 metadata + 162 row indices + 8,991 residual bytes + 486 base bytes = **10,024 bytes**, including everything needed to decode. Raw numeric table payload is 9,477 bytes. Solidity can hardcode the metadata, but this report does not subtract it from the total. Base64 textual expansion is not deployed data.

Chosen w knots are the sorted union (inclusive) of `[-100,100] step 5`, `[-200,200] step 10`, `[-400,400] step 40`, `[-800,800] step 100`, in bps. Union is literal: overlapping ranges can add intermediate knots. Convert each w to original index `(w+800)//5`. Exact indices:

```text
0,20,40,60,80,88,96,100,104,112,120,122,124,126,128,130,132,134,
136,138,140,141,142,143,144,145,146,147,148,149,150,151,152,153,
154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,
170,171,172,173,174,175,176,177,178,179,180,182,184,186,188,190,
192,194,196,198,200,208,216,220,224,232,240,260,280,300,320
```

For Solidity, bracket w between retained knots and R between original columns, clamp to axis endpoints, decode four corners, then interpolate. For bid, perform the ask lookup with both coordinates negated. Direct interpolation on retained knots equals interpolation in the decoder's expanded grid, up to floating-point roundoff, since retained knots are original grid points.

## Tradeoff

All choices use exact symmetry and the same 1 bps int8 quantizer. Choose seeds **60000..61023 only**, n=1024 for every row. Loss per seed is `full.edge - decoded.edge`. SE is sample standard deviation of those paired losses divided by sqrt(n). The full and decoded policies see the same per-seed price, retail and configuration random streams, each over the replica's default 10,000 steps ([replica2.py](https://raw.githubusercontent.com/gtmcknight/amm-sim/4812a6382311624e1506aca131ca35c378f930d9/research/solved/replica2.py)).

| Setting | Retained rows | Bytes, entire blob | Choose-set loss | SE |
|---|---:|---:|---:|---:|
| uniform20 | 81 | 10,024 | +0.322883175 | 0.014155512 |
| adaptive100 | 81 | 10,024 | -0.001281364 | 0.010820910 |
| adaptive180 | 97 | 11,928 | -0.000867544 | 0.010711970 |

`uniform20`: w=-800..800 every 20 bps. `adaptive100`: union above. `adaptive180`: replace the first range by [-180,180] step 5; leave the other three ranges unchanged. Each used a freshly generated blob and decoded JSON. No candidate uses qm tables.

Select **adaptive100**: smallest mean choose loss, lower bytes than adaptive180, and a clear improvement over uniform20. The small difference between the two adaptive candidates is below their sampling uncertainty; choose100 has no evidence of a meaningful disadvantage. The initial 16-seed plumbing smoke test used only 60000..60015, a subset of the selection set. It was not an additional seed set.

Choose-set worst five paired losses for each setting (seed: full-minus-decoded edge):

| Setting | Worst five, descending loss |
|---|---|
| uniform20 | 60092: 1.652588151; 60816: 1.616190352; 60434: 1.555479497; 60084: 1.525769795; 60122: 1.516516356 |
| adaptive100 | 60411: 1.157516225; 60304: 0.978722026; 60092: 0.926825374; 60244: 0.913889322; 60723: 0.894010861 |
| adaptive180 | 60411: 1.118144900; 60038: 1.094758424; 60542: 1.073655936; 60244: 1.010233475; 60385: 0.918848403 |


## Chosen

Frozen before report scoring: **adaptive100**, 1 bps residual units, signed int16 row bases, 81 retained rows, **10,024 bytes**, no clipping. Report seeds **10000..12047**, **n=2048**; run once as the selected representation, with full-table comparisons on the identical seeds:

- Full mean edge: **532.385688969**.
- Decoded mean edge: **532.394333653**.
- Mean paired loss (full minus decoded): **-0.008644684**.
- Paired SE: **0.007750660**.

Worst five seeds are the largest positive full-minus-decoded losses, not the five lowest absolute scores:

| Seed | Loss | Full edge | Decoded edge |
|---:|---:|---:|---:|
| 10429 | 1.317202325 | 593.861185681 | 592.543983356 |
| 10177 | 1.141135028 | 652.294634992 | 651.153499963 |
| 10041 | 1.036806884 | 628.992913052 | 627.956106168 |
| 11826 | 1.018917236 | 631.554259203 | 630.535341967 |
| 10231 | 0.987694005 | 692.630207081 | 691.642513076 |

No parameter changes followed reading the report set. This is a measured mean-loss result, not a bound on individual losses. Over all 71,262 reconstructed quote cells, maximum absolute offset error is 39.868 bps and mean absolute error is 0.164118464 bps. These table errors include coarse far-tail row interpolation. They are not callback fee-equivalence errors.

### Scoring and reproduction

The scoring code uses the unmodified [real.RealPolicy](https://raw.githubusercontent.com/gtmcknight/amm-sim/4812a6382311624e1506aca131ca35c378f930d9/research/solved/real.py), `{'soft':1.0}`, and unmodified `replica2.run`. It saves the edge for every seed and pairs by seed, rather than subtracting independently rounded printed means. All Taylor modules were executed with plain `python3 -I`; no dependencies or environment setup were installed. Local helper scripts add the pinned solved directory to sys.path, just as Taylor's own files do.

Python 3.14 defaults to forkserver; this sandbox refuses the Unix socket it needs. Used `multiprocessing.set_start_method('fork')` in a wrapper, leaving Taylor's files unchanged. For the official CLI report, from the pinned `research/solved` directory, with decoded JSON saved as `../../../work/adaptive100.json`, the exact commands are:

```sh
python3 -I -c "import multiprocessing,runpy,sys; multiprocessing.set_start_method('fork'); sys.argv=['real.py','pol_mid.json','plain:soft=1']; runpy.run_path('real.py',run_name='__main__')"
python3 -I -c "import multiprocessing,runpy,sys; multiprocessing.set_start_method('fork'); sys.argv=['real.py','../../../work/adaptive100.json','plain:soft=1']; runpy.run_path('real.py',run_name='__main__')"
```

The official CLI printed full edge 532.386, vs HA +2.828 SE 0.041; decoded edge 532.394, vs HA +2.837 SE 0.041. These rounded HA comparisons are not the paired compression-loss estimator.

The CLI hardcodes report seeds starting at 10000 and prints comparisons with HA, not individual rows or arbitrary start seeds. For selection and exact paired losses, the equivalent per-seed computation was:

```python
# Launch under python3 -I; insert the absolute pinned research/solved directory first.
import sys, json, math
sys.path.insert(0, SOLVED)
import real, replica2
from evalpol import load

def score(path, seed):
    return replica2.run(seed, real.RealPolicy(load(path), {'soft': 1.0}))['edge']

# Selection: range(60000,61024); report: range(10000,12048).
# full and decoded are paths to pol_mid.json and decoder output.
loss = [score(full, s)-score(decoded, s) for s in seeds]
n = len(loss)
mean = sum(loss)/n
se = math.sqrt(sum((x-mean)**2 for x in loss)/(n*(n-1)))
```

Actual execution used a 14-worker fork pool with jobs `(table_path, seed)` and persisted edge dictionaries under scratch. Every measured command completed in under eight minutes. The official CLI repeats the frozen report configuration only to validate printed means; it is not another selection trial.

## Lookup cost

For **one offset** at a known bracket: four signed residual byte reads plus two signed int16 base reads = **8 table bytes**, four sign extensions of int8 and two of int16, four base additions. Bilinear interpolation as three `lerp(a,b,t)=a+(b-a)*t` calls costs 3 subtractions, 3 multiplications and 3 additions. That is **13 arithmetic operations** after f and g are known, excluding address calculation and sign extension. Normalizing both interpolation fractions adds 4 subtractions and 2 divisions if coordinates and knot values are already in the same units.

Finding the w bracket by binary search over 81 knots needs at most 7 comparisons/probes, each a uint16 row-index read, plus two endpoint uint16 reads for the final bracket (conservative additional **18 bytes**). Phase 1/2 R bracketing takes at most 6 comparisons over the 49 fixed metadata constants, plus two endpoint accesses; phase 0 has an arithmetic column index. With axis constants compiled into code, they are not table residual reads. The whole ask/bid pair uses **16 table bytes** at the two reflected brackets, with possible sharing of weights and row search because the grid is symmetric. This is an operation count, not an EVM gas measurement. Filter, ln/exp, fee conversion and Solidity fixed-point rounding are additional work.

## Decoder

Standalone function, 33 lines, standard library only. Input is the binary bytes obtained by base64 decoding Data. Output can be saved with `json.dump(decode_sym_int8(blob), open('decoded.json','w'))`; unmodified `real.py` loads it. It emits all six original-shape policy arrays, rather than changing real.py's interpolation.

```python
def decode_sym_int8(data):
    """Decode SI81 bytes to the six plain fee tables and their grid metadata."""
    import json, struct, bisect
    if data[:4] != b'SI81':
        raise ValueError('bad magic')
    hlen, n = struct.unpack_from('<HH', data, 4)
    T = json.loads(data[8:8+hlen])
    pos = 8 + hlen
    rows = struct.unpack_from('<' + 'H'*n, data, pos)
    pos += 2*n
    if n < 2 or rows[0] != 0 or rows[-1] != T['NW']-1:
        raise ValueError('bad row endpoints')
    if any(a >= b for a, b in zip(rows, rows[1:])):
        raise ValueError('unsorted rows')
    for ph in range(3):
        nc = 2*T['FB']+1 if ph == 0 else T['N2']
        knots = []
        for _ in rows:
            base = struct.unpack_from('<h', data, pos)[0]
            pos += 2
            residual = struct.unpack_from('<' + 'b'*nc, data, pos)
            pos += nc
            knots.append([base + x for x in residual])
        A = []
        for i in range(T['NW']):
            k = min(max(bisect.bisect_right(rows, i)-1, 0), n-2)
            f = (i-rows[k]) / (rows[k+1]-rows[k])
            A.append([a*(1-f)+b*f for a,b in zip(knots[k],knots[k+1])])
        T['A'+str(ph)] = A
        T['B'+str(ph)] = [r[::-1] for r in A[::-1]]
    if pos != len(data):
        raise ValueError('trailing bytes')
    return T
```

## Data

The complete compressed blob follows; strip whitespace before base64 decoding. Binary size **10024 bytes**; SHA-256 **`eba055d55c77100f7a2e19282f740f1e690bacd79a028568b6714b2496d226ca`**. No network, external dependency, submodule, or original JSON is needed to decode it.

```base64
U0k4MXkBUQB7ImciOjAuMDUzNjgyMDYwOTgxMTQ0OTMsImxhbSI6MC44LCJzaWdtYSI6OS40NSwic2l6ZSI6MjAuMCwiSF9icHMi
OjUuMCwiTlciOjMyMSwiVzAiOjE2MCwiTjIiOjQ5LCJDMiI6MjQsIkZCIjo2LCJXMkwiOlstMTYwLjAsLTEzMC4wLC0xMDAuMCwt
ODAuMCwtNjAuMCwtNTAuMCwtNDAuMCwtMzAuMCwtMjUuMCwtMjAuMCwtMTcuMCwtMTQuMCwtMTIuMCwtMTEuMCwtMTAuMCwtOS4w
LC04LjAsLTcuMCwtNi4wLC01LjAsLTQuMCwtMy4wLC0yLjAsLTEuMCwwLjAsMS4wLDIuMCwzLjAsNC4wLDUuMCw2LjAsNy4wLDgu
MCw5LjAsMTAuMCwxMS4wLDEyLjAsMTQuMCwxNy4wLDIwLjAsMjUuMCwzMC4wLDQwLjAsNTAuMCw2MC4wLDgwLjAsMTAwLjAsMTMw
LjAsMTYwLjBdfQAAFAAoADwAUABYAGAAZABoAHAAeAB6AHwAfgCAAIIAhACGAIgAigCMAI0AjgCPAJAAkQCSAJMAlACVAJYAlwCY
AJkAmgCbAJwAnQCeAJ8AoAChAKIAowCkAKUApgCnAKgAqQCqAKsArACtAK4ArwCwALEAsgCzALQAtgC4ALoAvAC+AMAAwgDEAMYA
yADQANgA3ADgAOgA8AAEARgBLAFAAer//v7//wAAAAEBAQICAur//v//AAAAAQEBAgICA+v//f7///8AAAEBAQICAuz//f7+////
AAABAQECAu3//f3+/v//AAEBAQICA+3//f7+/wAAAQECAgMDA+7//f7+//8AAAECAgMDBO///P3+/v//AAEBAgIDA+///f3+//8A
AQECAwMEBPH//Pz9/v//AAECAgMDBAMA6+zt7u/w8PLy8w8SFQQA6+vs7e7v8PHy8g8TFQUA6uvs7e7v8PHyDBATFgYA6err7e7v
8PHxDBATFgYA6uvs7e/w8fIJDhIVFwcA6uvs7e/w8gULDxIVFwgA6ers7e/x9QYMDxIVFwkA6ers7e/yAQgMEBMVGAoA6ers7vH5
BAkNEBMWGAsA6ers7vL+BQkNEBMWGAwA6ert8PcBBgoNERQWGA0A6Ors8PkBBgoNEBMWGA4A6Ort8foBBQkNEBMVFw4A6evu9PwC
BgoNEBMWGA8A6Ovu9fwBBgkNEBMVGBAA6Ovv9fwBBQkMEBIVFxEA6evw9vwBBQkMDxIVFxIA6uzx9/wBBQgLDxEUFhMA6+3x9/wA
BAgLDhETFhUA7O7x9vv/AwYJDQ8SFBYA7fDz9vr+AgYJDA8RFBkA7+7y9fj8AAMGCQwPERoA8vDy9fj8/wMGCQwOERwA8/Xy9Pf6
/gEEBwoNDx0A8/by9Pf6/QAEBwkMDh4A9Pfz9Pb5/QADBgkMDh8A9Pfz9Pb5/P8DBQgLDSAA+vf49PX4+/8CBQgKDCEA+vf49PX4
+v4BBAcKDCIA+vf49PT3+v0BBAYJCyMA+vf59fX3+fwAAwYJCyMA/Pj69/b3+v0ABAYJCyQA/Pn6+vb3+fwAAwYICyUA/P36+vf2
+fv/AgUICiYA/f77+/j3+fv+AgUHCigA/P37+/n3+Pr9AAMGCCkA/f79/Pr5+Pr8AAMFCCoA/v/+/f35+fn8/wIFCC0A+/77/vv7
+/v7+wADBjAAAP39/f39/f39/f0BBDQA/v7+/v7+/v7+/v7+ATcAAAAAAAAAAAAAAAAAADwAAAAAAAAAAAAAAAAAAEEAAAAAAAAA
AAAAAAAAAEYAAAAAAAAAAAAAAAAAAEsAAAAAAAAAAAAAAAAAAFAAAAAAAAAAAAAAAAAAAFUAAAAAAAAAAAAAAAAAAFoAAAAAAAAA
AAAAAAAAAF8AAAAAAAAAAAAAAAAAAGQAAAAAAAAAAAAAAAAAAG4AAAAAAAAAAAAAAAAAAHgAAAAAAAAAAAAAAAAAAIIAAAAAAAAA
AAAAAAAAAIwAAAAAAAAAAAAAAAAAAJYAAAAAAAAAAAAAAAAAAKAAAAAAAAAAAAAAAAAAAKoAAAAAAAAAAAAAAAAAALQAAAAAAAAA
AAAAAAAAAL4AAAAAAAAAAAAAAAAAAMgAAAAAAAAAAAAAAAAAAPAAAAAAAAAAAAAAAAAAABgBAAAAAAAAAAAAAAAAACwBAAAAAAAA
AAAAAAAAAEABAAAAAAAAAAAAAAAAAGgBAAAAAAAAAAAAAAAAAJABAAAAAAAAAAAAAAAAAPQBAAAAAAAAAAAAAAAAAFgCAAAAAAAA
AAAAAAAAALwCAAAAAAAAAAAAAAAAACADAAAAAAAAAAAAAAAAAOX//Pz8/Pz8/Pz8/f39/v7+//8AAAAAAQEBAQEBAgICAgICAgID
AwMDAwMEBAQEBAUFBeb/+/v7+/v7+/z8/Pz9/f3+/v////8AAAAAAAEBAQEBAQICAgICAgICAwMDAwQEBAQEBOb/+/v8/Pz8/Pz8
/P39/v7+////AAAAAAEBAQEBAgICAgICAgIDAwMDAwQEBAQEBQUFBef/+/v7+/v7+/z8/Pz9/f3+/v7///8AAAAAAQEBAQICAgIC
AgICAwMDAwMEBAQEBAUFBej/+/v7+/v7+/z8/Pz9/f3+/v7///8AAAABAQEBAgICAgICAwMDAwMDBAQEBAUFBQUFBen/+/v7+/v7
+/v7/Pz8/f39/f7+////AAAAAAEBAQECAgICAgICAwMDAwQEBAQEBQUFBer/+vr6+vv7+/v7+/v8/Pz9/f3+/v///wAAAAEBAQEB
AgICAgICAgMDAwQEBAQEBQUFBQAA5eXl5eXl5eXl5ubm5ufn5+jo6enp6urq6+vr7Ozs7Ozs7e3t7e3t7u7u7+/v7xwcHAEA5OTk
5OTk5OXl5eXm5ubm5+fo6Ojp6erq6uvr6+vr7Ozs7Ozs7O3t7e3uGxsbHBwcHAMA4+Pj4+Pj4+Tk5OTl5eXl5ubn5+fo6Onp6urq
6urq6urq6urq6uvr6xobHBwcHR0dHgYA4eHh4eHi4uLi4uLj4+Pk5OTl5ebm5+fo6Ojo6Ojo6Ojo6Ojo6BcZGhsbHB0dHR4eHgYA
4uLi4uLi4uLi4uPj4+Tk5OXl5ubn5+jo6eno6Ojo6Ojo6OjoGBkaGxwcHR4eHh8fHwcA4eHh4eHh4eLi4uLj4+Pj5OTl5ebm5+jo
6Ojn5+fn5+jo6OgXGBkaGxwcHR4eHh8fHwgA4eHh4eHh4eHh4eLi4uLj4+Tk5eXm5+fn5+fn5+fn5+fnFhcXGBkaGxwcHR4eHh8f
HwgA4eHh4eHh4eLi4uLi4+Pj5OTl5ebm5+jo6Ojn5+fn5+gWFxgZGRobHB0dHh8fHyAgIAkA4ODh4eHh4eHh4eLi4uLj4+Tk5eXm
5+fn5+fn5+fn5xUWFxgZGRobHB0eHh8fICAgIAoA4ODg4ODg4ODh4eHh4uLi4+Pk5OXm5+fn5+fm5uYSFBYXGBgZGRobHB0eHx8f
ICAgIAsA39/f39/f4ODg4eHh4eLi4uPj5OXm5ufn5ubm5hASFBYXGBgZGhscHB0eHx8gICAgIAwA39/f39/f39/g4ODh4eHh4uLj
5OXl5ubm5ubmDRATFRYXGBkZGhscHR4eHyAgICAgIQwA39/f39/f3+Dg4eHh4uLi4uPk5eXm5+fn5+cLDxIUFhcYGRobGxwdHh8f
ICEhISIiIg0A3t7e39/f39/g4eHh4uLi4uPk5eXm5+fn5wgMDxIUFhgZGhobGxwdHh8gISEhIiIiIg4A3t7e3t7e3t7f4OHh4eHi
4uLj5OXm5+fnAwgLDxEUFhcYGRoaGxwdHh8fICEhISIiIg4A3t7e3t7e3t7f4OHh4uLi4uPk5ebn5+joBAkMDxIUFhgZGhobHB0e
Hh8gISIiIiIjIw8A3d3d3d3d3t7f3+Dh4eHi4uLj5OXm5+j/BAgMDxIUFhcYGRobGxwdHh8gISEhIiIiIhAA3d3d3d3d3d7e3+Dh
4eHi4uLj5OXm5+j/BAgMDhEUFhcYGRoaGxwdHh8fICEhIiIiIhAA3t7e3t7e3t7f4OHi4+Pj4+Pk5ebn6PkABQgMDxIUFhgZGhob
GxwdHh8gISEiIiIjIxEA3t7e3t7e3t/g4eHi4+Tk5OTl5ufo6vkABAgMDxEUFhcYGRoaGxwdHh8gISEiIiIiIhIA3t7e3t7e3t7f
4eLj5OXl5eXm5+jq8foABAgLDhETFRcYGRkaGxwdHh8fICEhIiIiIhMA3d3d3d3d3d7f4eLj5eXm5ufo6Ors8/r/BAcLDhATFRYX
GBkaGhscHR4fICEhISIiIhMA3d3d3d3d3t7f4ePl5ujo6enq6+3w9vsABAgLDhETFRcYGRoaGxwdHh8gISEiIiMjIxQA3d3d3d3d
3d3f4OLk5ufo6enr7O/y9vsABAcLDhATFRYYGBkaGhwdHh8gISEiIiIjIxQA3d3d3d3d3d7f4ePm5ujo6urt7fH1+PwABAgLDhET
FRcYGRoaGxwdHiAgIiIjIyMkJBUA3Nzc3Nzc3N3e4eLm6Ojq6u3t8PH1+fwABAcLDhETFRYYGBkaGxwdHh8gIiIjIyMkJBYA29vc
3Nzc3Nze4OLl5+rq6u3t8fH2+fwABAcKDRASFBYXGBkZGhsdHR8gIiIjIyQkJBcA29vb29vb29vd3+Ll5+rq6u708/f1+fz/AwYK
DQ8RFBUWFxgZGhscHR8gIiIjJCQkJRgA2tra2tra2trc3+Hk5unp7u719Pn2+fz/AgYJDA8RExUWFxgYGRocHSAhIiMkJSUlJRkA
2dnZ2dnZ2drb3uLk6ent7e729fr3+Pz+AgUICw4QEhQVFhgYGBocHh8hIyQlJiYnJxsA1tbW1tbW1tba3ODk5+fs7Pj2+/r7+Pr9
AAQHCgwPERMUFRYXFxkcHiAiJCUmKCgpKkYAsLCwsLCwsLCwsLW5vMHCz8/N0tDRztDS1dnc3+Lk5ujp6+vs7fL09vj7/QFQUFBQ
UEgAs7Ozs7Ozs7Ozs7O4u8HPz8/N0c/Rzc7R1Nfa3uDj5ebo6err7PP2+PwBIk5OTk5OTksAtbW1tbW1tbW1tbW1vs7Ozc3R0M3P
y8zO0dTY297g4uTl5+fo7PT4/QkhS0tLS0tLS04At7e3t7e3t7e3t7e3zM3OzMzPzszNysrMztLV2dve4OLj5OXp7PL9BxsxSEhI
SEhISFAAurq6urq6urq6urq6zMzNy8/Pzs/NzcnKzdDU19nc3uDi4+bp7vD8DyI3RkZGRkZGRlIAvb29vb29vb29vcPMzMvMzM/O
zc/MzcnJzM7S1djb3eDg5efq7O/7DSE6RERERERERFUAv7+/v7+/v7/CwsTMzMrLzs7NzM3Ky8jHyszP09bY293h4+To6fH4Ch43
QUFBQUFBQVgAwcHBwcHBwcHBxMrKysnJzc3Ly8zJysjGx8rN0NPW2dre4OTl5+72CBw0Pj4+Pj4+PloAxMTExMTExMTEysrKysrM
zM3Ly8zKysjHxMnLz9LU2Nrd4OLj5e31BhoyPDw8PDw8PFwAx8fHx8fHx8fHysrLys3NzMzMzczLysrHx8fKzdHU19nb3+Di5+v5
BRkxOjo6Ojo6Ol8AycnJycnJycnJycnJyczMzMnMzMnJycnJycnJyc7S1Nja3N7i5On3AhkuNzc3Nzc3N2IAy8vLy8vLy8vLy8vL
y8vLy8vLy8vLy8vLy8vLy8vP09XY2t7g4ub0ABcrNDQ0NDQ0NGQAzs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7O0dTX2tze
4Onz/hUpMjIyMjIyMmYA0dHR0dHR0dHR0dHR0dHR0dHR0dHR0dHR0dHR0dHR0dHW2Nvd3+fx/BMnMDAwMDAwMGkA09PT09PT09PT
09PT09PT09PT09PT09PT09PT09PT09PT1tjc3+Xv+hAkLS0tLS0tLWwA1dXV1dXV1dXV1dXV1dXV1dXV1dXV1dXV1dXV1dXV1dXV
1dXa3eLs+g0hKioqKioqKm4A2NjY2NjY2NjY2NjY2NjY2NjY2NjY2NjY2NjY2NjY2NjY2NjY2+Pt+AwgKCgoKCgoKHAA29vb29vb
29vb29vb29vb29vb29vb29vb29vb29vb29vb29vb2+Hs9wofJiYmJiYmJnMA3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d
3d3d3d3d3d3p9AgcIyMjIyMjI3YA39/f39/f39/f39/f39/f39/f39/f39/f39/f39/f39/f39/f39/n8wUZICAgICAgIHgA4uLi
4uLi4uLi4uLi4uLi4uLi4uLi4uLi4uLi4uLi4uLi4uLi4uLl8QQYHh4eHh4eHnoA5eXl5eXl5eXl5eXl5eXl5eXl5eXl5eXl5eXl
5eXl5eXl5eXl5eXl7wIWHBwcHBwcHH0A5+fn5+fn5+fn5+fn5+fn5+fn5+fn5+fn5+fn5+fn5+fn5+fn5+fn7f8TGRkZGRkZGYIA
7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7PsOFBQUFBQUFIcA8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fHx
8fHx8fHx8fHx8fHx8fHx8fcKDw8PDw8PD4wA9vb29vb29vb29vb29vb29vb29vb29vb29vb29vb29vb29vb29vb29vYFCgoKCgoK
CpEA+/v7+/v7+/v7+/v7+/v7+/v7+/v7+/v7+/v7+/v7+/v7+/v7+/v7+/sBBQUFBQUFBZYAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAKAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAKoAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAALQAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAL4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAMgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAPAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABgBAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAACwBAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEABAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGgBAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAJABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAPQBAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAFgCAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAALwCAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACADAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAOT//f39/f39/f39/f7+/v7//////wAAAAAAAAAAAQEB
AQEBAQEBAQEBAQICAgICAgICAuT//f39/f39/f39/v7+/v////8AAAAAAAABAQEBAQEBAQEBAQICAgICAgICAgMDAwMDA+T//f39
/v7+/v7+/v7/////AAAAAAABAQEBAQEBAQICAgICAgICAgICAwMDAwMDAwMDBOX//f39/f39/f3+/v7+/v////8AAAAAAAEBAQEB
AQECAgICAgICAgICAgMDAwMDAwMDA+b//f39/f39/f3+/v7+/v////8AAAAAAAEBAQEBAQICAgICAgICAgICAwMDAwMDAwQEBOf/
/f39/f39/f39/f3+/v7+//////8AAAAAAQEBAQEBAQICAgICAgICAgIDAwMDAwMDA+j//Pz8/Pz8/f39/f39/v7+/v7/////AAAA
AAEBAQEBAQEBAgICAgICAgIDAwMDAwMDA+j//f39/f39/f39/f3+/v7+/v///wAAAAABAQEBAQICAgICAgICAgIDAwMDAwMDBAQE
BOn//Pz8/Pz8/Pz9/f39/f3+/v7+////AAAAAAEBAQEBAQEBAQEBAgICAgICAwMDAwMDA+n//f39/f39/f3+/v7+/v7///8AAAAA
AQEBAgICAgICAQEBAQECAgICAgICAgMDAwMDA+r//f39/f39/f7+/v7+/v////8AAAABAQICAgICAgEBAQICAgICAgICAgIDAwMD
AwMDAwQA5OTk5OTk5OTk5OTl5eXl5ebm5ufn6Ojo6ejo6Ojo6Ojo6Ojo6Ojo6Ojp6enpHBwdHQUA4+Pj4+Pj4+Pk5OTk5OTl5eXm
5ubn5+jo6Ojn5+fn5+fn5+fn5+jo6Ojo6BwcHBwdHQYA4+Pj4+Pj4+Pj4+Pj5OTk5OXl5ebm5+fn5+fn5ubm5+fn5+fn5+fn5+fo
HBwcHBwdHQYA4+Pj4+Pj4+Pj5OTk5OTk5eXl5ubn5+jo6Ofn5+fn5+fn5+jo6Ojo6BwcHR0dHR4eHgcA4uLi4+Pj4+Pj4+Pj5OTk
5OXl5ebm5+fn5+fn5ufn5+fn5+fn5+foGxwcHR0dHh4eHggA4uLi4uLi4uLi4+Pj4+Pj5OTl5ebm5ubm5ubm5ubm5ufn5+fn5xob
GxwcHR0eHh4eHgkA4eHh4eHh4eLi4uLj4+Pj4+Tk5eXm5ubm5ubm5ubm5ufn5+cZGhobHBwdHR0eHh4eHgoA4eHh4eHh4eHh4uLi
4uLi4+Pk5OXl5ubm5ubm5ubm5uYYGRkaGhsbHBwdHR4eHh4eHgoA4eHh4eHh4eHi4+Pj4+Pj5OTk5ebm5+fn5+fn5+cWFxkZGhsb
GxwdHR4eHx8fHyAgIAsA4ODg4OHh4eHh4uPj4+Pj4+Tk5ebm5+fn5+fnERQWGBkaGhsbHBwdHR4eHx8fICAgIAwA4ODg4ODg4ODh
4uLi4+Pj4+Pk5eXm5ubm5uYNERMVFxkZGhobGxwcHR4eHx8fHyAgIAwA4ODg4ODg4ODh4uLj4+Pj4+Tk5ebm5+fn5+cOERQWGBka
GxsbHBwdHh4fHyAgICAgIA0A39/f39/f3+Dg4eLi4+Pj4+Pk5eXm5ubm5goOERMWFxkaGhsbGxwdHR4eHx8fICAgIA0A4ODg4ODg
4ODh4uPk5OTk5OTl5ubn5+fnBgsOERQWGBkaGxscHB0dHh4fHyAgICAgIQ4A4ODg4ODg4ODh4uPk5OTk5OXl5ubn5+fnBgoOERQW
GBkaGhsbHBwdHR4eHx8gICAgIA8A4ODg4ODg4OHh4uPk5OXl5eXm5ufn6OgBBgoNEBMVFxgZGhobGxwdHR4eHx8fICAgIBAA4ODg
4ODg4ODh4+Tl5ubn5+fn5+jo6OgBBgkNEBMVFxgZGhoaGxscHR0eHh8fHx8fIBAA4ODg4ODg4OHi5OXn6Ojp6enq6uvr7P0CBgoN
ERMWFxkZGhsbGxwdHR4eHx8gICAgIBEA39/f39/f3+Dh4+Xm6enp6urq7O3u9f0CBgoNEBMVFxgZGhobGxwcHR4eHx8fICAgIBEA
4ODg4ODg4ODh5OXn6erq6+vs7fDz+P4CBwoNERMWFxkaGhsbHBwdHh4fHyAgICAhIRIA39/f39/f3+Dh4+Xo6enp6+vt7vH1+f4C
BgoNEBMVFxgZGhobGxwdHR4eHyAgICAgIBIA39/f39/f3+Dh5Obo6urs7O7u7/P3/P8DBwoOERMWFxkaGhsbGxwdHh8fICAhISEh
IRMA3t7e39/f39/h4+jo6uzs7O/v8vP4/P8DBgoNEBMVFxgZGhobGxwdHh4fICAgISEhIRMA39/f39/f39/h5Ojq7e3t7fDv9PT5
/QADBwoNEBMWFxkZGhsbGx0dHh8fICAhIiIiIhQA3t7e3t7e3t7h4+js7Ozs8PD29Pr4/AADBgoNEBIVFxgZGhobGxwdHh8fICEi
IiIiIhUA3d3d3d3d3d7g4ufs7Ozw8PD29vz5/P8CBgkMDxIUFhcYGRoaGxwdHR4gISIiIiMjIxUA3Nzc3Nzc3Nzg5ufs7PHx8fn4
AP4A/QADBgoNEBIVFxgZGRobGxwdHiEiIyQkJCUlJRoA3Nzc3Nzc3Nzc4eTn7Ozs9/f1/Pv9+fv+AQUICw4QEhMUFRYXFxgdHh8f
ISEiIyMjIx8A3Nzc3Nzc3Nzc3ODj5+j19fT7+ff59ff6/QADBwkMDg8QERISExobHB4fICEiIyQkJEsAtbW1tbW1tbW1tbW8vMzL
y8rQz8zOy8vO0dTY297g4uTl5ufn7e7z9fj6/0tLS0tLS04At7e3t7e3t7e3t7e3ysrKys/OzcvNycrMztLV2dve3+Hj4+Tp6u/x
+gcdSEhISEhISFAAurq6urq6urq6urrKysrKz87Ozc7MzcnKzdDU19nc3uHi4+fo6O3v+h0yRkZGRkZGRlIAvb29vb29vb29ysrK
ysrOz87NzM7MzMnJzM7S1djb3d/g5OXm6uv0+Rs4RERERERERFUAv7+/v7+/v7/IycnJyc3Nzc3My83Ky8jHyszP09bZ3N7h4uPm
5+nyBRk1QUFBQUFBQVgAwcHBwcHBx8jIyMnJzMzMzMzLyszJysfGx8rN0NTW2dve3+Pk5ebvAxYzPj4+Pj4+PloAxMTExMfIyMjI
ycnJzMzMzMzLzMvKysrHxMnLz9LW2dzc4OHi4+nuARUxPDw8PDw8PFwAx8fHx8fHx8fHx8fMzMzMzMzLzMzLysrHx8fKzdHU19vd
3t/g5ejsABMvOjo6Ojo6Ol8AycnJycnJycnJyczMzMnMycnJzMnMycnJycnJyc7S1tja293h4uXz/RgsNzc3Nzc3N2IAy8vLy8vL
y8vLy8vLy8vLy8vLy8vLy8vLy8vLy8vQ09bZ293e4OPw+xUpNDQ0NDQ0NGQAzs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7O
0tXY2tvd3ubv+RMoMjIyMjIyMmYA0dHR0dHR0dHR0dHR0dHR0dHR0dHR0dHR0dHR0dHR0dTW2Nrb3eXu+BEmMDAwMDAwMGkA09PT
09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT1tjc3uLr9g8jLS0tLS0tLWwA1dXV1dXV1dXV1dXV1dXV1dXV1dXV1dXV1dXV
1dXV1dXV1dXZ3ODp+QwgKioqKioqKm4A2NjY2NjY2NjY2NjY2NjY2NjY2NjY2NjY2NjY2NjY2NjY2NjY3OLs9woeKCgoKCgoKHAA
29vb29vb29vb29vb29vb29vb29vb29vb29vb29vb29vb29vb2+Hq9QgfJiYmJiYmJnMA3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d3d
3d3d3d3d3d3d3d3d3d3o8wgcIyMjIyMjI3YA39/f39/f39/f39/f39/f39/f39/f39/f39/f39/f39/f39/f39/m8gUZICAgICAg
IHgA4uLi4uLi4uLi4uLi4uLi4uLi4uLi4uLi4uLi4uLi4uLi4uLi4uLm8QMXHh4eHh4eHnoA5eXl5eXl5eXl5eXl5eXl5eXl5eXl
5eXl5eXl5eXl5eXl5eXl5eXl7wEVHBwcHBwcHH0A5+fn5+fn5+fn5+fn5+fn5+fn5+fn5+fn5+fn5+fn5+fn5+fn5+fn7P8SGRkZ
GRkZGYIA7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7PsOFBQUFBQUFIcA8fHx8fHx8fHx8fHx8fHx8fHx
8fHx8fHx8fHx8fHx8fHx8fHx8fHx8fYJDw8PDw8PD4wA9vb29vb29vb29vb29vb29vb29vb29vb29vb29vb29vb29vb29vb29vYF
CgoKCgoKCpEA+/v7+/v7+/v7+/v7+/v7+/v7+/v7+/v7+/v7+/v7+/v7+/v7+/v7+/sBBQUFBQUFBZYAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAKAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAKoAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAALQAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAL4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAMgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAPAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABgBAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAACwBAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEABAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGgBAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAJABAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAPQBAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAFgCAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAALwCAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAD
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA==
```

To extract after saving this Markdown as result.md:

```python
import base64, hashlib, json, pathlib
s = pathlib.Path('result.md').read_text()
blob = base64.b64decode(s.split('```base64\n',1)[1].split('```',1)[0])
assert len(blob) == 10024
assert hashlib.sha256(blob).hexdigest() == 'eba055d55c77100f7a2e19282f740f1e690bacd79a028568b6714b2496d226ca'
# Define decode_sym_int8 using the exact function above, then:
pathlib.Path('decoded.json').write_text(json.dumps(decode_sym_int8(blob)))
```

## Problems

- The coarse grid has large maximum quote-offset errors in rare tail cells, despite negligible measured mean loss. A mean target does not guarantee individual-seed performance.
- Decoded JSON preserves policy tables and metadata but intentionally omits VD0/VD1, which real.py does not read. It is suitable for policy scoring, not resuming a value-function solve.
- Forkserver was unavailable in the sandbox; explicit fork resolved it without modifying reference files. No other setup was needed.
- This bounded compression item does not include a Solidity contract, real-engine batch, t03 comparison, deployed-bytecode size, gas statistics, or gate F callback validation. Those goal-level checks remain for the integrator. No Rust-engine seeds were consumed and no real-engine performance or gas claim is made.