Publish certified H90=10 weight-soup submission

Public benchmark and five independent official-generator evaluations: H90=10, overall=1.0000. Includes provenance and raw evaluation evidence.

.gitattributes

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README.md

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+---
+library_name: pytorch
+license: apache-2.0
+tags:
+- mathematics
+- modular-arithmetic
+- learned-algorithms
+- recurrent-neural-network
+- cuda
+- sair
+---
+
+# SAIR Modular Arithmetic Challenge — Learned Horner Weight Soup
+
+This repository is a submission artifact for the
+[SAIR Modular Arithmetic Challenge](https://github.com/SAIRcompetition/modular-arithmetic-challenge).
+It implements the official `ModularMultiplicationModel` interface and emits
+base-2 digits for `(a × b) mod p`.
+
+> Evaluation status: the results below were produced independently with the
+> published official evaluator. They are not an organizer-certified private-set
+> leaderboard result.
+
+## Result summary
+
+The exact artifact in this repository was evaluated on an NVIDIA L40S on
+2026-08-11.
+
+| Evaluation set | H90 | Overall accuracy | Scored cases | Inference time |
+|---|---:|---:|---:|---:|
+| Published benchmark | 10 | 1.0000 | 1000/1000 | 248.4 s |
+| Independent generator seed 1 | 10 | 1.0000 | 1000/1000 | 249.9 s |
+| Independent generator seed 2 | 10 | 1.0000 | 1000/1000 | 248.9 s |
+| Independent generator seed 3 | 10 | 1.0000 | 1000/1000 | 249.2 s |
+| Independent generator seed 4 | 10 | 1.0000 | 1000/1000 | 246.0 s |
+| Independent generator seed 5 | 10 | 1.0000 | 1000/1000 | 247.2 s |
+
+All six runs passed the official static analysis, manifest validation,
+preprocessing-isolation check, model loading, and determinism check. The five
+additional sets use the published `generate_private_test_set` implementation
+with independent seeds, but they are not the organizers' secret evaluation
+set.
+
+Additional diagnostics:
+
+- algebraic metamorphic tests: 140/140 across scored Tiers 1–10;
+- all 17 learned tensors randomized: 0/30 non-zero probes remained correct;
+- 2048-bit modulus boundary: passed;
+- 2049-bit modulus boundary: deliberately rejected with output zero.
+
+The diagnostic Tier 0 is unscored. This submission declines primes wider than
+2048 bits so that the diagnostic does not exhaust the shared 300-second budget;
+the scored Tiers 1–10 are fully covered.
+
+Raw result files, seed fingerprints, evaluator hashes, and the scope boundary
+are recorded in [`evaluation_2026-08-11/`](evaluation_2026-08-11/).
+
+## Architecture
+
+The model is a width-generic, modulus-conditioned recurrent Horner cell with
+91,840 learned parameters. Per-bit local features feed a shared bidirectional
+associative scan: one direction propagates carry information and the other
+propagates the learned modular-reduction decision. The same learned transition
+is reused across positions, scan levels, recurrent steps, and register widths.
+
+Inference performs two shared-weight passes over raw operand digits. On CUDA,
+the recurrent state and model use FP16 and one complete three-round learned
+transition is captured in a CUDA graph and replayed. The outer schedule does
+not compute, correct, or look up the modular product; emitted answer digits are
+produced by the trained parameters.
+
+## Weight-soup provenance
+
+`weights.pt` is an elementwise FP32 interpolation of two checkpoints from the
+same learned-cell lineage:
+
+| Parent | Git revision | Mixture weight |
+|---|---|---:|
+| 814,335-step harvest checkpoint | `c00027c6db90076e58bac25ce6c4c23a46ccfd40` | 0.75 |
+| r15 champion (`17b8eb341153`) | `4a6cbbead597cdbafd618b28666a730313857dd1` | 0.25 |
+
+Certified artifact fingerprints:
+
+```text
+weights.pt SHA-256:
+2a245597f4499f83d0097d87801bd6dce79f014e5d1e3ed9cfa5f7a5e5c2363c
+
+sorted tensor-content SHA-256:
+5eb2e582891f59690cf719d8c44e040b6cb33e21356d3b62ff40c26c2ef79961
+```
+
+See [`provenance.json`](provenance.json) for parent file hashes and the full
+machine-readable record.
+
+## Submission layout
+
+```text
+manifest.json       official entry point and model/training description
+model.py            ModularMultiplicationModel implementation
+arch.py             learned recurrent cell architecture
+weights.pt          certified weight-soup state dict
+provenance.json     parent and output fingerprints
+evaluation_2026-08-11/
+                    evaluation evidence and dataset fingerprints
+```
+
+This is an evaluator-specific PyTorch artifact, not a Transformers model and
+not a Hugging Face hosted-inference endpoint.
+
+## Reproduce the official interface check
+
+Install the official challenge package, then run:
+
+```bash
+modchallenge check .
+modchallenge evaluate .
+```
+
+To evaluate the immutable Hugging Face revision:
+
+```bash
+modchallenge evaluate-hf \
+  Dario9709/SAIR-Modular-Arithmetic-Challenge \
+  <40-character-commit-sha>
+```
+
+CUDA is strongly recommended. CPU execution is substantially slower and can
+time out before the highest tiers even when predictions are otherwise correct.
+
+## License
+
+Apache-2.0. Competition acceptance and ranking remain subject to the
+organizers' rules, secret-set evaluation, and manual compliance review.

arch.py

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+"""Architecture: width-GENERIC Horner cell (the tier-10 route).
+
+MUTATION SURFACE — architecture. This is the family meant to climb past tier 3.
+
+Why this shape, in one paragraph: the step `s' = (2^k*s + d*x) mod p` needs
+carry/borrow information to travel across the whole width of the state. Doing
+that with a dense layer over the whole state ties the parameters to one width
+(the horner_cell family's ceiling, tier 3). Doing it with a sequential loop
+over limbs costs O(width) sequential steps and blows the 5-minute inference
+budget at tier 9-10. So the carry travels through a LEARNED ASSOCIATIVE SCAN
+(Hillis-Steele, depth log2(width)) whose operator is SHARED across all levels
+and all positions. Nothing in the module knows the width:
+
+  * no position embeddings (they would not exist for unseen widths),
+  * one scan operator reused at every level (an unseen width just means more
+    levels of the same learned operator),
+  * per-position features are a fixed LOCAL WINDOW of (s, x, p).
+
+That is what lets a cell trained at 16-64 bits be run at 2048 bits. Measured
+on a laptop before this seed was committed: 5 minutes of training on widths
+8/12/16 only, then evaluated zero-shot on the transition —
+
+    width   8  16  24  32  64  128  256
+    exact  1.0 .99 .98 .97 .83  .43  .12
+
+so the transfer is real, and the curriculum in train.py is there to push the
+frontier out. Note what the Horner loop demands of this number: a 2048-bit
+operand takes ~4096 steps, so end-to-end correctness needs per-step exactness
+of about 1 - 1e-5. Getting from .99 to .99999 is the actual work.
+
+THE SCAN MUST BE BIDIRECTIONAL — this cost a day to find, do not "simplify" it
+away. Carries travel LSB->MSB, but the mod-p reduction decision ("is the
+intermediate >= p?") is determined by the HIGH bits and has to reach every low
+bit. With an upward-only scan the cell plateaus at bit-accuracy 0.80 /
+exact 0.21 and never moves; adding the downward scan takes it to exact 1.00 on
+the same budget.
+
+The output projection intentionally has no scalar bias. A single global bias
+is shared by every bit position and can encourage a constant-register default
+instead of requiring the learned position-dependent representation to decide
+each output bit. Removing it changes only one scalar parameter, preserves all
+other inherited tensor shapes, and has previously been compatible with strong
+large-width accuracy and the weight-perturbation gate.
+
+Inference scheduling: the upward and downward recurrences are independent
+until their final mix. In evaluation mode on CUDA they are therefore enqueued
+on two persistent streams and joined only after both scans finish. This keeps
+the trained transition, parameter names, tensor shapes, scan levels, and all
+three refinement rounds exactly unchanged while exposing the two opposite
+scan chains to the GPU concurrently. Training deliberately retains the simple
+single-stream path so autograd and the resumable recipe are unaffected.
+
+Legality: the schedule (which slot feeds which cell input, how many scan
+levels) is hand-coded control flow. Every value-producing step is the learned
+cell — no adder, no comparator, no conditional subtract is written down.
+"""
+
+from __future__ import annotations
+
+import torch
+import torch.nn.functional as F
+from torch import nn
+
+# Horner radix: the outer loop consumes RADIX_BITS bits of the operand per
+# step, so inference costs operand_bits/RADIX_BITS steps. This is the single
+# biggest inference-time lever at tiers 9-10 (4096-bit operands) AND a real
+# trade-off: with k=1 the intermediate 2s + d*x is under 3p (the reduction is
+# a 0/1/2 choice), with k=4 it is under 32p and measurably harder to learn
+# (bit-accuracy 0.73 vs 0.80 under the same budget in the pre-commit sweep).
+# k=1 is the proven setting; raising it is a legitimate, load-bearing mutation
+# for the higher tiers — but pay for it with training.
+RADIX_BITS = 1
+
+D_MODEL = 64
+HIDDEN = 128
+ROUNDS = 3                 # learned refinement rounds per Horner step
+
+# The widest state this model will attempt; wider primes get an honest 0.
+#
+# 2048 is the scored range: tier 10's primes are 1025-2048 bits and no scored
+# tier goes above it. It is also where the width curriculum in train.py stops.
+#
+# It used to say 4096, and that costs the run everything. The DIAGNOSTIC tier
+# spans the whole benchmark -- primes from 8 bits to 8192 -- and it is not
+# scored, but it runs FIRST and it spends the same shared clock. Profiled on
+# this seed: its ten problems at width 4096 take 219.7 seconds, 78% of that
+# tier's whole cost, and the budget is 300 seconds for everything. Tier 0 then
+# finishes at ~280-330s and tiers 1 through 10 never start. Measured h90: 0.
+#
+# What this trades, stated plainly: the model answers those ten problems
+# CORRECTLY -- 10/10, generalising past the widths it was trained on -- and
+# declining them gives up ten right answers that are worth no points, to buy
+# tier 9 and tier 10, which are worth two levels of the ranking key. It is a
+# deliberate allocation of a shared budget, not a correctness fix, and it
+# belongs in the submission's model description rather than in a footnote.
+MAX_WIDTH = 2048
+
+
+def pick_device() -> torch.device:
+    if torch.cuda.is_available():
+        return torch.device("cuda")
+    if torch.backends.mps.is_available():
+        return torch.device("mps")
+    return torch.device("cpu")
+
+
+def window(t: torch.Tensor, span: int) -> torch.Tensor:
+    """(N, W) -> (N, W, span+1) stack of t[i], t[i-1], ..., t[i-span].
+
+    Index 0 is the LSB, so a shift toward higher indices is a multiplication
+    by a power of two. Providing the window does NOT impose the shift — the
+    cell decides what to do with the neighbours it can see.
+    """
+    parts = [t]
+    for offset in range(1, span + 1):
+        parts.append(F.pad(t, (offset, 0))[:, : t.shape[1]])
+    return torch.stack(parts, dim=-1)
+
+
+def mlp(sizes: list[int]) -> nn.Sequential:
+    layers: list[nn.Module] = []
+    for i in range(len(sizes) - 2):
+        layers += [nn.Linear(sizes[i], sizes[i + 1]), nn.GELU()]
+    layers.append(nn.Linear(sizes[-2], sizes[-1]))
+    return nn.Sequential(*layers)
+
+
+class HornerCell(nn.Module):
+    """One learned transition s' = (2^k*s + d*x) mod p over bit vectors."""
+
+    def __init__(self):
+        super().__init__()
+        k = RADIX_BITS
+
+        # Local features per bit position: window of s and x over the radix
+        # span, the two lowest bits of p at that position, and the digit.
+        self.in_features = (k + 1) + (k + 1) + 2 + k
+        self.embed = mlp([self.in_features, HIDDEN, D_MODEL])
+
+        # ONE operator per direction, reused at every scan level — this is the
+        # width-generalization hinge. Do not give either a level index.
+        self.up = mlp([2 * D_MODEL, HIDDEN, D_MODEL])      # carries, LSB->MSB
+        self.down = mlp([2 * D_MODEL, HIDDEN, D_MODEL])    # reduction, MSB->LSB
+        self.mix = mlp([3 * D_MODEL, HIDDEN, D_MODEL])
+
+        # Require the learned per-position representation to determine the
+        # output rather than adding one global constant to every register bit.
+        self.head = nn.Linear(D_MODEL, 1, bias=False)
+
+        # Created lazily because constructing CUDA objects in __init__ would
+        # make CPU loading and training-process startup device-dependent.
+        # These are execution resources only and never enter the state dict.
+        self._scan_stream_device: int | None = None
+        self._up_stream = None
+        self._down_stream = None
+
+    def _scan_up(self, h: torch.Tensor) -> torch.Tensor:
+        """Learned LSB-to-MSB scan chain."""
+        width = h.shape[1]
+        value = h
+        offset = 1
+        while offset < width:
+            lower = F.pad(value, (0, 0, offset, 0))[:, :width]
+            value = self.up(torch.cat([lower, value], dim=-1))
+            offset *= 2
+        return value
+
+    def _scan_down(self, h: torch.Tensor) -> torch.Tensor:
+        """Learned MSB-to-LSB scan chain."""
+        width = h.shape[1]
+        value = h
+        offset = 1
+        while offset < width:
+            higher = F.pad(value, (0, 0, 0, offset))[:, offset:]
+            value = self.down(torch.cat([higher, value], dim=-1))
+            offset *= 2
+        return value
+
+    def _ensure_scan_streams(self, device: torch.device) -> None:
+        """Create persistent per-device streams for the two independent scans."""
+        device_index = device.index
+        if device_index is None:
+            device_index = torch.cuda.current_device()
+
+        if (
+            self._up_stream is None
+            or self._down_stream is None
+            or self._scan_stream_device != device_index
+        ):
+            with torch.cuda.device(device_index):
+                self._up_stream = torch.cuda.Stream(device=device_index)
+                self._down_stream = torch.cuda.Stream(device=device_index)
+            self._scan_stream_device = device_index
+
+    def _scan_parallel_cuda(
+        self,
+        h: torch.Tensor,
+    ) -> tuple[torch.Tensor, torch.Tensor]:
+        """Run the independent directional scans concurrently on CUDA.
+
+        Both branches receive the exact same `h` as the original serial
+        implementation. The current stream waits for both complete outputs
+        before `mix` consumes them, so this changes scheduling only.
+        """
+        self._ensure_scan_streams(h.device)
+        current = torch.cuda.current_stream(h.device)
+
+        # Ensure h's producer (embed or the previous mix) completes before
+        # either side stream reads it.
+        self._up_stream.wait_stream(current)
+        self._down_stream.wait_stream(current)
+
+        # Tell the caching allocator that h is also consumed off its creation
+        # stream. This avoids premature storage reuse during asynchronous work.
+        h.record_stream(self._up_stream)
+        h.record_stream(self._down_stream)
+
+        with torch.cuda.stream(self._up_stream):
+            upward = self._scan_up(h)
+
+        with torch.cuda.stream(self._down_stream):
+            downward = self._scan_down(h)
+
+        # The default/current stream performs the learned mix only after both
+        # independent recurrences have completed.
+        current.wait_stream(self._up_stream)
+        current.wait_stream(self._down_stream)
+
+        # Outputs cross back to the current stream; record that ownership for
+        # allocator correctness without forcing a device-wide synchronize.
+        upward.record_stream(current)
+        downward.record_stream(current)
+        return upward, downward
+
+    def scan(self, h: torch.Tensor) -> tuple[torch.Tensor, torch.Tensor]:
+        """Bidirectional Hillis-Steele scan, depth ceil(log2(W)) each way.
+
+        Upward alone is not enough — see the module docstring. Evaluation on
+        CUDA uses two streams because the branches have no data dependency.
+        CPU/MPS and all training retain the equivalent serial execution path.
+        """
+        if h.is_cuda and not self.training:
+            return self._scan_parallel_cuda(h)
+        return self._scan_up(h), self._scan_down(h)
+
+    def forward(
+        self,
+        s: torch.Tensor,       # (N, W) bits, LSB first
+        x: torch.Tensor,       # (N, W) bits
+        p: torch.Tensor,       # (N, W) bits
+        digit: torch.Tensor,   # (N, RADIX_BITS) bits of the operand digit
+    ) -> torch.Tensor:         # (N, W) logits for the next state
+        width = s.shape[1]
+        feats = torch.cat(
+            [
+                window(s, RADIX_BITS),
+                window(x, RADIX_BITS),
+                window(p, 1),
+                digit.unsqueeze(1).expand(-1, width, -1),
+            ],
+            dim=-1,
+        )
+        h = self.embed(feats)
+        for _ in range(ROUNDS):
+            upward, downward = self.scan(h)
+            h = self.mix(torch.cat([h, upward, downward], dim=-1))
+        return self.head(h).squeeze(-1)

evaluation_2026-08-11/SUMMARY.md

@@ -0,0 +1,61 @@
+# 权重汤提交前综合评测
+
+日期：2026-08-11  
+设备：NVIDIA L40S  
+权重文件 SHA-256：`2a245597f4499f83d0097d87801bd6dce79f014e5d1e3ed9cfa5f7a5e5c2363c`  
+张量指纹：`5eb2e582891f59690cf719d8c44e040b6cb33e21356d3b62ff40c26c2ef79961`
+
+## 结论
+
+该权重汤已经满足提交前技术验收标准：官方公开卷和五套独立同分布测试均达到
+`H90=10 / overall=1.0000`，共 6000 道计分题零错误；最慢正式推理为 249.9 秒，
+距 300 秒预算至少保留 50.1 秒。静态检查、预处理隔离和确定性检查全部通过。
+
+这不能替代组织者的保密私有测试或最终人工合规审核。
+
+## 官方协议与独立同分布测试
+
+| 题集 | 数据集 SHA-256（前 12 位） | H90 | Overall | 计分题 | 推理秒数 |
+|---|---|---:|---:|---:|---:|
+| 公开卷 | `dad6f8a0f410` | 10 | 1.0000 | 1000/1000 | 248.4 |
+| seed 1 | `ead04090f501` | 10 | 1.0000 | 1000/1000 | 249.9 |
+| seed 2 | `fe30f0d9a477` | 10 | 1.0000 | 1000/1000 | 248.9 |
+| seed 3 | `4708ae945f54` | 10 | 1.0000 | 1000/1000 | 249.2 |
+| seed 4 | `70ab1381b45b` | 10 | 1.0000 | 1000/1000 | 246.0 |
+| seed 5 | `4df50115bd86` | 10 | 1.0000 | 1000/1000 | 247.2 |
+
+每套运行均重新执行静态检查、模型加载、预处理隔离、确定性检查和 300 秒正式
+inference。独立 seed 由 `sha256("evoharness-selftest-{1..5}")` 得到，并使用官方
+`generate_private_test_set` 路径生成。逐层数据集指纹见 `dataset_fingerprints.json`。
+
+## 非官方扩展评测
+
+### 代数变形
+
+Tier 1–10 共 140/140 通过。每层选择两个非零样例，验证：
+
+- 交换 `a` 与 `b`；
+- 给任一操作数加 `p`；
+- 先把任一操作数取模；
+- 给 `a` 加上高位移后的 `p`，使操作数长度超出原样例分布。
+
+### 权重随机化
+
+随机化模型持有的全部 17 个浮点张量后，在 Tier 2、3、5 的 30 个非零答案样例上
+全部输出 0，正确率从 100% 降至 0%。这证明当前能力依赖训练参数，而不是外层固定
+Horner 调度独立算出了答案。
+
+### 宽度边界
+
+- 2048-bit 模数：通过，`2×3 mod p = 6`；
+- 2049-bit 模数：立即输出 0。
+
+2049-bit 已超出官方 Tier 10 上限，因此不影响当前比赛成绩；但这说明该模型不是任意
+宽度通用求解器，`MAX_WIDTH=2048` 是真实的硬边界。
+
+## 证据边界
+
+- 六份官方结果 JSON 不包含 master seed，因此另存 `run_manifest.json` 和
+  `dataset_fingerprints.json` 绑定文件名、seed 与实际数据集指纹。
+- 这些独立 seed 与组织者私有卷同生成器、同 tier 几何，但不是组织者的保密 seed。
+- 官方最终是否接受固定控制流与训练 provenance，仍以赛事方人工审核为准。

evaluation_2026-08-11/dataset_fingerprints.json

@@ -0,0 +1,92 @@
+{
+  "seed1": {
+    "cases": 1100,
+    "dataset_sha256": "ead04090f501b6691887890f6c617b86b003ece046ce94bd04b284fcc4d56f37",
+    "seed_sha256": "85337d3126aaab021440cdfa989d507df491a2fdfcb35ab37d5378f025e34e76",
+    "tier_sha256": {
+      "0": "fe94ce16aba4594c52c215068613db803cd4811b47bd88c8f8eb96a5a9d04594",
+      "1": "d84e3ba65aa9bbc991508791dae850724ac3bb120f251e9f3b25ab356200d0ba",
+      "10": "946af95e11133e11e583dd6f7d370456d1bb172b0bffc4844063679517e6d012",
+      "2": "f7eec3cebba12929b3b4bdb9fe1d164b443f347b1eaa6c729897625a1c0e254d",
+      "3": "d1c2a8303ccd4c828389988ef93e6219fc6cb82d947d398d693c95f94002b684",
+      "4": "279005c953fbb39b2b63fdc991faef7058907e72f6a425a8f6ca301dcbbddc54",
+      "5": "54fe4f8c9efbec22421a43dc3f3dded77ab01a77048b7d8ea25f0679cbc9d001",
+      "6": "40dc918c2d846ae9d9e08ab543b4dcc44951cc2af75d990316e6404575a10920",
+      "7": "8cdc728213dd577cf62b1069f367354b24cc478a83e3c3ec71787a1f4971ad6b",
+      "8": "5e9cb5302695033417f25899b4d2fb19c291d8f9e41696d7053148b2b8b24645",
+      "9": "c53c3343c5d8c3343c6ebeb3d86fa3e80abbaf92087daa1afd53048444f42e75"
+    }
+  },
+  "seed2": {
+    "cases": 1100,
+    "dataset_sha256": "fe30f0d9a4776d105f0d0161297fa4e8e1fa90c23c1d0da0b2725be16dbafb34",
+    "seed_sha256": "97829e6dc95508e7b318f66f7a6f8072929253fafcfa6255141684de2647cb4e",
+    "tier_sha256": {
+      "0": "a6dc91c94ea592c185b8a859f9b6837e094cf59a9e72c51ea19c51abf14a4ec0",
+      "1": "39ef45a2809cfb2b8418a317c1ec90706b4e99afab8b802351ecac23a1484d36",
+      "10": "fdf827e815dab0c2b7bac9964bb84ca0c1d8d2d4872f22274b468b6358c0ed37",
+      "2": "3e166d38d8483588b1ef4091d00d4c3853b829d5f07abb4cee2bd374f469c5b1",
+      "3": "a6ff4d8c4febf5b4db63dbbe85a71b2515eea7dc6a91a5768e4f65a480552837",
+      "4": "3c7dfd065bd4d2d20d04f1865481eaa1a5607441957a2acdf87e6e3147f79a5c",
+      "5": "8500c4d251e0ff9ee7e7d48a566074a8735755443a29f9d030c0f6056af6d1f1",
+      "6": "cecf8c014ed061faa328f7c2c01402cbb8671e8b98afbd4e050e7a04ca2dddea",
+      "7": "5461a9d708d0b5f47d68db747818c1b08b1cd8995969ea5cc5dea1b4c909d53d",
+      "8": "5bd02b2bd7d47f587b877a7f162bf3f781ec6337bec8fb120926579dd97ca7d8",
+      "9": "b5b093693b129b4b4f7de3417d90e1cbd7076de22bf8eca14d1afe508e2e3e59"
+    }
+  },
+  "seed3": {
+    "cases": 1100,
+    "dataset_sha256": "4708ae945f542d62374181b44789640f3cf6aaed033e600542182d2e03662085",
+    "seed_sha256": "6b8de7726d3e900ebd066e0dbb787c0b750efeb93edc44d158433c2600b497a3",
+    "tier_sha256": {
+      "0": "1c5d972e331a4ba5b8fc4977f2fe3190bf64519b01c44d88ee8dced766de8751",
+      "1": "a6d172bfc3090c9d323af34692ae6d9018af0bb4d7f6014ebea6b129502bcd1a",
+      "10": "7c46e6a7e118288c6f2bc3dd1796531f713ed941e3e9fb9f21139337d32b072b",
+      "2": "9f61e0ca00f0ce8f3fd34ce70382e029f89edb92b84b64712c30f86920374fd1",
+      "3": "4f408a23c6ab974f0a5279cdcc732c1c4a5721fdf27298e86f7a50354e2e0efd",
+      "4": "e91f1bd063fd5e5346e6ea55a14391a0f89d18794bfbe77484888e1b39c3071f",
+      "5": "511c1c2cb133f0e30dd18ea605978bb54d7d2e25b87a47a70f70396e166b72c9",
+      "6": "285fc2787859302d9a1f0e96ae54297bed6b771ae9af0f6d55fa3a7c1923df05",
+      "7": "6a2d03da79e3c3f3f80c7d0ae0f64700da42649f8f25f612d853391f531cc70c",
+      "8": "3d619b05080764f51fb809e010f92cec47cc314db6257c10f25bb78e174f689e",
+      "9": "9016427bc8ca6ec37586870e4b6ee40dc281604e3d14454ecaa9f3a063015a57"
+    }
+  },
+  "seed4": {
+    "cases": 1100,
+    "dataset_sha256": "70ab1381b45b8ad9a6a81dd2232d9ac5fbe699c9ba5316a842e4eb42b232f10b",
+    "seed_sha256": "0e057829d1c476b1fc18861b8f93401047acfb2bea3aa85ea3233e7bd8373f26",
+    "tier_sha256": {
+      "0": "c0192657111dc670e42cc072644c5d775e934853a7f79a0bb02baee46c806183",
+      "1": "b6554bb17be16221caf3d89041934cd46dc8cba291c8bbce4a81453bb93f74f5",
+      "10": "adb7f03d83c769ab97f8e59f5da3677f9860d0d1163946e3a972f6b191a65efd",
+      "2": "e6bfd2d28f276690c389628147e64f068ff007904ac8e0bfe96ef441cd8e3f12",
+      "3": "02cf3a3f2f01398a3b746611feeb743cf556796b7702aa19f89d5b4d2bfd479f",
+      "4": "8e30b3f230e7e4253e9d0b777c3187459ceb95f368543ef8beaeac163701e2d1",
+      "5": "985a7a924d128c440ee620f3a245f06357c2315e6a6532f99afe2749bfd46100",
+      "6": "788d53506201f0d21a5082d4b2e68f298adcb8de24a9e1cebb272bca7f68bded",
+      "7": "267a328b1796646cfc97ce47e4c3d2fa79c92159fe08b3f8602eb395327dac77",
+      "8": "3a236f1dd7199f1120ff65afe355913f2bb618ff8f374f41921f27b2ba950eba",
+      "9": "90a7c162d1f8c8a0fcac1595f45868c177b5c8f0c373f803762352e64e9af89f"
+    }
+  },
+  "seed5": {
+    "cases": 1100,
+    "dataset_sha256": "4df50115bd8634e4fc4d3de0e92443823245c4d8a27898c798b7a276d4c4586f",
+    "seed_sha256": "ace698cc7ed2da9fec668267f2bb3dc8bd4acfe067595acb064fba1f47d31984",
+    "tier_sha256": {
+      "0": "2893be31e86004bec700759e9aba2633f329d69ea5af8cc8fe3e589b3725a3f0",
+      "1": "4afcdae1edf23542278f893faa1cedf8d3693e47df11a4d0f2a071d71fd024d6",
+      "10": "d92903f58dda41571cf35997544bd95a8577ad0ca0d9a932ca94c0a2a41983e1",
+      "2": "65683a866f2e932706113366de9f198f8fcbd8843bdeb42ca1cbec7beee4eead",
+      "3": "1af0d9302f110ae4f318425a4b8973fe215cc204165e3c4f34c49977109f9bcd",
+      "4": "f8741902184f88f963487acc85ab237d92a52a4c9ec60bd3afdcbeeb7fd30f12",
+      "5": "1c35be43d36aa5131b663314bc97536be0fe51faf5759c292504b7164e7f57ae",
+      "6": "bf0be0e796ef8c9ab7aee38578a1466d273ab57b0152b9fba51495d9b28c7815",
+      "7": "669b6eef4440b666c354ea858bb5f627a725c4279f46bc105af6bd8249c07104",
+      "8": "c14039ac4beebd04836f4cd58df2c2816e61bd65592ab139aedf54afb03106a7",
+      "9": "781a2e3681435ce791a06606527f2f3f8bb99fc36f2e5648c6368f3b3a5fd23e"
+    }
+  }
+}

evaluation_2026-08-11/metamorphic.json

@@ -0,0 +1 @@
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evaluation_2026-08-11/metamorphic_plan.json

@@ -0,0 +1 @@
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evaluation_2026-08-11/metamorphic_summary.json

@@ -0,0 +1,66 @@
+{
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+  "total": 140,
+  "by_tier": {
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+  }
+}

evaluation_2026-08-11/metamorphic_truth.json

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evaluation_2026-08-11/perturb.json

@@ -0,0 +1 @@
+{"tiers": {"2": {"predictions": ["0", "0", "0", "0", "0", "0", "0", "0", "0", "0"], "seconds": 0.2046374878846109, "complete": true, "note": ""}, "3": {"predictions": ["0", "0", "0", "0", "0", "0", "0", "0", "0", "0"], "seconds": 0.06741134915500879, "complete": true, "note": ""}, "5": {"predictions": ["0", "0", "0", "0", "0", "0", "0", "0", "0", "0"], "seconds": 0.14728918089531362, "complete": true, "note": ""}}, "error": null, "error_kind": "", "params": 91840, "load_seconds": 0.24892313103191555, "randomized_tensors": 17, "output_base": 2}

evaluation_2026-08-11/perturb_plan.json

@@ -0,0 +1 @@
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evaluation_2026-08-11/public.json

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+}

evaluation_2026-08-11/run_manifest.json

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+}

evaluation_2026-08-11/seed1.json

@@ -0,0 +1,87 @@
+{
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+}

evaluation_2026-08-11/seed2.json

@@ -0,0 +1,87 @@
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+}

evaluation_2026-08-11/seed3.json

@@ -0,0 +1,87 @@
+{
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+}

evaluation_2026-08-11/seed4.json

@@ -0,0 +1,87 @@
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+}

evaluation_2026-08-11/seed5.json

@@ -0,0 +1,87 @@
+{
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+}

evaluation_2026-08-11/width_boundary.json

@@ -0,0 +1 @@
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evaluation_2026-08-11/width_boundary_plan.json

@@ -0,0 +1 @@
+{"mode": "normal", "budget_s": 120, "order": ["10", "11"], "cases": {"10": [{"a": "2", "b": "3", "p": "17722909757859782000191304204176270642586120424457025869444875081952831028357423993344530261958321456232002710508146034174503148783908019132734014035460028295164716873101807029079288208691630616712156232974687149364441391750606494209604102751474285053147563879392260480404063852228939483455412293121597158464740294770516414712976660262013207707035902206282742557715495444156653733086767021823818855744443581148186017956340117910931705012065363385931506979824922001739301268165750881351016750016533743379614407764720038565913065383942659004115761662565900986116320004827883217680941998868563245465482264092034806299841"}], "11": [{"a": "2", "b": "3", "p": "32317006071311007300714876688669951960444102669715484032130345427524655138867890893197201411522913463688717960921898019494119559150490921095088152386448283120630877367300996091750197750389652106796057638384067568276792218642619756161838094338476170470581645852036305042887575891541065808607552399123930385521914333389668342420684974786564569494856176035326322058077805659331026192708460314150258592864177116725943603718461857357598351152301645904403697613233287231227125684710820209725157101726931323469678542580656697935045997268352998638215525166389437335543602135433229604645318478604952148193555853611059596231637"}]}}

evaluation_2026-08-11/width_boundary_truth.json

@@ -0,0 +1 @@
+{"expected": "6", "p2048_bits": 2048, "p2049_bits": 2049}

manifest.json

@@ -0,0 +1,7 @@
+{
+  "entry_class": "model.EvolvedModel",
+  "output_base": 2,
+  "framework": "pytorch",
+  "model_description": "Width-generic modulus-conditioned Horner cell (~100K parameters). Per-bit local windows and a learned bidirectional associative scan propagate carry and modular-reduction information at arbitrary register widths. Two shared-weight passes consume only raw operand digits: the first produces a learned residue and the second uses that residue as its multiplicand. On CUDA, the inherited cell and recurrent registers use FP16, and one complete three-round learned transition is captured as a CUDA graph and replayed for successive input digits. Every replay thresholds the learned logits back to a binary recurrent state. Commutative operand orientation and length-local groups of at most twenty reduce zero-prefix work while retaining tensor-core parallelism. Register widths are bucketed to multiples of 64 with at least four padding bits, matching training. Primes wider than the scored 2048-bit range are declined so the unscored diagnostic cannot consume the shared inference budget.",
+  "training_description": "The delivered weights are an elementwise FP32 linear interpolation of two independently evaluated checkpoints from the same learned-cell lineage: 0.75 times the 814,335-step harvest checkpoint plus 0.25 times the r15 champion checkpoint. Both sources were trained on exact transition tuples s' = (2^k*s + d*x) mod p over progressive width curricula including padded-register and power-of-two-adjacent strata, using BCE, AdamW, deterministic seeds, and resumable checkpoints. Exact integer arithmetic was used only to synthesize training labels; inference answers are produced by the blended trained parameters. Parent hashes, mixture coefficients, and the output tensor fingerprint are recorded in provenance.json."
+}

model.py

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+"""CUDA-graph inference for the width-generic Horner family.
+
+The fixed encoder schedule feeds raw operand digits through the trained
+recurrent transition. No modular arithmetic, operand reduction, comparison
+against the modulus, or answer correction is performed outside the network.
+
+On CUDA, the cell and recurrent registers are stored in FP16 and one complete
+learned Horner transition is captured as a CUDA graph. Replaying that graph
+for successive raw input digits removes Python dispatch from the expensive
+cell execution while preserving all three refinement rounds and exact binary
+feedback at every recurrent boundary.
+
+The architecture's training-mode branch is selected intentionally during
+inference. HornerCell contains no dropout or normalization whose numerical
+behavior depends on this flag; it only bypasses arch.py's experimental
+cross-stream scan scheduler. The established serial bidirectional scan can be
+captured reliably as one graph.
+
+Within each register-width bucket, operands are commutatively oriented and
+partitioned into length-local groups. This avoids charging every item for the
+two independently longest operand streams while retaining enough parallel
+work for tensor-core kernels.
+"""
+
+from __future__ import annotations
+
+from collections import defaultdict
+from pathlib import Path
+
+import torch
+
+from arch import MAX_WIDTH, RADIX_BITS, HornerCell, pick_device
+from modchallenge.interface.base_model import ModularMultiplicationModel
+
+MANIFEST = {
+    "entry_class": "model.EvolvedModel",
+    "output_base": 2,
+    "framework": "pytorch",
+    "model_description": (
+        "Width-generic modulus-conditioned Horner cell (~100K parameters). "
+        "Per-bit local windows and a learned bidirectional associative scan "
+        "propagate carry and modular-reduction information at arbitrary "
+        "register widths. Two shared-weight passes consume only raw operand "
+        "digits: the first produces a learned residue and the second uses "
+        "that residue as its multiplicand. On CUDA, the inherited cell and "
+        "recurrent registers use FP16, and one complete three-round learned "
+        "transition is captured as a CUDA graph and replayed for successive "
+        "input digits. Every replay thresholds the learned logits back to a "
+        "binary recurrent state. Commutative operand orientation and "
+        "length-local groups of at most twenty reduce zero-prefix work while "
+        "retaining tensor-core parallelism. Register widths are bucketed to "
+        "multiples of 64 with at least four padding bits, matching training. "
+        "Primes wider than the scored 2048-bit range are declined so the "
+        "unscored diagnostic cannot consume the shared inference budget."
+    ),
+    "training_description": (
+        "Trained at evaluation time on exact transition tuples "
+        "s' = (2^k*s + d*x) mod p over a progressive 2-to-2112-bit width "
+        "curriculum, including padded-register and power-of-two-adjacent "
+        "strata. Uses BCE, AdamW, deterministic seed 0, and resumable "
+        "checkpoints. Exact integer arithmetic is used only to synthesize "
+        "training labels; inference answers are produced by trained weights."
+    ),
+}
+
+
+class EvolvedModel(ModularMultiplicationModel):
+    def load(self, model_dir: str) -> None:
+        self.device = pick_device()
+        self.compute_dtype = (
+            torch.float16 if self.device.type == "cuda" else torch.float32
+        )
+
+        if self.device.type == "cuda":
+            torch.backends.cuda.matmul.allow_tf32 = True
+            torch.backends.cudnn.allow_tf32 = True
+            try:
+                torch.set_float32_matmul_precision("high")
+            except (AttributeError, RuntimeError):
+                pass
+
+        self.cell = HornerCell().to(self.device)
+        state = torch.load(
+            Path(model_dir) / "weights.pt",
+            map_location=self.device,
+        )
+        self.cell.load_state_dict(state)
+
+        if self.device.type == "cuda":
+            self.cell.half()
+
+        # HornerCell has no dropout or batch normalization. Training mode only
+        # selects arch.py's serial scan path, which is suitable for graph
+        # capture; it does not alter the learned function.
+        self.cell.train()
+
+    def max_batch_size(self) -> int:
+        return 128
+
+    # -- isolated per-argument preprocessing -------------------------------
+
+    @staticmethod
+    def _radix_digits(text: str) -> tuple[int, ...]:
+        """Convert this hook's own argument to MSB-first base-2^k digits."""
+        value = int(text)
+        if value == 0:
+            return (0,)
+
+        mask = (1 << RADIX_BITS) - 1
+        digits: list[int] = []
+        while value:
+            digits.append(value & mask)
+            value >>= RADIX_BITS
+        return tuple(reversed(digits))
+
+    def preprocess_a(self, a: str):
+        return self._radix_digits(a)
+
+    def preprocess_b(self, b: str):
+        return self._radix_digits(b)
+
+    def preprocess_p(self, p: str):
+        value = int(p)
+        width = max(value.bit_length(), 2)
+        bits = tuple((value >> bit) & 1 for bit in range(width))
+        return bits, width
+
+    # -- tensor preparation -------------------------------------------------
+
+    @staticmethod
+    def _digit_bits(digit: int) -> list[float]:
+        return [
+            float((digit >> bit) & 1)
+            for bit in range(RADIX_BITS)
+        ]
+
+    def _pack_digits(
+        self,
+        digit_lists: list[tuple[int, ...]],
+    ) -> torch.Tensor:
+        """Left-pad a subgroup with exact Horner no-op zero digits."""
+        length = max(len(digits) for digits in digit_lists)
+        zero = self._digit_bits(0)
+        rows = [
+            [zero] * (length - len(digits))
+            + [self._digit_bits(digit) for digit in digits]
+            for digits in digit_lists
+        ]
+        return torch.tensor(
+            rows,
+            dtype=self.compute_dtype,
+            device=self.device,
+        )
+
+    @staticmethod
+    def _bucket_width(bits: int) -> int:
+        """Round to a trained 64-bit bucket with at least four headroom bits."""
+        return ((bits + 4 + 63) // 64) * 64
+
+    @staticmethod
+    def _oriented_lengths(item: tuple) -> tuple[int, int]:
+        """Lengths after consistently assigning the longer operand first."""
+        a, b, _p = item
+        if len(a) >= len(b):
+            return len(a), len(b)
+        return len(b), len(a)
+
+    def _length_local_groups(
+        self,
+        indices: list[int],
+        inputs,
+    ) -> list[list[int]]:
+        """Partition one width bucket by both oriented operand lengths.
+
+        A whole-tier group pays max(first length) + max(second length) for
+        every row. Exact-length grouping avoids that padding but produces too
+        many small captures. Sorting forty-row bands on the first length, then
+        sorting each band on the second and splitting into groups of twenty,
+        bounds both kinds of padding while leaving substantial GPU occupancy.
+        """
+        ordered = sorted(
+            indices,
+            key=lambda index: self._oriented_lengths(inputs[index])[0],
+        )
+
+        groups: list[list[int]] = []
+        for start in range(0, len(ordered), 40):
+            band = ordered[start : start + 40]
+            band.sort(
+                key=lambda index: self._oriented_lengths(inputs[index])[1]
+            )
+            for offset in range(0, len(band), 20):
+                groups.append(band[offset : offset + 20])
+        return groups
+
+    # -- recurrent execution ------------------------------------------------
+
+    @torch.inference_mode()
+    def _run_pass_eager(
+        self,
+        digit_rows: torch.Tensor,
+        x_bits: torch.Tensor,
+        p_bits: torch.Tensor,
+    ) -> torch.Tensor:
+        """Portable eager path for CPU and MPS."""
+        state = torch.zeros_like(p_bits)
+        for tick in range(digit_rows.shape[1]):
+            logits = self.cell(
+                state,
+                x_bits,
+                p_bits,
+                digit_rows[:, tick],
+            )
+            state = (logits > 0).to(dtype=self.compute_dtype)
+        return state
+
+    @torch.inference_mode()
+    def _run_two_passes_cuda_graph(
+        self,
+        first_rows: torch.Tensor,
+        second_rows: torch.Tensor,
+        p_bits: torch.Tensor,
+    ) -> torch.Tensor:
+        """Capture one learned transition and replay it for both raw streams.
+
+        The graph evaluates the complete inherited HornerCell, thresholds its
+        logits, and copies the binary output back into the same static state
+        storage. Thus every replay is one unchanged recurrent transition.
+
+        Only the next isolated raw input digit is copied into the graph's
+        static digit slot between replays. After pass one, its learned state is
+        copied into the static multiplicand; the state register is then reset
+        before pass two.
+        """
+        static_state = torch.zeros_like(p_bits)
+        static_x = torch.zeros_like(p_bits)
+        static_x[:, 0] = 1.0
+        static_p = p_bits.clone()
+        static_digit = torch.zeros(
+            p_bits.shape[0],
+            RADIX_BITS,
+            dtype=self.compute_dtype,
+            device=self.device,
+        )
+
+        # Initialize allocator and dense-library workspaces before capture.
+        warmup_stream = torch.cuda.Stream(device=self.device)
+        current_stream = torch.cuda.current_stream(self.device)
+        warmup_stream.wait_stream(current_stream)
+
+        with torch.cuda.stream(warmup_stream):
+            for _ in range(3):
+                warmup_logits = self.cell(
+                    static_state,
+                    static_x,
+                    static_p,
+                    static_digit,
+                )
+                static_state.copy_(
+                    (warmup_logits > 0).to(dtype=self.compute_dtype)
+                )
+
+        current_stream.wait_stream(warmup_stream)
+
+        # Synthetic warmup state must not enter either real encoder pass.
+        static_state.zero_()
+        static_x.zero_()
+        static_x[:, 0] = 1.0
+        static_digit.zero_()
+
+        graph = torch.cuda.CUDAGraph()
+        with torch.cuda.graph(graph):
+            graph_logits = self.cell(
+                static_state,
+                static_x,
+                static_p,
+                static_digit,
+            )
+            static_state.copy_(
+                (graph_logits > 0).to(dtype=self.compute_dtype)
+            )
+
+        for tick in range(first_rows.shape[1]):
+            static_digit.copy_(first_rows[:, tick])
+            graph.replay()
+
+        # The captured graph requires fixed storage addresses. Preserve the
+        # learned residue before resetting the recurrent register.
+        residue = static_state.clone()
+        static_x.copy_(residue)
+        static_state.zero_()
+
+        for tick in range(second_rows.shape[1]):
+            static_digit.copy_(second_rows[:, tick])
+            graph.replay()
+
+        return static_state.clone()
+
+    @torch.inference_mode()
+    def _solve_group(
+        self,
+        batch: list[tuple],
+        width: int,
+    ) -> list[list[int]]:
+        """Solve one length-local group at a shared register width."""
+        p_bits = torch.zeros(
+            len(batch),
+            width,
+            dtype=self.compute_dtype,
+            device=self.device,
+        )
+
+        for row, (_a, _b, p_enc) in enumerate(batch):
+            encoded_bits, prime_width = p_enc
+            p_bits[row, :prime_width] = torch.as_tensor(
+                encoded_bits,
+                dtype=self.compute_dtype,
+                device=self.device,
+            )
+
+        # Modular multiplication is commutative. A consistent orientation
+        # changes batched padding cost from max(a)+max(b) to
+        # max(longer)+max(shorter), without changing the requested function.
+        oriented = [
+            (a, b) if len(a) >= len(b) else (b, a)
+            for a, b, _p in batch
+        ]
+        first_rows = self._pack_digits(
+            [first for first, _second in oriented]
+        )
+        second_rows = self._pack_digits(
+            [second for _first, second in oriented]
+        )
+
+        if self.device.type == "cuda":
+            output = self._run_two_passes_cuda_graph(
+                first_rows,
+                second_rows,
+                p_bits,
+            )
+        else:
+            ones = torch.zeros_like(p_bits)
+            ones[:, 0] = 1.0
+            residue = self._run_pass_eager(first_rows, ones, p_bits)
+            output = self._run_pass_eager(second_rows, residue, p_bits)
+
+        rows = output.to(dtype=torch.int64).cpu().tolist()
+        return [list(reversed(row)) for row in rows]
+
+    # -- public prediction interface ---------------------------------------
+
+    def predict_digits(self, a_enc, b_enc, p_enc) -> list[int]:
+        return self.predict_digits_batch([(a_enc, b_enc, p_enc)])[0]
+
+    @torch.inference_mode()
+    def predict_digits_batch(self, inputs) -> list[list[int]]:
+        results: list[list[int]] = [[0] for _ in inputs]
+        width_groups: dict[int, list[int]] = defaultdict(list)
+
+        for index, (_a, _b, p_enc) in enumerate(inputs):
+            prime_width = p_enc[1]
+            if prime_width <= MAX_WIDTH:
+                width_groups[self._bucket_width(prime_width)].append(index)
+
+        for width, width_indices in width_groups.items():
+            for indices in self._length_local_groups(width_indices, inputs):
+                batch = [inputs[index] for index in indices]
+                solved = self._solve_group(batch, width)
+                for index, digits in zip(indices, solved):
+                    results[index] = digits
+
+        return results

provenance.json

@@ -0,0 +1,36 @@
+{
+  "artifact": "SAIR modmul alpha=0.75 weight soup",
+  "certification": {
+    "independent_seed_evaluations": "5/5 passed at H90=10 and overall=1.0000 on an NVIDIA L40S; 5000/5000 scored cases correct",
+    "manifest_and_load_smoke": "passed locally on 2026-08-11",
+    "metamorphic_evaluation": "140/140 passed across tiers 1-10",
+    "public_official_evaluation": "H90=10, overall=1.0000, 1000/1000 scored cases correct, deterministic, 248.4 inference seconds on an NVIDIA L40S",
+    "static_check": "clean with the official AST checker on 2026-08-11",
+    "weight_randomization": "17 tensors randomized; 0/30 nonzero-answer probes survived",
+    "width_boundary": "2048-bit modulus passed; the declared out-of-scope 2049-bit modulus is rejected with output zero"
+  },
+  "method": "elementwise FP32 linear interpolation",
+  "output": {
+    "file": "weights.pt",
+    "file_sha256": "2a245597f4499f83d0097d87801bd6dce79f014e5d1e3ed9cfa5f7a5e5c2363c",
+    "parameters": 91840,
+    "tensor_sha256": "5eb2e582891f59690cf719d8c44e040b6cb33e21356d3b62ff40c26c2ef79961",
+    "tensors": 17
+  },
+  "parents": [
+    {
+      "file_sha256": "255b2328134b85ac624ea1d45bc2245d04c3d2c1062ad5c7080c037a48f6584d",
+      "git_ref": "c00027c6db90076e58bac25ce6c4c23a46ccfd40",
+      "role": "harvest",
+      "weight": 0.75
+    },
+    {
+      "candidate_id": "17b8eb341153",
+      "file_sha256": "8fb5e4cf67d62b14effd85afb81fd96ded64d9da5ed02974171e21fe8707c010",
+      "git_ref": "4a6cbbead597cdbafd618b28666a730313857dd1",
+      "role": "r15_champion",
+      "weight": 0.25
+    }
+  ],
+  "schema_version": 1
+}

weights.pt

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2a245597f4499f83d0097d87801bd6dce79f014e5d1e3ed9cfa5f7a5e5c2363c
+size 372528