VeriLoop E2

27B Post-Trained Model for Code, Mathematics, and Physics
VeriLoop-Governed Recurrence (VGR) for Evidence-Convergent Reasoning

Built on Qwen3.8-27B · 262K native context · Apache License 2.0
Developed by Tsinghua SIGS Robot Lab · Libo Wang

Hugging Face · ModelScope (Global) · ModelScope (China)

Technical Report · Evaluation Evidence · Riemann ζ Artifact · Black-Hole Artifact

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Overview

VeriLoop E2 is an open 27B post-trained model built on Qwen3.8-27B, targeting code, mathematics, and physics. Its core reasoning discipline is VeriLoop-Governed Recurrence (VGR): candidate states are recursively proposed, externally checked, and retained only when the protected evidence state improves without regression.

The system separates generative intelligence from verification authority. VeriLoop E2 is responsible for proposal generation, abstraction, diagnosis, repair hypotheses, and structured reasoning. The VeriLoop Harness governs evidence admission, deterministic checks, external verification, commit/rollback, stopping, and evidence-state persistence. The model therefore does not self-certify its own progress.

This release focuses on the model weights, public inference path, evaluation record, and public functional description of the Harness. The production Harness implementation itself is not included in this repository.

Release highlights

• 27B open-weight post-trained model for code, mathematics, and physics, derived from Qwen3.8-27B.
• 262,144-token native context window in the released tokenizer configuration.
• Strong release results across nine code-agent, mathematics, and science benchmarks, including 76.2% SWE-bench Pro, 88.8% Terminal-Bench 2.1, 98.3% AIME 2026, 93.9% GPQA Diamond, and 89.6% Apex 2025.
• A reproducible scientific-reasoning program built around verifier-governed recurrence rather than unconstrained retry.
• Two public scientific demonstrations with released evidence artifacts: a strict finite-dimensional Riemann ζ zero-proportion certificate at 67.350003708785593%, and Asymptotic Graviton Tomography, which establishes an exact-and-quantitative completeness framework for free asymptotic radiative graviton data.
• OpenAI-compatible serving through vLLM 0.17.0 with a validated 131,072-token serving configuration.

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Model Summary

The post-training mix spans repository-level software engineering, terminal and tool use, mathematical reasoning, scientific reasoning, verifier-sensitive repair, and recurrence-oriented training. Exact data construction, filtering, and training methodology are documented in the technical report rather than duplicated here.

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Benchmark Results

The README reports the frozen release scores for VeriLoop E2. Agentic benchmarks use the E2 checkpoint inside the frozen evaluation workflow, including the internal VeriLoop Harness where required by the task, benchmark-native tools, and the benchmark's official or designated evaluator. Exact per-benchmark protocols, task-level outputs, evaluator receipts, and integrity metadata are published separately in the Evaluation Evidence package.

Attribution boundary. The reported results characterize the evaluated E2 system configuration. They should not be interpreted as evidence that an untouched Qwen3.8-27B base checkpoint, or the E2 checkpoint outside the evaluated runtime, reproduces the same numbers.

_{Figure 1. VeriLoop E2 release snapshot across nine public benchmarks. Higher is better. Provider colors are fixed across panels; exact public model variants are shown in the comparison tables below. Full protocol and source provenance: Evaluation Evidence.}

Code and agentic benchmarks

Mathematics and science benchmarks

A dash means that the release figure does not include a public comparison point for that provider on that benchmark. Each linked VeriLoop E2 score above resolves directly to its benchmark-specific public evidence directory or release source. External reference values mirror the frozen comparison set used in Figure 1; harness notes and protocol caveats are retained in the evaluation ledger rather than duplicated here. Seven results currently map to Hugging Face Native Benchmark leaderboards: AIME 2026, DeepSWE v1.1, GPQA Diamond, SWE-bench Pro, Terminal-Bench 2.1, Terminal-Bench 3.0, and Terminal-Bench 4.0. Apex 2025 (89.6) and SWE-Marathon v1.1 (45.0) are presented here as laboratory self-published release results with public source links. Apex 2025 is retained as a structured model result with public evidence, but MathArena/apex_2025 is not currently a Hugging Face Native Benchmark leaderboard; SWE-Marathon v1.1 now has public task-level evidence in the Evaluation Evidence repository, while a stable Hugging Face Native Benchmark registration/task identifier is not currently available.

Evaluation evidence

The public evidence package is intended to make the benchmark record inspectable rather than merely declarative. Where available, each task record binds:

task identity
    ↓
model / system output
    ↓
benchmark-native execution or evaluator record
    ↓
score / pass-fail decision
    ↓
integrity metadata and provenance

Evidence repository: https://huggingface.co/datasets/tsinghua-sigs-robot-lab/VeriLoop-E2-Evaluation-Evidence

The model repository publishes eight structured evaluation descriptors under /.eval_results/. Seven of them currently map to Hugging Face Native Benchmark leaderboards; the Apex 2025 descriptor is retained for structured reporting and provenance, but does not currently produce a Hugging Face leaderboard rank. SWE-Marathon v1.1 is published with task-level evidence in the Evaluation Evidence repository as a laboratory self-published release result and is not included in /.eval_results/ because a stable Hugging Face Native Benchmark registration/task identifier is not currently available.

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VeriLoop Harness

VeriLoop is not designed around the idea that a model should announce its own improvement. The Harness treats model output as a candidate state that must earn admission through external evidence.

The current public abstraction is VeriLoop-Governed Recurrence (VGR):

Current request
    ↓
Contract compilation
    ↓
VeriLoop E2 proposes a candidate
    ↓
External / deterministic verification
    ↓
Protected evidence state comparison
    ├── no protected regression + at least one strict improvement → COMMIT
    ├── otherwise                                             → ROLLBACK
    └── zero-rank certificate                                → STOP
    ↓
Verified evidence becomes the next recurrence state

The key boundary is deliberate:

• Model authority: propose, reason, abstract, diagnose, synthesize, repair.
• Harness authority: admit evidence, execute deterministic checks, verify, commit, roll back, stop, and persist verified state.
• Benchmark / domain authority: define task truth through native evaluators, tests, formal checks, numerical certificates, or other domain-specific validators.

This architecture is intended to preserve capability while preventing self-reported success from becoming system state. In software engineering, that means tests and execution receipts dominate plausible-looking patches. In mathematics and physics, it means a retained derivation must survive the relevant symbolic, numerical, or formal checks before it is promoted.

The production implementation contains private orchestration, routing, thresholds, prompt compilation, evidence-state machinery, repair arbitration, and deployment controls. Those implementation details are not part of this open model release. The README exposes the functional contract, not the proprietary runtime.

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Public 14-Rule Engineering Contract

The public Golden Rules are the model-visible execution discipline used to keep long-horizon work bounded, testable, and auditable.

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Scientific Demonstrations

The scientific demonstrations are not presented as isolated chat transcripts. They are examples of how the E2 model and the internal Harness can divide a difficult research problem into candidate derivations, falsifiable subclaims, executable checks, retained evidence, and explicit claim boundaries.

Riemann ζ: 67.350003708785593% strict finite-dimensional certificate

The released Riemann artifact reports a frozen assembly value of

[ \kappa = 67.350003708785593%. ]

The current strict package closes 3/3 local inequalities, resolves 327/327 difficult wells, executes 190,375,830 strict branch-and-bound nodes, and passes the final exact rational assembly check.

Established result. Within the released analytic setup and its explicitly imported assumptions, the artifact establishes a strict finite-dimensional computer-assisted certificate at the stated zero-proportion value. The claim is therefore the certificate itself, together with its reproducible derivation, computation, and assembly evidence.

Boundary and current work. This result is not a proof of the Riemann Hypothesis, and it is not yet an end-to-end Lean/nanoda kernel proof of the complete upstream analytic chain. The remaining work is being directed at that exact boundary: formalizing the imported analytic normalization steps, binding them to the finite-dimensional certificate, and closing a complete kernel-replay path from the upstream analytic assumptions through the final assembly. Until that bridge is closed, the public claim remains the strict finite-dimensional certificate under the stated framework rather than a formal proof of the full analytic chain.

Artifact: https://github.com/brucewang123456789/GeniusTrail/tree/VeriLoop-E2/riemann-hypothesis

Black-hole information problem: Asymptotic Graviton Tomography

The second scientific demonstration is Asymptotic Graviton Tomography, a verifier-governed theoretical-physics research artifact focused on information reconstruction from free asymptotic radiative graviton data at future null infinity.

Established result. The released artifact establishes an exact-and-quantitative tomography framework with nine stated results, T1–T9. The exact layer includes the Sector Connectivity Theorem, the hard-Fock commutant [ \mathcal{A}_F' = W^*(\hat N), ] a linear-connector completion theorem, and a two-branch classification of the infrared-memory layer. The quantitative layer identifies the algebraic connectivity (\lambda_2) of the coherence-transfer Laplacian as the modulus of informational completeness; in the stated two-mode (su(2)) reduction it obtains [ \operatorname{spec}(L)=\lambda^2 k(k+1), \qquad \lambda_2 = 2\lambda^2, ] with the gap independent of graviton number (N) and extremal operator (N_R). The repository contains the analytic derivations, a derivation walkthrough, theorem-status metadata, the reference computation transcript, and six executable numerical/structural certificates; the released reference suite reports 6/6 PASS.

Boundary and current work. This artifact does not solve the black-hole information paradox. It does not yet provide interacting or evaporating black-hole dynamics, initial-to-out faithfulness, a Hawking-radiation derivation, or a proof of evaporation unitarity. Those missing dynamical layers define the active research frontier rather than being hidden behind the present result. Current work is focused on deriving the infrared exponent from first principles for specified dressing geometries, extending the spectral-gap analysis to genuinely multi-mode connectors, replacing the discrete memory label with the physical direct-integral continuum formulation, extending the Laplacian framework beyond exactly block-diagonal base algebras, and developing a dynamical completeness modulus capable of connecting initial data to outgoing radiation. Until that bridge is closed, the claim remains deliberately restricted to the free-asymptotic radiative setting.

Artifact: https://github.com/brucewang123456789/GeniusTrail/tree/VeriLoop-E2/black%20hole%20information%20paradox

The scientific artifacts are released separately from the model weights and retain their own artifact-specific terms. The Riemann ζ artifact follows its own research-use terms; Asymptotic Graviton Tomography is released under CC BY 4.0 as stated in its repository. Neither artifact should be assumed to inherit the Apache-2.0 grant that applies to the model weights and public inference utilities.

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Inference

Recommended environment

The following stack is the validated reference environment for the public serving path:

The released tokenizer advertises a native maximum length of 262,144 tokens. The 131,072-token value above is the validated public serving configuration, not a redefinition of the model's native context length. Longer serving windows require appropriate accelerator memory and KV-cache planning.

vLLM server

Use the tokenizer and chat template shipped with the model repository.

python -m pip install "vllm==0.17.0"

MODEL="<MODEL_PATH_OR_HF_ID>"

vllm serve "${MODEL}" \
  --served-model-name veriloop-e2 \
  --dtype bfloat16 \
  --model-impl vllm \
  --language-model-only \
  --max-model-len 131072 \
  --max-num-seqs 16 \
  --gpu-memory-utilization 0.92 \
  --generation-config vllm \
  --disable-uvicorn-access-log \
  --host 127.0.0.1 \
  --port 8001

OpenAI-compatible request

curl http://127.0.0.1:8001/v1/chat/completions \
  -H "Content-Type: application/json" \
  -d '{
    "model": "veriloop-e2",
    "messages": [
      {"role": "user", "content": "Reply exactly: 8001_OK"}
    ],
    "temperature": 0,
    "max_tokens": 16,
    "stream": false
  }'

A validated smoke test returns:

8001_OK

Python client

from openai import OpenAI

client = OpenAI(
    base_url="http://127.0.0.1:8001/v1",
    api_key="EMPTY",
)

response = client.chat.completions.create(
    model="veriloop-e2",
    messages=[
        {"role": "user", "content": "Explain why rollback matters in verifier-governed reasoning."}
    ],
    temperature=0.2,
    max_tokens=1024,
)

print(response.choices[0].message.content)

Protocol note

For tool use or long multi-turn reasoning, treat the repository-shipped tokenizer and chat template as part of the model protocol. Replacing role delimiters, tool-call syntax, stop semantics, or reasoning-history behavior can change observed system behavior even when the weights are unchanged.

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Release Boundary and Artifact Terms

Different artifacts intentionally carry different permissions. Do not infer that the model-weight license automatically applies to separately published scientific artifacts or private system components.

The open model license does not disclose or license unpublished Harness orchestration, prompt compilation, verifier routing, private evidence-state schemas, repair arbitration, deployment infrastructure, private training data, or other non-distributed internal systems.

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Limitations

• VeriLoop E2 is a post-trained model component; the complete production VeriLoop Harness is not part of this release.
• Reported system benchmarks may depend on benchmark-native tools, sandbox behavior, evaluator versions, and the frozen Harness configuration described in the evidence package.
• The model can still produce incorrect code, invalid proofs, physically unsupported arguments, insecure commands, or incomplete analyses.
• A plausible-looking derivation is not equivalent to a verified result; domain-native verification remains necessary.
• Long-context performance depends on serving configuration, accelerator memory, KV-cache budget, and workload shape.
• Community-modified templates, stop rules, parsers, or client logic can materially change observed tool-use and reasoning behavior.
• Scientific demonstration artifacts have explicit scope boundaries and should not be generalized beyond the claims actually certified by their released evidence.

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Links

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Citation

If you use VeriLoop E2 in research, please cite the model release and the relevant evaluation or scientific artifact separately.

@misc{wang2026veriloope2,
  title        = {VeriLoop E2: A 27B Post-Trained Model for Code, Mathematics, and Scientific Reasoning},
  author       = {Wang, Libo},
  year         = {2026},
  note         = {Tsinghua Shenzhen International Graduate School (SIGS)},
  howpublished = {Open model release},
  url          = {https://huggingface.co/tsinghua-sigs-robot-lab/VeriLoop-E2}
}

For benchmark figures or evaluation records, attribution should identify VeriLoop E2 / Libo Wang and link to the public evaluation evidence package: https://huggingface.co/datasets/tsinghua-sigs-robot-lab/VeriLoop-E2-Evaluation-Evidence.

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Acknowledgements

VeriLoop E2 builds on Qwen3.8-27B and the broader open-source model-serving, evaluation, and scientific-computing ecosystem. We thank the communities behind Qwen, Transformers, vLLM, Safetensors, software-engineering benchmarks, mathematical evaluation suites, and reproducible scientific computation.

The model, benchmark evidence, and scientific artifacts are published with explicit boundaries so that capability claims can be inspected at the level at which they were actually produced and verified.