Datasets:

Snapkitty
/

cpsc-qft-paper

---
license: gpl-3.0
language:
- en
tags:
- research-paper
- snapkitty
- quantum-computing
- quantum-field-theory
- lattice
- transverse-field-ising
- trotter
- compiler
- formal-verification
- lean4
- qsharp
- research
task_categories:
- other
size_categories:
- n<1K
pretty_name: Conservation-Preserving Compilation for a 1+1D Lattice Shadow of φ⁴
---
# Conservation-Preserving Compilation for a 1+1D Lattice Shadow of φ⁴

> 💬 **Feedback wanted.** Rebuilt the Lean proofs, reproduced the audit, or found an error in the paper? [Open a discussion](https://huggingface.co/datasets/Snapkitty/cpsc-qft-paper/discussions/new). Part of our [flagship releases](https://huggingface.co/collections/Snapkitty/flagship-releases-october-2026-6acd83199105403d2fc0a4f2).

**Ahmad Ali Parr · SnapKitty Collective · 7 October 2026**

[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.23287576.svg)](https://doi.org/10.5281/zenodo.23287576) · Archived on Zenodo: [10.5281/zenodo.23287576](https://doi.org/10.5281/zenodo.23287576)

📄 **[Read the paper (PDF, 12 pages)](https://huggingface.co/datasets/Snapkitty/cpsc-qft-paper/blob/main/paper.pdf)** · 💻 Code: [Snapkitty/cpsc-qft](https://huggingface.co/Snapkitty/cpsc-qft) · 🔏 [Lean proofs](https://huggingface.co/datasets/Snapkitty/cpsc-qft-paper/tree/main/proofs/lean) · [GitHub](https://github.com/AHMADALIPARR/cpsc-qft)

---

## Abstract

We implement a compilation architecture for lattice scattering in which the symmetries of the target Hamiltonian constrain circuit synthesis rather than filter measured shots. The working model is the periodic transverse-field Ising chain, the qubit shadow of 1+1D φ⁴, not continuum φ⁴.

Two facts fix the compiler. The quartic written as Σᵢ Xᵢ⁴ is a multiple of the identity. Z-parity is a symmetry only at λ = 0; for λ ≠ 0 the conserved operator is the global spin flip Πᵢ Xᵢ.

The repository supplies a symmetry analyzer, a translation-orbit check, a first-order Trotter product of admitted gates, a Q# emission of those factors, and a certificate whose SHA-256 digest is bound to the gate list. On a 4-site chain the Ising schedule has Z-parity leakage 0, and the spin-flip schedule has Π X leakage 0 within roundoff. Inserting a forbidden gate fails compilation. A Lean development proves, without project axioms, that every admitted Trotter schedule commutes with the conserved operator on (ℂ²)^⊗N for every lattice size and every angle.

This paper describes what the code does. It proves operator commutation in Lean for every admitted schedule. It does not claim a continuum scattering amplitude.

## Contents of the paper

1. Introduction
2. Which operator is actually conserved (magnetization fails at λ ≠ 0; the spin flip Π_X is conserved for all λ)
3. Compiler (`compile_scattering`: emit a certified Trotter schedule or raise `CompilationRejected`)
4. Certificate (SHA-256 of the canonical schedule payload, rendered as a Lean fragment)
5. Q# emission
6. Checks (six numerical checks on N = 4; `pytest` 14 passed)
7. Related work
8. Conclusion
- Appendix A: Operator proofs (main result: Theorem A.9, `admitted_trotter_commutes`)
- Appendix B: Lean development (Lean 4.22.0; axiom audit lists only `propext`, `Classical.choice`, `Quot.sound`)

## Files

| File | Contents |
|---|---|
| `paper.pdf` | The paper, 12 pages; byte-identical to the Zenodo record's PDF (MD5 `1c9e80b76bf4ee3bf36439d07ab17673`). SHA-256 `3e22507dbdacdf88491b4397d393d5452c5dfe0dab4ecc650adf34644eb36243` |
| `paper.tex` | LaTeX source of the paper, from [AHMADALIPARR/cpsc-qft@34c4bab](https://github.com/AHMADALIPARR/cpsc-qft/blob/34c4bab/paper/PAPER.tex). Build with `latexmk -xelatex paper.tex` |
| `proofs/lean/` | The Lean 4 development from [AHMADALIPARR/cpsc-qft@9b102cf](https://github.com/AHMADALIPARR/cpsc-qft/tree/9b102cf/lean). `CPSC/Operator.lean` holds the operator model and Theorem A.9 (`admitted_trotter_commutes`); `Audit.lean` prints the axioms of the main results |
| `proofs/OPERATOR_PROOFS.md` | Appendix A in Markdown, with each step mapped to its Lean theorem |
| `proofs/audit-output.txt` | Output of `lake env lean Audit.lean` (see Verification) |
| `LICENSE`, `LICENSES/` | License split (paper: GPL-3.0-or-later; code: CPSC-ESCL-1.0 or AGPL-3.0-only) and full texts |

## Verification

Reproduced on 2026-10-10 with a clean build from `AHMADALIPARR/cpsc-qft` at commit `9b102cf`:

```bash
cd lean && lake build                 # Lean 4.22.0: Build completed successfully (CPSC.Certificate, Operator, Lemmas, Emitted)
lake env lean Audit.lean              # axiom audit, output below
cd .. && PYTHONPATH=src python3 -m pytest -q   # 14 passed
```

```
'CPSC.Operator.admitted_trotter_commutes' depends on axioms: [propext, Classical.choice, Quot.sound]
'CPSC.operator_commutation' depends on axioms: [propext, Classical.choice, Quot.sound]
'CPSC.transverse_flip_breaks_magnetization' depends on axioms: [propext, Classical.choice, Quot.sound]
'CPSC.loneZ_breaks_spin_flip_op' depends on axioms: [propext, Classical.choice, Quot.sound]
'CPSC.Operator.rx_inverse' depends on axioms: [propext, Classical.choice, Quot.sound]
'CPSC.Emitted.emitted_commutes' depends on axioms: [propext, Classical.choice, Quot.sound]
```

Only Lean's three standard axioms appear; no project axiom and no `sorry`.

## Citation

```bibtex
@misc{parr2026cpsc,
  title  = {Conservation-Preserving Compilation for a 1+1D Lattice Shadow of $\phi^4$},
  author = {Parr, Ahmad Ali},
  year   = {2026},
  month  = oct,
  publisher = {Zenodo},
  doi    = {10.5281/zenodo.23287576},
  url    = {https://doi.org/10.5281/zenodo.23287576},
  note   = {SnapKitty Collective}
}
```

## License

The paper and the code are licensed separately.

| Material | Files | License |
|---|---|---|
| Paper text | `paper.pdf`, `paper.tex`, `proofs/OPERATOR_PROOFS.md` | **GPL-3.0-or-later**, as on [Zenodo](https://doi.org/10.5281/zenodo.23287576) |
| Code | `proofs/lean/` (and [Snapkitty/cpsc-qft](https://huggingface.co/Snapkitty/cpsc-qft)) | **CPSC-ESCL-1.0 or AGPL-3.0-only** |

Full texts are in `LICENSES/`; `LICENSE` summarises the split. Copyright © 2026 Ahmad Ali Parr and others.

### 💼 Commercial License

The code is published under **CPSC-ESCL-1.0 or AGPL-3.0**. Building a commercial product or service? A **proprietary commercial license** from Snapkitty Collective LLC lets you ship this code on terms other than CPSC-ESCL-1.0 or AGPL-3.0.

**[→ Get a commercial license](mailto:A.parr@belespritdaccord.uk?subject=Commercial%20license:%20cpsc-qft)** · A.parr@belespritdaccord.uk

	---
	license: gpl-3.0
	language:
	- en
	tags:
	- research-paper
	- snapkitty
	- quantum-computing
	- quantum-field-theory
	- lattice
	- transverse-field-ising
	- trotter
	- compiler
	- formal-verification
	- lean4
	- qsharp
	- research
	task_categories:
	- other
	size_categories:
	- n<1K
	pretty_name: Conservation-Preserving Compilation for a 1+1D Lattice Shadow of φ⁴
	---

	# Conservation-Preserving Compilation for a 1+1D Lattice Shadow of φ⁴

	> 💬 Feedback wanted. Rebuilt the Lean proofs, reproduced the audit, or found an error in the paper? [Open a discussion](https://huggingface.co/datasets/Snapkitty/cpsc-qft-paper/discussions/new). Part of our [flagship releases](https://huggingface.co/collections/Snapkitty/flagship-releases-october-2026-6acd83199105403d2fc0a4f2).

	Ahmad Ali Parr · SnapKitty Collective · 7 October 2026

	[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.23287576.svg)](https://doi.org/10.5281/zenodo.23287576) · Archived on Zenodo: [10.5281/zenodo.23287576](https://doi.org/10.5281/zenodo.23287576)

	📄 [Read the paper (PDF, 12 pages)](https://huggingface.co/datasets/Snapkitty/cpsc-qft-paper/blob/main/paper.pdf) · 💻 Code: [Snapkitty/cpsc-qft](https://huggingface.co/Snapkitty/cpsc-qft) · 🔏 [Lean proofs](https://huggingface.co/datasets/Snapkitty/cpsc-qft-paper/tree/main/proofs/lean) · [GitHub](https://github.com/AHMADALIPARR/cpsc-qft)

	---

	## Abstract

	We implement a compilation architecture for lattice scattering in which the symmetries of the target Hamiltonian constrain circuit synthesis rather than filter measured shots. The working model is the periodic transverse-field Ising chain, the qubit shadow of 1+1D φ⁴, not continuum φ⁴.

	Two facts fix the compiler. The quartic written as Σᵢ Xᵢ⁴ is a multiple of the identity. Z-parity is a symmetry only at λ = 0; for λ ≠ 0 the conserved operator is the global spin flip Πᵢ Xᵢ.

	The repository supplies a symmetry analyzer, a translation-orbit check, a first-order Trotter product of admitted gates, a Q# emission of those factors, and a certificate whose SHA-256 digest is bound to the gate list. On a 4-site chain the Ising schedule has Z-parity leakage 0, and the spin-flip schedule has Π X leakage 0 within roundoff. Inserting a forbidden gate fails compilation. A Lean development proves, without project axioms, that every admitted Trotter schedule commutes with the conserved operator on (ℂ²)^⊗N for every lattice size and every angle.

	This paper describes what the code does. It proves operator commutation in Lean for every admitted schedule. It does not claim a continuum scattering amplitude.

	## Contents of the paper

	1. Introduction
	2. Which operator is actually conserved (magnetization fails at λ ≠ 0; the spin flip Π_X is conserved for all λ)
	3. Compiler (`compile_scattering`: emit a certified Trotter schedule or raise `CompilationRejected`)
	4. Certificate (SHA-256 of the canonical schedule payload, rendered as a Lean fragment)
	5. Q# emission
	6. Checks (six numerical checks on N = 4; `pytest` 14 passed)
	7. Related work
	8. Conclusion
	- Appendix A: Operator proofs (main result: Theorem A.9, `admitted_trotter_commutes`)
	- Appendix B: Lean development (Lean 4.22.0; axiom audit lists only `propext`, `Classical.choice`, `Quot.sound`)

	## Files

	\| File \| Contents \|
	\|---\|---\|
	\| `paper.pdf` \| The paper, 12 pages; byte-identical to the Zenodo record's PDF (MD5 `1c9e80b76bf4ee3bf36439d07ab17673`). SHA-256 `3e22507dbdacdf88491b4397d393d5452c5dfe0dab4ecc650adf34644eb36243` \|
	\| `paper.tex` \| LaTeX source of the paper, from [AHMADALIPARR/cpsc-qft@34c4bab](https://github.com/AHMADALIPARR/cpsc-qft/blob/34c4bab/paper/PAPER.tex). Build with `latexmk -xelatex paper.tex` \|
	\| `proofs/lean/` \| The Lean 4 development from [AHMADALIPARR/cpsc-qft@9b102cf](https://github.com/AHMADALIPARR/cpsc-qft/tree/9b102cf/lean). `CPSC/Operator.lean` holds the operator model and Theorem A.9 (`admitted_trotter_commutes`); `Audit.lean` prints the axioms of the main results \|
	\| `proofs/OPERATOR_PROOFS.md` \| Appendix A in Markdown, with each step mapped to its Lean theorem \|
	\| `proofs/audit-output.txt` \| Output of `lake env lean Audit.lean` (see Verification) \|
	\| `LICENSE`, `LICENSES/` \| License split (paper: GPL-3.0-or-later; code: CPSC-ESCL-1.0 or AGPL-3.0-only) and full texts \|

	## Verification

	Reproduced on 2026-10-10 with a clean build from `AHMADALIPARR/cpsc-qft` at commit `9b102cf`:

	```bash
	cd lean && lake build # Lean 4.22.0: Build completed successfully (CPSC.Certificate, Operator, Lemmas, Emitted)
	lake env lean Audit.lean # axiom audit, output below
	cd .. && PYTHONPATH=src python3 -m pytest -q # 14 passed
	```

	```
	'CPSC.Operator.admitted_trotter_commutes' depends on axioms: [propext, Classical.choice, Quot.sound]
	'CPSC.operator_commutation' depends on axioms: [propext, Classical.choice, Quot.sound]
	'CPSC.transverse_flip_breaks_magnetization' depends on axioms: [propext, Classical.choice, Quot.sound]
	'CPSC.loneZ_breaks_spin_flip_op' depends on axioms: [propext, Classical.choice, Quot.sound]
	'CPSC.Operator.rx_inverse' depends on axioms: [propext, Classical.choice, Quot.sound]
	'CPSC.Emitted.emitted_commutes' depends on axioms: [propext, Classical.choice, Quot.sound]
	```

	Only Lean's three standard axioms appear; no project axiom and no `sorry`.

	## Citation

	```bibtex
	@misc{parr2026cpsc,
	title = {Conservation-Preserving Compilation for a 1+1D Lattice Shadow of $\phi^4$},
	author = {Parr, Ahmad Ali},
	year = {2026},
	month = oct,
	publisher = {Zenodo},
	doi = {10.5281/zenodo.23287576},
	url = {https://doi.org/10.5281/zenodo.23287576},
	note = {SnapKitty Collective}
	}
	```

	## License

	The paper and the code are licensed separately.

	\| Material \| Files \| License \|
	\|---\|---\|---\|
	\| Paper text \| `paper.pdf`, `paper.tex`, `proofs/OPERATOR_PROOFS.md` \| GPL-3.0-or-later, as on [Zenodo](https://doi.org/10.5281/zenodo.23287576) \|
	\| Code \| `proofs/lean/` (and [Snapkitty/cpsc-qft](https://huggingface.co/Snapkitty/cpsc-qft)) \| CPSC-ESCL-1.0 or AGPL-3.0-only \|

	Full texts are in `LICENSES/`; `LICENSE` summarises the split. Copyright © 2026 Ahmad Ali Parr and others.

	### 💼 Commercial License

	The code is published under CPSC-ESCL-1.0 or AGPL-3.0. Building a commercial product or service? A proprietary commercial license from Snapkitty Collective LLC lets you ship this code on terms other than CPSC-ESCL-1.0 or AGPL-3.0.

	[→ Get a commercial license](mailto:A.parr@belespritdaccord.uk?subject=Commercial%20license:%20cpsc-qft) · A.parr@belespritdaccord.uk