A computer-assisted theorem showing that exact preservation of a declared finite response can coexist with strict decrease of an independent implementation objective along an intrinsic response-fibre ODE.
Can a computation move through implementation space while preserving a declared finite response and strictly descending an independent objective? This repository answers that local question with frozen sources, interval certificates, and reproduction entrypoints. The theorem separates response invariance from dynamical stationarity: there is a direction invisible to the declared finite response, yet it gives strict descent of an independent objective.
The model has fourteen phase
parameters for a driven-qubit detuning scan and is verified with
192-bit Arb interval arithmetic. The archived v1.2.12 manuscript is
Computation as Geometric Flow: An Arb-Certified
Local Intrinsic ODE on a Quantum-Control Response Fibre. It incorporates the
recorded v1.2.9 errata and subsequent textual clarifications into a
self-contained recommended reading version and establishes the
Level-I local theorem. It does not change the mathematical
conclusions, theorem-bearing constants, frozen certificates, or the v0.7.4 +
v0.9.3 theorem boundary. No Arb rerun was performed or required. Later
repository artifacts are continuing work and are outside the theorem boundary of the
published Zenodo version; see
published paper boundary. The historical
version DOI
10.5281/zenodo.21728432
identifies the earlier public manuscript boundary; it is not the preferred
current-manuscript citation. The v1.2.9 DOI
10.5281/zenodo.21882158 and
paper-local-ode-v1.5
remain immutable historical records. The recommended v1.2.12 release is
archived at 10.5281/zenodo.21895917
and paper-local-ode-v1.6.
The historical raw record URL https://zenodo.org/records/21728432 is not the
current paper record.
| Purpose | Link |
|---|---|
| Read the recommended v1.2.12 manuscript | docs/manuscript/geometric_flow_v1_2_12_freeze_candidate.pdf |
| Inspect the matching v1.2.12 source ZIP | docs/manuscript/geometric_flow_v1_2_12_source.zip |
| Cite the recommended v1.2.12 public version | Zenodo DOI 10.5281/zenodo.21895917 |
| Download the matching GitHub release | GitHub Release paper-local-ode-v1.6 |
| Audit the historical v1.2.9 public release | GitHub Release paper-local-ode-v1.5 |
| Verify the published theorem boundary | python reproduce/published_paper.py |
| Follow the proof and certificate map | Proof navigation |
| View the wider research programme | Y.Y.N. Li - Open and Current Research |
Proved, Level I. For the frozen fourteen-phase driven-qubit model, the repository certifies existence and uniqueness of a local solution for an initial-value problem over one validated microstep:
[ 0 \le t \le 10^{-14}. ]
This local solution preserves the declared response map, strictly decreases the independent objective, and remains inside a formally validated local response-fibre chart.
"Frozen" means the model parameters, atlas coefficients, code, and reference artifacts are hash-bound; changing any of them defines a different computational statement.
For v0.7.4, all 16 theorem-bearing rank, near-tangency, nonstationarity, and descent boxes pass. A separate KKT-alignment diagnostic misses its predeclared threshold, so the serialized parent-box atlas is not claimed to be an ODE trajectory.
Milestone, Level II. The repository stores v0.10.6 as the latest stored reference certificate for finite same-chart continuation evidence. It does not yet prove a fifth frame or a global flow.
Conditional theorem, Level III. A separate analytic conditional-continuation manuscript concerns compactness, uniform rank, and uniform nonstationarity hypotheses. Those hypotheses are not yet certified on the complete response fibre and are outside the theorem boundary of the published Zenodo paper. This does not yet prove a fifth frame or a global flow.
The theorem is local. No global response-fibre flow, arbitrary endpoint connection, hardware result, or QPU claim is made.
The computation acts on a frozen analytic pulse model: fourteen phase coordinates (\theta\in\mathbb R^{14}), exact segment propagators, and a projective jet response (\mathcal R_3=(a_0,\dots,a_3)) produced by exact finite jet recurrences, not polynomial truncation. "Exact preservation" means this declared finite response map only: not higher-order coefficients, not the full physical output, and not hardware behaviour. Improvement means strict decrease of the independent objective (L_6) along the response fibre. Everything outside the layers below, including arbitrary endpoint connection and unconditional global flow, is not claimed here.
| Layer | Current Repository Status | Claim | Boundary |
|---|---|---|---|
| I. Local theorem | v0.9.3 intrinsic ODE microstep | Certified reference theorem | One Picard microstep, (0\le t\le 10^{-14}), near child 15 |
| II. Frozen finite continuation | v0.10.6 fourth-chart Lohner support flowpipe | Latest stored repository reference certificate | Declared finite chain of recentered charts only; instance-specific |
| III. Next-frame / global work | v0.10.13.1 source chain and v0.10.15 fail-closed harness | Implementation-open; not a fifth-frame or global-flow theorem | Holds only where compactness, uniform rank, and uniform nonstationarity are assumed; not certified on the complete fibre |
v0.10.6 is the packaged reference certificate. v0.10.13.1 records a stronger reindexed source chain, but reference-result packaging is still pending. v0.10.15 is implementation-open fifth-frame fail-closed scaffold work.
git clone https://github.com/papasop/Geometric-Flow.git
cd Geometric-Flow
python -m pip install -r requirements.txt
python scripts/verify_reference_results.py
python reproduce/published_paper.pypython scripts/verify_reference_results.py checks frozen SHA-256 entries and stored reference
certificates. python reproduce/published_paper.py checks frozen stored artifacts
and the published theorem boundary; only
python reproduce/published_paper.py --run recomputes the v0.7.4 + v0.9.3
theorem pair from frozen source. Python 3.12 and python-flint==0.8.0 are
recommended.
Certified:
- v0.7.4 complete-parent-box regularity, nonstationarity, and descent certificate;
- v0.9.3 local intrinsic ODE existence and uniqueness;
- exact preservation of the declared finite response (\mathcal R_3);
- strict (L_6) descent;
- one local Picard microstep.
Not certified:
- fifth frame;
- complete child traversal;
- complete ten-chart continuation;
- arbitrary endpoint connection;
- complete fibre connectedness;
- unconditional global flow;
- hardware or QPU behaviour.
The affine atlas-arclength derivative-label correction is documented in paper wording and changes no frozen certificate or strict-descent claim.
| Goal | Command |
|---|---|
| Verify the published Zenodo paper boundary | python reproduce/published_paper.py |
| Recompute the published v0.7.4 + v0.9.3 theorem pair | python reproduce/published_paper.py --run |
| Verify stored certificates and hashes | python scripts/verify_reference_results.py |
| Recompute the v0.9.3 local ODE theorem only | python reproduce/local_theorem.py |
| Reproduce the fourth-chart Lohner flowpipe | python reproduce/finite_continuation.py |
| Audit the open fifth-frame target | python reproduce/open_next_frame_audit.py |
The stable entry points verify the relevant frozen SHA-256 entries before calling archived proof drivers. The finite-continuation and fifth-frame commands are not part of the published Zenodo paper theorem boundary.
Compatibility commands remain available under scripts/, including
scripts/reproduce_finite_continuation.py and
scripts/reproduce_field_jacobian.py; these wrappers verify the relevant
frozen SHA-256 entries before delegating to archived drivers.
src/: core geometric code and maintained formal backends.reproduce/: published-paper and research-line reproduction entry points.archive/milestones/: historical v0.9.x/v0.10.x milestone scripts with original filenames preserved.docs/: claim boundaries, proof navigation, release provenance, and post-publication research maps.results/: stored reference certificates and reports.
Avoid adding another user-facing versioned script. Prefer the stable
reproduce/ entry points and archive raw historical drivers under
archive/milestones/.
The v1.2.12 manuscript revision and the published v1.2.9 theorem boundary remain frozen in scope. Later finite-continuation, controlled-attraction, feedback, process-time, two-metric, certificate-DAG, and K=1 investigations do not enlarge the local theorem.
The immediate continuation research direction is Toward a global response-fibre flow. The immediate open step is the fifth-frame backend; v0.10.15 is fail-closed scaffold work. The stored v0.10.6 reference records finite same-chart continuation evidence. The fifth-frame backend remains open, and later v0.10.x material is outside the v1.2.12 theorem boundary. K=1, physical time, and global flow are not established. Neural response-fibre material is an independent analogue; see neural network response fibres. It is not a theorem of the published paper.
See:
Paper and claim boundary:
- Claim scope
- Published paper boundary
- Paper wording
- Manuscript v1.2.9 clarifications and errata
- Manuscript provenance
- Reviewer reproduction
Proof and reproduction:
Post-publication research:
- Roadmap
- Theory architecture
- Research status matrix
- Control extension scope
- Wiener feedback scope
- Process-time scope
- Two-metric scope
- Certificate DAG scope
- K=1 bridge scope
Historical and archive material:
The recommended reading version is the frozen v1.2.12 manuscript archived in this repository and published through the following immutable release records:
- PDF:
docs/manuscript/geometric_flow_v1_2_12_freeze_candidate.pdf - source ZIP:
docs/manuscript/geometric_flow_v1_2_12_source.zip - DOI: 10.5281/zenodo.21895917
- GitHub Release:
paper-local-ode-v1.6
Historical v1.2.9 public archive:
The historical version DOI 10.5281/zenodo.21728432 identifies the earlier public manuscript boundary; it is not the preferred current-manuscript citation.
Suggested citation for the local theorem and published paper boundary: cite
v1.2.12 using DOI 10.5281/zenodo.21895917 and identify the theorem-bearing
software boundary as v0.7.4 + v0.9.3.
Software is released under the MIT license. The v1.2.12 manuscript and manuscript source ZIP are released under Creative Commons Attribution 4.0 International (CC BY 4.0).
展开摘要
本仓库归档并复现 v1.2.12 冻结文稿：在一个十四相位驱动量子比特模型中， 严格证明声明响应 (\mathcal R_3) 可被精确保持，同时独立目标 (L_6) 沿局部响应纤维 ODE 严格下降。
当前已严格证明局部 ODE 微步：已证明 v0.7.4 父盒证书和 v0.9.3 局部 ODE 微步；尚未证明第五框架、完整子域遍历、十图册延拓、任意端点连接、 硬件/QPU 行为或全局几何流。
v1.2.12 吸收了 v1.2.9 勘误和后续文字澄清；它不改变定理常数、证书或 v0.7.4 + v0.9.3 软件边界。v0.10.x、受控吸引、反馈、过程时间、双度量、 证书 DAG 和 K=1 相关内容是发表后研究路线，不扩大本地定理边界。 神经网络 响应纤维只是独立类比方向，不属于本发表论文定理。