A computer-assisted local theorem: in a frozen fourteen-phase driven-qubit model, exact preservation of a declared finite response can coexist with strict decrease of an independent implementation objective along an intrinsic response-fibre ODE.
The certified result is local. It does not claim a fifth frame, complete child traversal, complete-atlas continuation, hardware/QPU behaviour, arbitrary endpoint connection, or a global response-fibre flow.
| Purpose | Link or command |
|---|---|
| Read the recommended manuscript | docs/manuscript/geometric_flow_v1_2_13_disclosure_revision.pdf |
| Inspect the matching source ZIP | docs/manuscript/geometric_flow_v1_2_13_source.zip |
| Cite the current public version | DOI 10.5281/zenodo.21947745 |
| Download the GitHub release | paper-local-ode-v1.7 |
| Verify the published theorem boundary | python reproduce/published_paper.py |
| Follow the proof map | docs/PROOF_NAVIGATION.md |
git clone https://github.com/papasop/Geometric-Flow.git
cd Geometric-Flow
python -m pip install -r requirements.txt
# Identity and hash checks
python scripts/verify_reference_results.py
# Published theorem boundary check
python reproduce/published_paper.py
# Optional, slower Arb recomputation of the theorem pair
python reproduce/published_paper.py --runPython 3.12 and python-flint==0.8.0 are recommended. The default
published_paper.py mode checks stored frozen artifacts; only --run
recomputes the v0.7.4 + v0.9.3 theorem pair from frozen source.
The recommended v1.2.13 manuscript is frozen in scope. Its theorem-bearing software boundary remains v0.7.4 + v0.9.3.
For the frozen model, the repository certifies existence and uniqueness of a local initial-value problem over one Picard microstep,
[ 0 \le t \le 10^{-14}. ]
The certified solution:
- preserves the declared finite response map (\mathcal R_3);
- strictly decreases the independent objective (L_6);
- remains inside a formally validated local response-fibre chart.
"Frozen" means the model parameters, atlas coefficients, code, inputs, and reference artifacts are hash-bound. Changing any of them defines a different computational statement.
The model is an analytic pulse model with fourteen phase coordinates (\theta\in\mathbb R^{14}), exact segment propagators, and a projective jet response produced by exact finite jet recurrences. "Exact preservation" means preservation of this declared finite response only: not higher-order response coefficients, not the full physical output, and not hardware behaviour.
| Proved in the published local theorem | Not proved here |
|---|---|
| v0.7.4 complete-parent-box regularity, nonstationarity, and descent certificate | fifth frame |
| v0.9.3 local intrinsic ODE existence and uniqueness | complete child traversal |
| exact preservation of the declared finite response (\mathcal R_3) | complete ten-chart continuation |
| strict (L_6) descent over one local Picard microstep | arbitrary endpoint connection |
GLOBAL_FLOW_CLAIMED=false |
hardware/QPU validation or global flow |
For v0.7.4, all sixteen 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.
The affine atlas-arclength derivative-label correction is documented in
docs/PAPER_WORDING.md and changes no frozen
certificate or strict-descent claim.
Recommended reading version:
- Manuscript: v1.2.13 disclosure and notation revision
- PDF:
docs/manuscript/geometric_flow_v1_2_13_disclosure_revision.pdf - Source ZIP:
docs/manuscript/geometric_flow_v1_2_13_source.zip - Zenodo record: https://zenodo.org/records/21947745
- Version DOI: 10.5281/zenodo.21947745
- Concept DOI: 10.5281/zenodo.15879392
- GitHub Release:
paper-local-ode-v1.7 - Release provenance:
docs/manuscript/V1_2_13_RELEASE_PROVENANCE.md
v1.2.13 is derived from v1.2.12 and incorporates the recorded v1.2.9 errata and later textual clarifications. It changes no theorem-bearing constants, certificates, protocols, JSON records, atlas data, gate thresholds, or Arb computations.
| Goal | Command |
|---|---|
| Verify stored certificate hashes | python scripts/verify_reference_results.py |
| Verify the published theorem boundary | python reproduce/published_paper.py |
| Recompute the published v0.7.4 + v0.9.3 theorem pair | python reproduce/published_paper.py --run |
| Recompute the v0.9.3 local ODE theorem only | python reproduce/local_theorem.py |
| Reproduce stored finite-continuation evidence | python reproduce/finite_continuation.py |
| Audit the open fifth-frame target | python reproduce/open_next_frame_audit.py |
Finite-continuation and fifth-frame commands are post-publication research entry points. They are not part of the v1.2.13 published theorem boundary.
src/: core geometric code and maintained formal backends.reproduce/: stable 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 stable
reproduce/ entry points and archive raw historical drivers under
archive/milestones/.
These tracks are useful research evidence but do not enlarge the local published theorem:
- Stored finite-continuation evidence: v0.10.6 fourth-chart Lohner support flowpipe.
- Open global-continuation programme: v0.10.13.1 source chain and v0.10.15 fail-closed fifth-frame harness.
- C4 controlled-attraction and C4-E2b research artifacts.
- Wiener-type memory feedback, process-time, two-metric, certificate-DAG, and K=1 bridge investigations.
- Neural-network response-fibre analogues.
The immediate continuation research direction is toward a global response-fibre flow: certified chart overlaps, uniform rank bounds, and uniform nonstationarity bounds across a complete response component remain open.
See docs/ROADMAP.md,
docs/THEORY_ARCHITECTURE.md, and
docs/RESEARCH_STATUS_MATRIX.md for the
full research-status map.
Published paper and claim boundary:
docs/PUBLISHED_PAPER_BOUNDARY.mddocs/CLAIM_SCOPE.mddocs/PAPER_WORDING.mddocs/MANUSCRIPT_PROVENANCE.mddocs/REVIEWER_REPRODUCTION.md
Proof and reproduction:
docs/PROOF_NAVIGATION.mddocs/MATHEMATICS.mddocs/REFERENCE_RESULTS.mddocs/REPRODUCIBILITY.mddocs/PROOF_MAP.md
Post-publication research and archive:
docs/ROADMAP.mddocs/THEORY_ARCHITECTURE.mddocs/RESEARCH_STATUS_MATRIX.mddocs/CONTROL_EXTENSION_SCOPE.mddocs/WIENER_FEEDBACK_SCOPE.mddocs/PROCESS_TIME_SCOPE.mddocs/TWO_METRIC_SCOPE.mddocs/CERTIFICATE_DAG_SCOPE.mddocs/K1_BRIDGE_SCOPE.mddocs/ARTIFACT_INDEX.mddocs/releases/docs/archive/
Suggested citation for the local theorem and published paper boundary: cite
v1.2.13 using DOI 10.5281/zenodo.21947745 and identify the theorem-bearing
software boundary as v0.7.4 + v0.9.3.
Software is released under the MIT license. The v1.2.13 manuscript and manuscript source ZIP are released under Creative Commons Attribution 4.0 International (CC BY 4.0).
- v1.2.12 public archive: DOI
10.5281/zenodo.21895917,paper-local-ode-v1.6 - v1.2.9 public archive: DOI
10.5281/zenodo.21882158, Zenodo record 21882158,paper-local-ode-v1.5 - Earlier public boundary: historical version DOI
10.5281/zenodo.21728432
The historical version DOI 10.5281/zenodo.21728432 identifies an earlier
public manuscript boundary; it is not the preferred v1.2.13 citation. The raw
record URL https://zenodo.org/records/21728432 is not the current paper
record.
展开摘要
本仓库归档并复现 v1.2.13 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 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。
v1.2.13 是从 v1.2.12 派生的 disclosure/notation 修订，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。