Tensorscope

These changes do not necessarily capture the semantic context required to justify a transformation.</p><p dir="ltr">TensorScope investigates <b>Semantic Transformation Locality</b>:</p><blockquote><p dir="ltr">To what extent can the correctness of a quantum compiler transformation be established locally, and what structural, causal, and tensor-network factors govern this semantic proof footprint?</p></blockquote><p dir="ltr">The study measures residuals relative to an explicit normalization and bounded rewrite policy.</p><h2 dir="ltr">2.

Locality Dimensions</h2><p dir="ltr">TensorScope reports four complementary views:</p><ol><li><b>L1 — Structural Edit Locality:</b> Gate edit ratio $L_G$ and affected qubit ratio $L_Q$.</li><li><b>L2 — Causal Locality:</b> Causal cone expansion metrics $L<i>{CG}$ and $L</i>{CQ}$ derived from DAG wire dependencies.</li><li><b>L3 — Sound-Rewrite Residual:</b> Normalized residual ratio $L_{RT}$ and residual components after normalization and locally certified rewrites, including bounded semantic-window reduction.</li><li><b>L4 — Tensor Complexity:</b> Tensor-network size and contraction-path complexity of the residual, evaluated using a bounded, seeded planner.

These are representation- and budget-dependent measurements.</li></ol><h2 dir="ltr">3. Archived Study Results</h2><p dir="ltr">The empirical study covers <b>1,962 pass-boundary transformation pairs from 45 source circuits</b>, including 1,860 Qiskit pairs and 102 PyTKET pairs.</p><table><tr><th><p dir="ltr">Measurement</p></th><th><p dir="ltr">Archived result</p></th></tr><tr><td><p dir="ltr">Empty residuals</p></td><td><p>811 / 1,962 (41.3%)</p></td></tr><tr><td><p dir="ltr">Residual ratio below 1</p></td><td><p>1,745 / 1,962 (88.9%)</p></td></tr><tr><td><p dir="ltr">Independent method-validation cases</p></td><td><p dir="ltr">60, from 16 source circuits</p></td></tr><tr><td><p dir="ltr">Independent dense-operator checks passed</p></td><td><p>60 / 60</p></td></tr><tr><td><p dir="ltr">Heuristic-B matches to the bounded exact reference</p></td><td><p>60 / 60</p></td></tr></table><p dir="ltr">The method-validation counts apply to the independent bounded validation set; they do not establish global minimality for all transformations.</p><p dir="ltr">The primary result file is tensorscope_empirical_results.json.

Its accompanying manifest.jsonrecords hashes of the analysis and generated files. The result file also records hashes of its inputs. Group profiles, case studies, and figures are included in the same directory.</p><h3 dir="ltr">Proof-Rule Sensitivity</h3><p dir="ltr">The sensitivity experiment compares three explicitly defined proof systems on the same population of 1,962 transformations:</p><table><tr><th><p dir="ltr">Proof system</p></th><th><p dir="ltr">Definition</p></th><th><p dir="ltr">Mean $L_{RT}$</p></th><th><p dir="ltr">Median $L_{RT}$</p></th><th><p dir="ltr">Empty residuals</p></th></tr><tr><td><p dir="ltr">B0</p></td><td><p dir="ltr">Canonicalization and normalization with base local identity/inverse cancellation; no bounded window reducer</p></td><td><p>0.541</p></td><td><p>0.735</p></td><td><p>697 (35.5%)</p></td></tr><tr><td><p dir="ltr">B1</p></td><td><p dir="ltr">Full bounded semantic-window reducer with seam rescanning bound 11</p></td><td><p>0.473</p></td><td><p>0.582</p></td><td><p>811 (41.3%)</p></td></tr><tr><td><p dir="ltr">B2</p></td><td><p dir="ltr">B1 plus certified same-axis single-qubit rotation fusion and cancellation</p></td><td><p>0.472</p></td><td><p>0.577</p></td><td><p>811 (41.3%)</p></td></tr></table><p dir="ltr">The archived configuration uses tolerance $10^{-10}$, seed <code>20260909</code>, and 2,000 bootstrap repetitions.

Results, category summaries, configuration, and provenance are stored in results/proof_rule_sensitivity</p><h2 dir="ltr">4. Using This Package</h2><h3 dir="ltr">Inspect the Archived Results</h3><p dir="ltr">The JSON summaries can be inspected without running quantum experiments. From the package root:</p><pre><pre>python -m json.tool results/processed/tensorscope_empirical_study/tensorscope_empirical_results.json<br>python -m json.tool results/proof_rule_sensitivity/aggregated_statistics.json<br>python -m json.tool results/proof_rule_sensitivity/configuration.json<br></pre></pre><h3 dir="ltr">Analysis and Reproduction Scripts</h3><table><tr><th><p dir="ltr">Script</p></th><th><p dir="ltr">Purpose</p></th></tr><tr><td><code>scripts/analyze_tensorscope_empirical_study.py</code></td><td><p dir="ltr">Generate empirical analysis from the archived study inputs</p></td></tr><tr><td><code>scripts/analyze_recovered_rqs.py</code></td><td><p dir="ltr">Join and analyze the source, residual, and tensor-planner archives</p></td></tr><tr><td><code>scripts/build_l3_seam_archive.py</code></td><td><p dir="ltr">Reconstruct the bounded-seam residual archive from source circuit pairs</p></td></tr><tr><td><code>scripts/run_l4_fixed_planner_archive.py</code></td><td><p dir="ltr">Compute bounded tensor contraction-path metrics</p></td></tr><tr><td><code>scripts/run_proof_rule_sensitivity.py</code></td><td><p dir="ltr">Compute the B0/B1/B2 comparison and associated outputs</p></td></tr><tr><td><code>scripts/generate_tensorscope_paper_assets.py</code></td><td><p dir="ltr">Generate manuscript tables and copy study figures</p></td></tr><tr><td><code>scripts/verify_tensorscope_manuscript.py</code></td><td><p dir="ltr">Check archived study inputs and generated manuscript assets</p></td></tr></table><p dir="ltr">These scripts have different input and environment requirements.

Analysis or generation scripts may write outputs; their presence does not imply that every stage can run from this distribution alone.</p><h3 dir="ltr">Environment and Full Reproduction</h3><p dir="ltr">The archived sensitivity run records Python <b>3.12.10</b> on Windows. The current distribution does not include the environment specification or project installation metadata. It also omits the original <code>data/</code> circuit inputs, <code>benchmarks/</code>, and <code>paper/</code> assets referenced by parts of the workflow.</p><p dir="ltr">Full recollection, reconstruction from original circuit pairs, and manuscript verification therefore require the corresponding inputs, assets, and dependency specifications from the complete project.</p><p dir="ltr">Once the required dependencies and test inputs are available, the test-suite entry point is:</p><pre><pre>python -m pytest tests/ -v<br></pre></pre><h2 dir="ltr">5.

Data and Provenance</h2><p dir="ltr">The empirical analysis binds the following supporting artifacts by hash:</p><ul><li><code>results/processed/better_result/pairs.json</code></li><li><code>results/processed/l3_bounded_seam_archive/l3_bounded_seam_pairs.json</code></li><li><code>results/processed/l4_fixed8_heuristic_b_archive/l4_archive_rows.json</code></li><li><code>results/processed/l3_two_tier_independent_validation/summary.json</code></li></ul><p dir="ltr">Version labels in these paths identify the input artifacts used by the documented study.

Preserve the paths and their contents when checking provenance. The L3 archive also contains method-specific residual circuits and certificates used in the analysis and sensitivity experiment.</p><h2 dir="ltr">6. Package Structure</h2><p dir="ltr">tensorscope_replication/</p><p dir="ltr">|-- README.md</p><p dir="ltr">|-- src/</p><p dir="ltr">| `-- tensorscope/</p><p dir="ltr">| |-- alignment/</p><p dir="ltr">| |-- canonicalization/</p><p dir="ltr">| |-- causal/</p><p dir="ltr">| |-- differencing/</p><p dir="ltr">| |-- instrumentation/</p><p dir="ltr">| |-- locality/</p><p dir="ltr">| |-- metrics/</p><p dir="ltr">| |-- residual/</p><p dir="ltr">| |-- tensor/</p><p dir="ltr">| |-- utils/</p><p dir="ltr">| `-- verification/</p><p dir="ltr">|-- scripts/</p><p dir="ltr">|-- tests/</p><p dir="ltr">`-- results/</p><p dir="ltr">|-- processed/</p><p dir="ltr">| |-- l3_bounded_seam_archive/</p><p dir="ltr">| |-- l3_two_tier_independent_validation/</p><p dir="ltr">| |-- l4_fixed8_heuristic_b_archive/</p><p dir="ltr">| |-- recovered_original_rqs/</p><p dir="ltr">| |-- tensorscope_empirical_study/</p><p dir="ltr">| `-- better_result/</p><p dir="ltr">`-- proof_rule_sensitivity/</p>