Add audited ancilla–depth robustness companion for the global Hopf frame

[GoGoKo699]

Status

This is a research companion and theorem candidate. It does not alter the manuscript-level direct-angle theorem and should not be merged until the mathematical review is complete.

What this branch adds

• an exact conditioned-prefix identity for the addressed real Hopf frame;

• an exact unary-code realization of the prefix frame as parallel disjoint Givens layers;

• a conservative clean-workspace construction using at most m+1 ancillary qubits when the matched state compiler uses m;

• an asymptotic term ledger for the candidate depth bound

  O(n (n - t + 1) + 2**n/(n + m)), with t = min(n, max(0, floor(log2(m/3))));

• reductions to the three upper profiles in Figure 1 of Sun–Tian–Yang–Yuan–Zhang;

• a record-wise Walsh decoder with O(S 2**n) arithmetic and O(2**n) storage;

• deterministic tests for the exact structural bridge, unary-code action and leakage, workspace accounting, and decoder parity.

Evidence boundary

The finite tests establish exact Hopf identities and bookkeeping premises. The asymptotic depth conclusion additionally relies on the published exact synthesis results for uniformly controlled gates, unary-to-binary conversion, and multi-controlled X gates. This PR does not implement their complete elementary compiler or claim routed-device depth.

The result is limited to the global differential-frame method. It does not establish that the inverse of an arbitrary state-preparation circuit is valid, and it does not establish arbitrary-compiler invariance of checkpoint interfaces.

Validation

• local Qibo-free checks for the new modules: 13 tests passed;
• GitHub Actions analytic: passed;
• GitHub Actions exact-logical: passed.

Repository commands:

python validate_qbp.py --analytic
python qbp_ancilla_depth_ledger.py --n 10

The PR remains a draft because passing finite tests does not by itself prove the asymptotic compiler theorem.

[GoGoKo699]

This research seed has been migrated and refactored into a dedicated private repository for the new paper. It will not be merged into Hopf-QBP/main.

The established repository remains the source of truth for Compass in the Mirror and the validated Möttönen-style robustness result. The ancilla-depth-robustness-2026 branch is retained only as an exact provenance checkpoint at commit 9cc564f493caff62b847fc362df522a68c6e83bf.

The new project records this PR and commit in machine-readable provenance. Closing this PR avoids mixing a theorem candidate with the established paper repository.