[polyopt] Killer Queen: certify truncated-boson bulk-gap bounds

[justin2099]

Team

Team name	Killer Queen
Members	唐鼎文 (Tang Dingwen); 聂芃 (Nie Peng)

Challenge

Row
Challenge	Extend the thermodynamic state-polynomial hierarchy to occupation-truncated bosons and calculate bulk-gap upper statements and local Mott diagnostics on three infinite hyperbolic graphs.
Catalog issue	Addresses #92 — Certified bulk spectral-gap bounds for truncated Bose-Hubbard models on hyperbolic lattices.
Track	tracks/polyopt/ — semidefinite programming and noncommutative polynomial optimization.

Results

Target 1 is reproduced. At t=0, U=1, and mu=0.5, the analytic product state, radius-one ED on all three graphs and cutoffs nmax=1,2,3, the atomic SDP, and the complete Julia hierarchy recover the atomic gap Delta/U=0.5 and local values rho0=1, F0=K0=0 within their stated numerical or certified precision. The ED conclusion is graph independence because the sites decouple at t=0.

For Target 2, radius-one finite-patch ED is complete at nmax=1,2,3. At nmax=3, increasing t lowers the finite-patch gap and increases fluctuations on every graph; the line graph is the most delocalized of the three patches. These ED results are diagnostics and are not thermodynamic bounds.

The certified thermodynamic snapshot currently contains:

• 10 exact-projected hard-core finite-level gap upper statements at complete matrix level (L,d)=(1,2);
• 51 independently verified EXCLUDED trial rows, including checked search spans [0.165,0.170] for line-graph P4 and [0.750,0.800] for {12,4} P5;
• 26 accepted one-sided observable endpoints and 2 accepted two-sided intervals;
• explicit UNKNOWN classifications for numerical, certificate, and resource failures.

The Target 2 campaign remains partial. Complete hard-core (1,3) and (2,2) solves exhausted 192 GiB, and complete cutoff-two (1,2) factorization exhausted 192–237 GiB. The requested cutoff-two TS2 grid, ladder and unrestricted comparisons, and optional cutoff three are incomplete.

FEASIBLE means only non-exclusion at the tested finite level. A value is called EXCLUDED only after exact identity projection, rigorous PSD checks, 256-bit algebraic coefficient evaluation, and a positive normalized Farkas margin.

The short academic report is available as submission/report.html and submission/FINAL_REPORT.md. It includes two compact figures: the Target 2 finite-ED trends and the certified hierarchy search spans.

Verification

• Julia hierarchy and certificate suite: 577 assertions passed.
• Python graph and reporting suite: 21 tests passed.
• Deliberately corrupted certificates are rejected.
• The academic report rebuild completes and git diff --check passes.

Raw primal and dual payloads remain excluded from Git. The committed data manifest records the aggregate source hashes and the role of each raw campaign directory.

[justin2099]

Final report

The final professor-facing report for this challenge is:

• Final HTML report — canonical presentation with the two result figures.
• Markdown report — GitHub-readable version of the same report.
• Reproduction guide — pinned environment, Target 1/ED commands, exact Target 2 manifests, SCNet array map, expected outputs, and certificate acceptance rules.

The final PR snapshot is commit 2eb6322. It reports Target 1 as completed and Target 2 as a partial certified hard-core thermodynamic baseline, with finite-patch ED kept explicitly separate from thermodynamic bounds. The documented clean-worktree checks pass: 21 Python tests, 577 Julia assertions, and the independent exact-projected atomic certificate replay.