[qmc] 格格巫: three interacting sign-free DQMC constructions

[Joe-Nor]

Team

Team name	格格巫
Members	Bei Qiao (乔北), Zongyue Liu (刘宗岳), Kexiang Mao (毛柯翔)

Challenge

Row
Challenge	Construct physically interacting fermion models whose determinantal-QMC weights are provably nonnegative at arbitrary auxiliary-field depth, and delimit failed extensions with exact certificates.
Catalog issue	Addresses #121 — Sign-problem-free hunter, released by Lei Wang.
Track	qmc, following the challenge issue.

Final submission

This PR is the dedicated Challenge 121 registration for team 格格巫. Its
solution folder contains the immutable links and clean-checkout command; the
complete source and evidence are kept in a separate public repository so that
Challenge 121 is not mixed with Challenge 15.

Earlier Challenge 121 PRs #259 and #261 are retained only as immutable
technical provenance for the joint report, not as separate final team claims.

• English final report
• Reproduction guide
• Machine-readable manifest
• Dedicated repository

The main report covers three interacting sign-problem-free DQMC model
constructions—2D TN tensor, exterior representation, and conjugate tensor—and
their Hamiltonian-to-HS-to-determinant proofs. It also reports small-system
DQMC/exact-Trotter/ED checks of particle number and energy at multiple chemical
potentials, the exact local PGL(2,7) HS result and its hopping no-go boundary,
and an explicitly scoped archive of other positive and negative results.

Validation

• Final manifest and stored-evidence gate: passed.
• Focused regression: 103 tests and 21 subtests passed.
• Complete local regression: 301 tests and 45 subtests passed.
• Stored sign audits: 778,011 determinant/local-ratio evaluations and 8,000
  independent-field draws, with zero negative and zero zero weights.
• PGL exact closure: 336 states, 50 fields, 16,800 transitions.
• Static HTML: strict KaTeX rendering and local-link validation passed.

Finite numerical tests validate implementation correctness; arbitrary-depth
sign freedom follows from the analytic proofs. Novelty and reduction boundaries
are stated separately for every promoted result.

[Joe-Nor]

CI scope note: the initial Ubuntu failure was inherited from upstream main at a0562a5. The dedicated infrastructure fix in #264 passes Ubuntu and Windows, but this account cannot merge it upstream. At the team’s request, #273 now temporarily mirrors that exact two-file fix so the required checks execute successfully rather than being skipped. The scientific submission remains isolated in tracks/qmc/solutions/GeGeWu-121/README.md; the mirrored files contain no Challenge 121 scientific content. Independent submission CI: https://github.com/Joe-Nor/gegewu-challenge-121-sign-free-hunter/actions/runs/30537377076.