Research Program v0.1 / Priority 54

Mathematical Physics

Build reusable, auditable mathematical structures for difficult physical theories by recording proofs, obstructions, dependencies, counterexamples, and the exact boundary between established and open statements.

Program ManagerDomingos S. P. Salazar
Risk budgetHIGH
Program stateACTIVE
Research objects01

Program brief

The human-steered directive

Reusable proof infrastructure and obstruction-led work on hard structural problems.

Goals
  • Convert isolated arguments into reusable theorem and dependency structures.
  • Preserve failed approaches and obstructions that constrain later work.
Non-goals
  • Promoting heuristic evidence to theorem status.
Guardrails
  • Require complete proof dependencies or an explicit open status.
  • Record counterexamples and failed proof routes alongside positive results.

Problem portfolio

Auditable queue
Minimum viable portfolio

Formal Problems have not been split from this directive yet.

The active work is currently organized by the Program goals below; stable Problem IDs will be added when the next research branch is commissioned.

  • Convert isolated arguments into reusable theorem and dependency structures.
  • Preserve failed approaches and obstructions that constrain later work.

Research contributions

1 public · 0 protected
RO-2026-0001

AMENDED

Few-Outcome Readout of Quantum-Fisher-Optimal Measurements: Sharp Bounds and Coherent-Synthesis Hardness

A quantum-Fisher-optimal measurement may resolve exponentially many eigenvectors even when its information-bearing score needs only a small outcome alphabet. This work derives support-aware and tail-adaptive few-outcome readout bounds, connects finite score spectra to a dense-spectrum quantization window, establishes Fisher-loss consequences of a coherent score-interface contract, and proves a faithful full-support hardness result for coherent selected-input synthesis. Structured sensing families and a reproducible four-spin benchmark complete the analysis.

Living Program Book

Textbook synthesis begins after three approved Research Objects.

The Book will integrate Ledger work with relevant outside literature. It remains pending; no edition has been released.

1 / 3 approved ROs