Mechanism family
Finite matrices, norms and registers
Are dimensions, basis order, scalar field and selected subspace fixed?
A structure accepting a proposition is an interface, not an unconditional construction theorem.
Structure before circuit tricks
Mathematical methods
Search by problem structure, then inspect the hypotheses, mathematical mechanism, exact Lean substrates and unresolved boundaries. One declaration has one identity across every view.
Overview = curated organization. Lean graph = generated imports and declaration ownership. Hypergraph = conditional conceptual transport. None of these is an automatic novelty or theorem-implication oracle.
Matrix analysis
What is preserved by a map? Norm, rank, adjoint and singular values.
Mechanism family
Local Gram normalization
Can normalization be computed without summing exponentially many amplitudes?
An exact-real operation count is not a bit-complexity bound or a floating-point stability theorem.
Mechanism family
Canonicalization, completion and local compilation
Can a bounded-rank description be turned into an actual primitive list?
The current symbolic resource theorem does not include a full stable finite-precision T-gate compiler.
Mechanism family
Charged access and finite-precision compilation
Does a query or symbolic gate hide the dominant work?
The local norm theorem is only a substrate. It is not the entire displayed end-to-end cost decomposition certified in Lean.
Approximation theory
Which basis or partition exposes finite-dimensional structure?
Mechanism family
Hermite matching and Bernstein subdivision
Does a known function admit an exact low-degree local update?
This is exact representation of the chosen polynomial, not automatic spectral convergence of a PDE solver. The general function-to-MPS idea predates ASPBE.
Mechanism family
Bounded-memory function representations
Can each bit update a small state instead of selecting a table entry?
Smoothness or a symbolic formula alone does not guarantee low TT rank or a cheap core supplier in arbitrary dimension.
Harmonic analysis
Can a derivative or convolution become a diagonal multiplier?
Mechanism family
Fourier multipliers and Schrödingerisation
Can a nonunitary evolution be represented as transport in an auxiliary coordinate?
This is a candidate mathematical route, not an end-to-end PDE theorem inferred from Hermite state preparation.
Tensor networks
How much information must pass across each bit cut?
Mechanism family
Bounded-memory function representations
Can each bit update a small state instead of selecting a table entry?
Smoothness or a symbolic formula alone does not guarantee low TT rank or a cheap core supplier in arbitrary dimension.
Mechanism family
Local Gram normalization
Can normalization be computed without summing exponentially many amplitudes?
An exact-real operation count is not a bit-complexity bound or a floating-point stability theorem.
Mechanism family
Canonicalization, completion and local compilation
Can a bounded-rank description be turned into an actual primitive list?
The current symbolic resource theorem does not include a full stable finite-precision T-gate compiler.
Mechanism family
Structure-aware preparation and verification
Can the preparation structure supply a cheap experimental witness?
The candidate hardware paper is not primary-verified here; no reported numerical performance is used as a proved bound.
Probability and sampling
What normalizer, overlap, envelope or mixing certificate is available?
Mechanism family
Envelopes and coherent rejection
Is a reference state closer to the target than the uniform state in a controllable sense?
Changing from probability sampling to amplitudes requires square roots and phase handling. An envelope with small kappa is not automatically easy to prepare.
Mechanism family
Gibbs invariance versus mixing
Does the generator only preserve the target, or converge to it with a useful rate?
This is a conceptual connection to Samplinglib, not a transfer of classical LSI results to arbitrary quantum generators.
Oracle and circuit complexity
Which input model, gate set, precision and resource are actually charged?
Mechanism family
Charged access and finite-precision compilation
Does a query or symbolic gate hide the dominant work?
The local norm theorem is only a substrate. It is not the entire displayed end-to-end cost decomposition certified in Lean.
Operator and semigroup theory
What are the domains, invariant state and convergence assumptions?
Mechanism family
Block extraction and spectral filtering
What norm, overlap and polynomial approximation determine success?
Block encoding does not make normalized state preparation deterministic or uniformly cheap.
Mechanism family
Fourier multipliers and Schrödingerisation
Can a nonunitary evolution be represented as transport in an auxiliary coordinate?
This is a candidate mathematical route, not an end-to-end PDE theorem inferred from Hermite state preparation.
Mechanism family
Gibbs invariance versus mixing
Does the generator only preserve the target, or converge to it with a useful rate?
This is a conceptual connection to Samplinglib, not a transfer of classical LSI results to arbitrary quantum generators.
State Preparation
Prepare a normalized state, coherently and with declared garbage/success sectors.
Mechanism family
Canonicalization, completion and local compilation
Can a bounded-rank description be turned into an actual primitive list?
The current symbolic resource theorem does not include a full stable finite-precision T-gate compiler.
Mechanism family
State-action and coherent preparation contracts
Is the requested object one state, a coherent family, or a mixed state?
Correctness up to a parameter-dependent global phase is not sufficient for a coherent family.
Mechanism family
PREPARE–SELECT–unprepare
Are coefficient preparation and controlled operator access both available?
SP can be a BE ingredient, but one isolated state does not determine a general matrix. This explanatory bridge has no newly certified transport root.
Mechanism family
Block extraction and spectral filtering
What norm, overlap and polynomial approximation determine success?
Block encoding does not make normalized state preparation deterministic or uniformly cheap.
Mechanism family
Envelopes and coherent rejection
Is a reference state closer to the target than the uniform state in a controllable sense?
Changing from probability sampling to amplitudes requires square roots and phase handling. An envelope with small kappa is not automatically easy to prepare.
Mechanism family
Structure-aware preparation and verification
Can the preparation structure supply a cheap experimental witness?
The candidate hardware paper is not primary-verified here; no reported numerical performance is used as a proved bound.
Block Encoding
Realize a scaled operator as a specified clean projected block.
Mechanism family
PREPARE–SELECT–unprepare
Are coefficient preparation and controlled operator access both available?
SP can be a BE ingredient, but one isolated state does not determine a general matrix. This explanatory bridge has no newly certified transport root.
Mechanism family
Block extraction and spectral filtering
What norm, overlap and polynomial approximation determine success?
Block encoding does not make normalized state preparation deterministic or uniformly cheap.
Verification and metrology
Separate formal circuit correctness from experimental state certification.
Mechanism family
Structure-aware preparation and verification
Can the preparation structure supply a cheap experimental witness?
The candidate hardware paper is not primary-verified here; no reported numerical performance is used as a proved bound.
Agent retrieval without graph dumps
The same authored records produce a bounded packet. It contains assumptions and failure boundaries, not only similar keywords.
python3 website/scripts/research_atlas.py context --query "localized function envelope"
python3 website/scripts/research_atlas.py context --route spw-envelope