Alphabeta Math
Open problemQuestion: AI-adaptedProof: Not applicable
How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
  • AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
  • AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Continuously monitored and dissipatively stabilized encodings

PDF p. 5: Discussion, final paragraph

Open problem

How can the article's checking-time and distinguishability analysis be extended to an encoding under continuous monitoring or engineered dissipative stabilization, including regimes in which measurement and engineered dissipation act on comparable timescales?

Here the checking time for a specified recovered logical channel is the infimum of times at which its entanglement fidelity falls strictly below a chosen target, with infinity if there is no such time. Distinguishability concerns information about error paths available in environmental or monitoring records. A continuous-monitoring model specifies a time-indexed measurement record, conditional evolution, measurement coupling and strength, detection efficiency, and any feedback rule. Engineered dissipative stabilization specifies additional generator terms intended to influence the evolution without requiring a measurement record; a model may combine the two.

A concrete answer requires specifying the encoding, noise and recovery or feedback, the relevant record and performance measure, and the measurement and dissipation rates. If a pulsed checking protocol is compared with a continuous model, the family of protocols, comparison topology and limiting statement must also be specified. The question does not assume that such a limit exists or that finite-strength monitoring has the performance of ideal rapid checks.

Status

The article presents this extension as future work. The supplied article does not solve the question in this formulation; no subsequent literature search or claim that every instance remains unsolved is made here.

Depends on

Dependency tree · 2 levels

Each result is drawn at its shortest distance from this item. Arrows run from prerequisites to the items that use them; this item has a heavier outline. External source nodes link directly to the cited text. The view shows up to two dependency steps; open a prerequisite to continue.

Sources