Manuscript Psy04-A@1 · Psy04-A-v1.tex · section · d5800e2a

Claim-status and debugging ledger

Claim-status and debugging ledger · lines 2187–2268

scope of the principal conclusions.
Claim	Status	Certificate or boundary
Claim	Status	Certificate or boundary
Every stochastic two-state classical memory has score at most $3/4$	Proved benchmark	Complete factorization, fresh uniform bits, independent late query.
Sequential arrival strengthens that bound	Not asserted	The batch class already supplies the valid upper bound.
One qubit attains the standard RAC value	Proved benchmark	Printed states, gates, and complete projective instruments.
Any nonzero coherence beats the classical task	False generally	Task score must exceed the threshold, not only have a nonzero contrast.
Neutral output erasures invalidate the bound	False within the factorized class	They can be replaced by fair guesses without changing the mean.
The independent-loss formula covers arbitrary losses	Excluded	Input- and outcome-dependence need a separate complete law.
Observed rejection requires subtracting $e_{Q}$ twice	False	$e_{Q}$ supplies a design/power allowance, not a second data penalty.
A fixed-sample radius permits arbitrary stopping	False	Use the printed anytime allocation or another proved sequential test.
A numerical best strategy is an upper bound	False	It is feasible and therefore a lower bound on the maximum.
A RAC violation certifies quantum environmental memory	False	A Markovian qubit already wins.
A causal-break witness certifies nonclassical memory	False generally	A classical hidden register can generate the same kind of history dependence.
The present witness excludes every classical simulation	Not asserted	Only the capacity- and access-restricted class is excluded.
Biological or clinical memory identification	Not established	No participating-state, control, or observation correspondence.
Asymptotic computational advantage	Not established	No scalable task and full resource comparison supplied.
Spacetime emergence or inherited analytic admission	Outside scope	No characteristic-map, representation, or admission gate constructed.

• Pauli notation. The input $X$ is a classical bit string. The operators are written $σ_{x}, σ_{y}, σ_{z}$ , avoiding a type collision.

• Sequential rotation sign. The convention $R_{y} (θ) = e^{- i θ σ_{y} /2}$ sends $∣ 0 ⟩$ to $cos (θ /2) ∣ 0 ⟩ + sin (θ /2) ∣ 1 ⟩$ . The later $σ_{x}$ flips the $Z$ component but not the $X$ component.

• Depolarizing linearity. The replacement term is $Tr (A) I /2$ . Writing $I /2$ without the trace is only a state-level formula, not the channel on arbitrary operators.

• Zero delay. The empty storage product is one. No ambiguity at $η = 0, T = 0$ is used.

Claim-status and debugging ledger

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