Certification Resources and the Value of Retained Quantum-Reader Records
What is being certified
What is being certified
This paper develops task-relative validation and retained-record resource comparisons within Shadow Theory’s pre-existing source–readout programme [6]. The results concern the declared reader and validation interfaces. A reader is frozen before validation. Each complete
-copy experiment returns a sign at its deadline, retaining all settings, signs, nulls, root seeds and declared timings. A trusted evaluator knows the source label for scoring; the reader does not. The deployment contract is the nominated maximum label error
, not recovery of a hidden source or characterization of all unread outputs. For the structured comparisons, the informative trajectory alphabet is the root seed, commanded actions and ternary outcomes (+
0). Declared timing fields are determined by these records or have the same source-and model-independent conditional law in all compared worlds. They add no likelihood factor. A source-or visibility-dependent arrival-time observation would enlarge the statistical experiment and requires its own response model; it is not supplied by the declared effects or by a different detector construction. We separate three interfaces: unrestricted terminal Bernoulli risks; richer records with specified trusted ancillary laws; and a shared physical response model whose trial likelihood can be evaluated. Their information minima need not agree. Both sides of each resource comparison receive the same preparation and response promises. Validation stock, policy/controller state, archive access, clocks, phase references and arithmetic are separate resources. Unless a finite-cap theorem explicitly says otherwise, a finite expected stopping cost does not imply a finite worst-case duration. The concrete reader is the 697-node frozen rational fourteen-copy DAG in the supplement, with action/three-child pointers and terminal signs. Its two fresh uniform root bits implement sign reversal and axis exchange. The source is fixed within an experiment among
2; the target is its common sign. Copies are independent conditional on that label, not
an independently redrawn axis mixture. The physical effects are
cos
sin![θY ])/2,](/publications/source-readout/constructive/certification-and-retained-records/math/p002-00011.svg)
. General sections below do not assume that family; the structured comparison explicitly assumes known
8 and fixed unknown shared
Conventions, conditioning and information access
Readable validation records in this paper are classical records of a quantum reader; access to unread residual quantum systems is not supplied. Unless specialized below, 0
1, the experiment horizon
and label count
are positive integers, and a planning risk satisfies 0
A power parameter obeys 0
. We use natural logarithms and
log(
) log[(1![−p)/(1 −q)],](/publications/source-readout/constructive/certification-and-retained-records/math/p002-00022.svg)
) = sup 
with the usual limiting convention for zero event masses. For discrete laws, TV
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2 ∑︁ z |P(z) − Q(z)|. One validation observation is a complete B-copy experiment; source-copy cost is B times the number of such observations. The proof filtration contains completed experiment records and their mathematically defined scoring truths. During trusted validation the evaluator can use the known preparation label; the reader remains adapted only to its permitted record subfiltration. Conditional source, response and tube promises are imposed on this augmented past, including admitted timing metadata. They do not follow merely by enlarging a smaller observed-history filtration. In the structured four-state comparisons, each new experiment draws an independent uniform root seed conditional on the completed past and its chosen label. The unrestricted-record and general trusted-seed models state their own ancillary-law promises instead. Structured block drift averages over its fresh seed; local likelihood validity is pointwise once the seed and command are known. No future validation-success event is conditioned on as initial information.
Organization. Section 2 gives terminal-risk gates, and Section 3 their restricted information floor. Section 4 separates unrestricted records from trusted-seed access. Section 5 proves the structured trajectory advantage and finite cap; Section 6 supplies a separate conditional response-tube guarantee. The appendix compares validation resources for two specified deployed readers.
A complete frozen-policy interface
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The finite DAG is a mathematical input, not a controller that can inspect the hidden label. At a node
i with t trials left, its action is one rational unit direction ai = (ci, si) and its three outcome edges lead
to nodes ji,o with t −1 trials left. At t = 0, the node stores a sign di. With R(h) the nominated sign,
define
r0,i,h(v) = 1{di ̸= R(h)},
rt,i,h(v) =
∑︂
o∈{+,−,0}
Kv(o | h, ai)rt−1,ji,o,h(v).Here
and (
). The recursion is a conditional calculation, not label access by the controller. It evaluates the exact conditional error including every null. The root’s independent sign/axis symmetries give
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4 ∑︁ h r14,root,h(v) for each physical label under the shared-response model. All actions and edges are supplied in supplement/readers/research12/rich/policy_14.json; the byte-identical reader input also appears in research11/nominal/ within that supplement. The input manifest fixes its identity. Consequently the risk and likelihood proofs below need neither an optimality assertion about that policy nor a theorem promised by another manuscript.
Safe likelihood testing, reverse information projection and sequential change-of-measure have established antecedents[2–4, 7]. Our contribution is their precise operational integration, matched comparison and exact certificates within the declared source–readout programme. No worldwide priority, empirical validation or Born-selection claim is made.