ReplayLens: Auditing Agents' Use of Outcomes

Dong Xu; Zhangfan Yang; Jiantao Wu; Shipeng Zhang; Zexuan Zhu; Jiangqiang Li; Jun Zhang; Junkai Ji

cs.AISep 28, 2026

ReplayLens: Auditing Agents' Use of Outcomes

Authors: Dong Xu, Zhangfan Yang, Jiantao Wu, Shipeng Zhang, Zexuan Zhu, Jiangqiang Li, Jun Zhang, Junkai Ji

Organizations: School of Artificial Intelligence, Shenzhen University · EasternDawn · School of Computer Science, University of Nottingham Ningbo

Abstract

When an agent reuses logged experience, a changed decision may reflect the recorded score, the action's name, or the record's position in storage. Standard memory evaluations do not reveal which relationship drives that change. We introduce ReplayLens, a black-box audit that changes one relationship in the stored history at a time, holds the remaining interface fixed, and measures the resulting decision. Four interventions target four relationships. Outcome reassignment swaps which scores belong to which actions. Pair transport moves intact action-score pairs to new record slots. Consistent renaming relabels actions in both history and menu. Key-slot reassignment changes both score attachment and position. A constructive separation shows why the audit is needed: two memory writers with identical endpoint accuracy respond differently to the same replay, so conventional evaluation cannot resolve the underlying dependence. On black-box LLM interfaces, swapping scores changes decisions while moving intact pairs does not, separating score attachment from record order. A bounded-memory study exposes ingestion-order sensitivity that endpoint comparison misses. In sequential experiment planning, altered historical scores redirect exploration and reduce final utility despite fresh measurements. A code-debugging agent with sealed hidden tests shows the same pattern outside model selection. ReplayLens provides a relationship-level audit for deciding whether logged experience can be merged, reordered, or reindexed safely.

Figures & tables

Fit	Additive	Recurrent
1	0.000	0.738
2	0.000	0.538
3	0.000	0.654
4	0.000	0.683
5	0.000	0.796

Table 1: Matched endpoints, different replay responses. Each independently fitted pair has identical aligned and empty-state actions. Entries are holdout action-disagreement proportions after moving intact key–outcome pairs, preserving the per-key sums defining the training target. Writers are frozen before replay. Each estimate averages five permutations over 48 holdout histories, and each action is scored on 48 fixed evaluator rows. Per-fit intervals are in Table 15 .

Figure 1: Overview of the ReplayLens audit. The audit starts from a logged action–outcome history and applies interventions with different preservation conditions. It then rebuilds memory under a fixed writer and initial state and queries the same future interface. Action disagreement and utility differences provide complementary readouts of the resulting dependence.

Figure 2: A worked outcome-assignment audit. The left panel shows the original action–outcome log and shared future menu. Each replay panel changes one relationship. Outcome reassignment changes which value belongs to a key. Pair transport moves an intact pair. Consistent renaming changes history and menu labels together. Key-slot reassignment changes both attachment and placement. Every condition uses the same writer, initial state, future query, and evaluator. Figure 1 gives the complete replay boundary.

Family	$n_{\rm op}$	$A_{\rm rekey}$	$D_{A}^{\rm value}$	$D_{A}^{\rm pair}$	Profiles
Replay-invariant	3	0.000	0.000	0.000	1
Key-only	3	0.664	0.000	0.000	1
Commutative-pairing	3	0.666	0.163	0.000	1
Order-sensitive	3	0.667	0.000	0.090	2

Table 2: Canonical calibration of four writer families.

n_{\rm op}

counts parameterizations, and Profiles counts distinct response profiles over 48 streams. All parameterizations are classified correctly. Responses average parameterizations, maps, and tasks. Positive scaling or recency settings can produce duplicate profiles (Appendix E ).

Table 5

Table 6

History / ref.	First	Final	$U$
Aligned	—	—	0.618
Value reassigned	0.708	0.875	0.359
Pair transport	0.031	0.000	0.617
Consistent renaming	-0.042	-0.021	0.619
Random search (aligned)	—	—	0.610
Random search (value)	—	—	0.443

Table 7: First and Final give

T_{\rm gr}

for the first experiment and submitted pipeline, relative to aligned. Each of 48 tasks has two trajectories per condition and three experiment calls per trajectory.

U

is final-test utility. The random-search reference rows report

U

only, as First and Final are not applicable. The dash marks an unavailable comparison. Intervals and intermediate choices appear in Appendix R .

Condition	First	Final	Hidden $U$	$\Delta U$
Aligned	—	—	1.000	0.000
Value reassigned	0.604	0.167	0.875	-0.125
Pair transport	0.042	0.000	1.000	0.000
Consistent renaming	0.083	0.000	1.000	0.000

Table 8: Code-debugging replay responses on 24 tasks. First and Final are action-disagreement proportions relative to aligned. Hidden

U

is held-out test utility and

\Delta U

is its paired difference from aligned.

Readout	$A_{\rm rekey}$	$D_{A}^{\rm value}$	$D_{A}^{\rm pair}$
GPT-5.6 Luna	$0.865$	$0.115$	$0.016$
GPT-5.6 Sol	$0.996$	$0.325$	$0.010$
GPT-5.6 Terra	$0.984$	$0.247$	$0.017$
Qwen3-8B	$0.946$	$0.246$	$0.154$

Table 9: Cross-model typed replay responses by protocol. Each row is a separate evidence tier and readout protocol; only within-row contrasts share an estimand, so rows are not pooled or ranked. GPT-5.6 rows use readable arm keys and 48 replicate streams; the Qwen3-8B row uses the frozen action-key namespace on the same stream count. Value exceeds pair in every row, and Qwen3-8B has the largest pair response on its protocol.

Appendix figures & tables91 assets

Supplementary material from the paper’s appendix.

Appendix

	Aligned	Value	Pair	Key–slot
Key $\ell_{t}^{q}$	$k_{t}^{\rho}$	$k_{t}^{\rho}$	$k_{\sigma_{\mathrm{p}}(t)}^{\rho}$	$k_{\sigma_{\mathrm{t}}(t)}^{\rho}$
Utility $u_{t}^{q}$	$y_{t}$	$y_{\sigma_{\mathrm{v}}(t)}$	$y_{\sigma_{\mathrm{p}}(t)}$	$y_{t}$

Appendix

Table 10: Complete key–utility map for the replay cells. At slot

t

, the blockwise permutations stay fixed across label maps within a comparison, and public task inputs remain at their original slots.

Quantity	Relation writer	Support lookup
Aligned action mismatch (proportion)	0.000	0.000
Maximum aligned utility gap	0.000	0.000
Maximum aligned oracle gap (proportion)	0.000	0.000
Mean replay action response (proportion)	0.666	0.000
Mean replay utility change	$-0.164$	0.000

Appendix

Table 11: Endpoint-matched finite-support witness. The aligned checks compare the two writers on 13,824 future decisions. Replay responses average over 432 paired replicate–map summaries, with the mapped-minus-identity utility change shown for the same future support. Action and oracle quantities are proportions; utility quantities are normalized units. The relation writer changes all 432 map–stream pairs, whereas the support lookup changes none. The support lookup is frozen before replay and has no adaptation state.

Block	Maps	Future	$\boldsymbol{A_{R}}$	$\boldsymbol{A_{L}}$	$\boldsymbol{\Delta U_{R}}$	$\boldsymbol{\Delta U_{L}}$	$\boldsymbol{\Delta O_{R}}$	$\boldsymbol{\Delta O_{L}}$	$\boldsymbol{B_{\mathrm{dec}}}$
Calibration	4	27,648	0.667	0.000	$-0.180$	0.000	$-0.297$	0.000	1.000
Holdout	5	34,560	0.665	0.000	$-0.151$	0.000	$-0.268$	0.000	1.000

Appendix

Table 12: Held-out replay signatures in the diagnostic-dominance test. The relation writer and support lookup are matched on the aligned endpoint and on the state-on–state-off endpoint contrast before labels are opened. Calibration uses maps 1–4 and future indices 0–23; holdout uses maps 5–9 and future indices 24–47.

A

is changed-action proportion,

U

is mapped-minus-identity future utility in normalized units, and

O

is mapped-minus-identity executor-relative oracle-agreement difference in proportion units. Subscripts

R

and

L

denote the relation and lookup writers. The final column is decoder accuracy as a proportion.

Writer	$A_{\varnothing}$	$U_{\varnothing}$	$O_{\varnothing}$	$A_{\rm cal}$	$A_{\rm ho}$	$B_{\rm dec}$
Relation	0.372	0.008	0.029	0.667	0.665	1.000
Lookup	0.372	0.008	0.029	0.000	0.000	1.000
Recurrent	0.750	$-0.001$	$-0.004$	0.675	0.682	1.000
Additive	0.750	$-0.001$	$-0.004$	0.000	0.000	1.000

Appendix

Table 13: Endpoint-matched writers.

A_{0}

and

U_{0}

compare aligned actions and utility between writers.

A_{\varnothing}

is written-versus-empty action disagreement;

U_{\varnothing}

and

O_{\varnothing}

are written-minus-empty utility and oracle agreement.

A_{\rm cal}

and

A_{\rm ho}

report rekey responses for Relation/Lookup and pair responses for Recurrent/Additive;

B_{\rm dec}

is decoder accuracy. Action and oracle quantities are proportions; utility is normalized. Relation/Lookup uses 48 streams; Recurrent/Additive averages five fitted pairs. Bold and underlined entries distinguish the paired writers.

Fit	$A_{0}$	$A_{\varnothing}$	$U_{\varnothing}$	$O_{\varnothing}$	$A_{0}$	$A_{\varnothing}$	$U_{\varnothing}$	$O_{\varnothing}$
	Additive				Recurrent
1	0.000	0.750	0.000	0.001	0.000	0.750	0.000	0.001
2	0.000	0.750	$-0.002$	$-0.008$	0.000	0.750	$-0.002$	$-0.008$
3	0.000	0.750	$-0.003$	$-0.006$	0.000	0.750	$-0.003$	$-0.006$
4	0.000	0.750	$-0.002$	$-0.005$	0.000	0.750	$-0.002$	$-0.005$
5	0.000	0.750	0.002	0.000	0.000	0.750	0.002	0.000

Appendix

Table 14: Per-fit endpoint contrasts for the independently learned pair.

A_{0}

and

A_{\varnothing}

are action-disagreement proportions;

U_{\varnothing}

is a normalized utility contrast; and

O_{\varnothing}

is an oracle-agreement contrast reported as a proportion. Values are rounded to three decimals; nonzero claims use unrounded values. The five fits are paired by fit index.

Writer	Fit	$A_{\rm cal}$			$A_{\rm ho}$
		Estimate	Lower	Upper	Estimate	Lower	Upper
Additive	1	0.000	0.000	0.000	0.000	0.000	0.000
Recurrent	1	0.703	0.635	0.776	0.738	0.671	0.804
Additive	2	0.000	0.000	0.000	0.000	0.000	0.000
Recurrent	2	0.646	0.531	0.750	0.538	0.431	0.642
Additive	3	0.000	0.000	0.000	0.000	0.000	0.000

Appendix

Table 15: Per-fit replay responses for five independently fitted endpoint pairs. Each additive–recurrent pair is fitted on separate sequence streams, with parameters frozen before evaluation.

A_{\rm cal}

and

A_{\rm ho}

are complete-pair action response proportions on calibration and holdout episodes. Lower and Upper give the endpoints of 95% bootstrap confidence intervals; episodes are resampled within each frozen fit. Bold and underlined estimates denote recurrent and additive writers, respectively.

	Additive		Recurrent
Fit	$B_{\rm cal}$	$B_{\rm ho}$	$B_{\rm cal}$	$B_{\rm ho}$
1	1.000	1.000	1.000	1.000
2	1.000	1.000	1.000	1.000
3	1.000	1.000	1.000	1.000
4	1.000	1.000	1.000	1.000
5	1.000	1.000	1.000	1.000

Appendix

Table 16: Per-fit blind classification accuracies for the independently learned pair.

B_{\rm cal}

and

B_{\rm ho}

are calibration and holdout accuracies from a decoder fixed on calibration replay; the five fit pairs are the same as in the endpoint and replay tables. Accuracies are proportions and Fit is an integer index.

Evaluation	$\boldsymbol{\Gamma_{U}^{\mathrm{value}}}$	$\boldsymbol{\Gamma_{A}^{\mathrm{value}}}$ (proportion)	$\boldsymbol{\Gamma_{O}^{\mathrm{value}}}$ (proportion)
Policy-disjoint	0.022	$-0.014$	$-0.064$
Reverse policy	0.063	0.023	$-0.214$
Independent fit	0.025	0.013	$-0.094$
Changed substrate	0.012	0.054	$-0.049$

Appendix

Table 17: Cross-interface value-null interactions. Entries are fixed-draw aligned-minus-value estimates of

\Gamma_{U}^{\mathrm{value}}

\Gamma_{A}^{\mathrm{value}}

, and

\Gamma_{O}^{\mathrm{value}}

for the stated evaluation setting. Utility is normalized; action and oracle interactions are differences of proportions.

Writer	Contrast	$n_{\rm fit}$	$n_{\rm eval}$	$\widehat{\Gamma}_{U}$	$\widehat{\Gamma}_{A}$	$\widehat{\Gamma}_{O}$
Selected-only	Value null	48	48	0.024	0.003	$-0.089$
Selected-only	Time placebo	48	48	0.024	0.005	$-0.089$
Fitted associative	Value null	48	48	0.039	0.018	$-0.094$
Dense continuous	Value null	0	48	0.019	0.027	$-0.055$
Cross-namespace	Value null	0	48	0.021	0.019	$-0.069$
Changed substrate	Value null	24	24	0.012	0.054	$-0.049$

Appendix

Table 18: Fitted-state and changed-substrate transport checks.

n_{\rm fit}

and

n_{\rm eval}

count fitting and evaluation streams;

n_{\rm fit}=0

denotes a fixed analytic binding.

\widehat{\Gamma}

is the aligned-minus-condition estimate in Eq. ( 15 ), conditional on the intervention draw; the final row pools the value condition across strata. Utility is normalized; action and oracle interactions are differences of proportions. Fitted parameters are frozen before evaluation.

A. Replay interactions
Writer	Comparison	Utility	Action	Oracle
OCRR	Aligned $-$ value	0.304	$-0.038$	$-0.412$
OCRR	Aligned $-$ time	0.323	$-0.049$	$-0.427$
OCRR	Pair $-$ value	0.302	$-0.003$	$-0.405$
UCB1	Aligned $-$ time	0.129	$-0.468$	$-0.113$
Local-only	Aligned $-$ time	0.241	$-0.341$	$-0.310$

Appendix

Table 19: Matched replay contrasts on 48 streams. Panel A reports differences in replay responses. Panel B compares OCRR’s written and empty states: utility and oracle agreement are written minus empty, whereas action is disagreement. Utility is normalized; action and oracle entries use proportion units. Complete intervals are reported in Appendix D .

Figure 3: Executor-relative consequences of fixed-label replay. The two panels give the map-level increase in held-out oracle regret and the corresponding drop in exact oracle-arm agreement. Both readouts use the same future records as the primary fixed-label replay and remain outside the controller state.

Family	Context	$n$	Estimate	Lower	Upper
Source	Low	2304	1.000	1.000	1.000
Source	High	2304	1.000	1.000	1.000
Temporal	Low	2304	0.875	0.771	0.958
Temporal	High	2304	0.750	0.625	0.875
Survival	Balanced	2304	1.000	1.000	1.000
Survival	Rare	2304	1.000	1.000	1.000

Appendix

Table 20: Fraction of future tasks on which the action-sequence-preserving Permutation replay selects a different arm from OCRR. The short family labels Source, Temporal, and Survival denote source localization, temporal discount, and survival risk. Each row contains

n=2304

future tasks from 48 replicate clusters; Estimate, Lower, and Upper are the point estimate and approximate 95% replicate-cluster interval endpoints, all reported as proportions.

State variant	Mean utility	Minimum	Maximum	Action	Oracle
OCRR	0.196	0.024	0.330	0.938	$-0.293$
UCB1	0.002	$-0.138$	0.090	0.519	0.022
Local-only	0.114	0.016	0.179	0.645	$-0.176$
Global-only	0.171	$-0.024$	0.373	1.000	$-0.139$
TP placebo	$-0.127$	$-0.207$	0.022	0.986	0.134

Appendix

Table 21: Matched state variants on the primary fixed trace. Mean utility is the normalized identity-minus-mapped utility gap. Minimum and Maximum give its range over the nine producer-key derangements. Action is mapped-versus-identity disagreement; oracle is mapped-minus-identity agreement. Action and oracle use proportion units. All rows reuse 48 replicate streams. TP denotes the time-preserving placebo.

Figure 4: Structural-control responses across replay maps. Panels show future-action response, future-utility response, and executor-relative oracle response for the arm-indexed ledger, matched state variants, and the time-preserving placebo. The nine columns are paired derangements of the same replicate streams; the heatmaps display pooled point estimates under the fixed measurement protocol.

Metric	Estimate	Lower	Upper	$p$
Future utility	0.323	0.286	0.359	$<0.001$
Future actions changed	$-0.049$	$-0.069$	$-0.028$	$<0.001$
Oracle-match change	$-0.427$	$-0.467$	$-0.389$	$<0.001$

Appendix

Table 22: Paired OCRR–time-preserving-placebo interaction. The utility estimate contrasts aligned-minus-map responses, whereas action-change and oracle-match use mapped-minus-aligned responses; each interaction is OCRR minus the corresponding placebo response on the same derangement and replicate. Utility is normalized; action-change and oracle-match are differences expressed in proportion units. Estimate is the point estimate, while Lower and Upper are 95% percentile replicate-cluster interval endpoints from 20,000 complete block resamples;

p

is the sign-flip value.

Contrast	Utility	Action (proportion)	Oracle (proportion)
OCRR $-$ value null	0.304	$-0.038$	$-0.412$
OCRR $-$ time placebo	0.323	$-0.049$	$-0.427$
Value null $-$ time placebo	0.019	$-0.010$	$-0.016$

Appendix

Table 23: Matched value-permutation control on the primary fixed trace. The value-permutation null keeps the observed arm labels, per-key prefix counts, update slots, and blockwise utility multiset, while permuting utilities across adaptation slots. Utility is normalized, and action and oracle entries are differences of proportions. The first two rows are aligned-minus-cell interactions; the last row is the value-null minus time-placebo contrast. Uncertainty intervals and sign-flip values are given in Appendix H.1 .

Contrast	Readout	Estimate	Lower	Upper	$p$
OCRR $-$ value null	Future utility	0.304	0.266	0.341	$<0.001$
OCRR $-$ value null	Action change	$-0.038$	$-0.063$	$-0.017$	0.001
OCRR $-$ value null	Oracle match	$-0.412$	$-0.454$	$-0.369$	$<0.001$
OCRR $-$ time placebo	Future utility	0.323	0.286	0.359	$<0.001$
OCRR $-$ time placebo	Action change	$-0.049$	$-0.069$	$-0.028$	$<0.001$
OCRR $-$ time placebo	Oracle match	$-0.427$	$-0.467$	$-0.389$	$<0.001$

Appendix

Table 24: Full uncertainty estimates for the matched value-permutation interactions. Utility is normalized, while action-change and oracle-match entries are differences expressed in proportion units. Estimate is the point estimate, while Lower and Upper are 95% replicate-cluster bootstrap interval endpoints from 20,000 complete block resamples;

p

is the two-sided cluster sign-flip value.

Contrast	Readout	Estimate	Lower	Upper	$p$
Pair placebo $-$ value null	Future utility	0.302	0.263	0.340	$<0.001$
Pair placebo $-$ value null	Action change	$-0.003$	$-0.028$	0.021	0.694
Pair placebo $-$ value null	Oracle match	$-0.405$	$-0.449$	$-0.362$	$<0.001$

Appendix

Table 25: Pair-preserving placebo relative to the value-permutation null. The placebo uses the same utility permutation as the value null and moves each observed label–utility pair within its adaptation block, so producer association is retained while temporal placement changes. Utility entries are normalized, while action-change and oracle-match entries are differences expressed in proportion units. Estimate is the point estimate, while Lower and Upper are 95% replicate-cluster interval endpoints; utility entries are differences of the two utility interactions under the signed identity-minus-replay convention.

Writer	$\widehat{\Gamma}_{U}$			$p_{U}$	$\widehat{\Gamma}_{A}$	$\widehat{\Gamma}_{O}$
	Estimate	Lower	Upper
OCRR	0.323	0.286	0.359	$<0.001$	$-0.049$	$-0.427$
UCB1	0.129	0.093	0.164	$<0.001$	$-0.468$	$-0.113$
Local-only	0.241	0.206	0.274	$<0.001$	$-0.341$	$-0.310$
Global-only	0.298	0.262	0.333	$<0.001$	0.014	$-0.273$

Appendix

Table 26: Aligned-minus-time interactions for each state writer. Utility is normalized; Lower and Upper delimit its 95% replicate-cluster bootstrap interval, and

p_{U}

is its sign-flip value. Action and oracle interactions are differences of proportions. All rows use the same 48 replicate streams and nine paired derangements.

Family	$n$	$\bar{A}_{\mathrm{rekey}}$	$\bar{D}_{A,\mathrm{value}}$	$\bar{D}_{A,\mathrm{pair}}$	Correct
Replay-invariant	3	0.000	0.000	0.000	3
Key-only	3	0.664	0.000	0.000	3
Commutative-pairing	3	0.666	0.163	0.000	3
Order-sensitive	3	0.667	0.000	0.090	3

Appendix

Table 27: Blinded operator-family signatures. Entries are direct action proportions averaged over three parameterizations, each evaluated on 48 replicate streams and nine outer arm derangements under the realized slot draw.

n

counts operator parameterizations, not inference units. Correct is the number of parameterizations recovered by the predeclared rule; these are calibration outputs rather than population accuracy estimates.

Figure 5: Writer calibration and blinded operator recovery. Panel A summarizes value-null interactions for the calibrated writer controls; panel B reports the transport signature across held-out fits; panel C checks training-label permutations; and panel D shows the action signature used to recover the hidden operator family. These are fixed-draw calibration summaries, with operator counts distinct from inferential replicate streams.

Family	$n$	$\bar{A}_{\mathrm{rekey}}$	$\bar{D}_{A,\mathrm{value}}$	$\bar{D}_{A,\mathrm{pair}}$
Value–order	4	0.000	0.162	0.162
Key–value	2	0.667	0.021	0.000
Key–order	2	0.665	0.160	0.142

Appendix

Table 28: Direct action signatures of eight held-out composite state operators. Rows pool opaque operators assigned to each update family;

n

is the number of operators, not an inference sample size. Each operator is evaluated on 48 replicate streams and nine outer arm derangements under the realized slot draw. Entries are proportions of future actions changed and are calibration outputs for the declared composite families.

Generating law	$n$	$\bar{A}_{\mathrm{rekey}}$	$\bar{D}_{A,\mathrm{value}}$	$\bar{D}_{A,\mathrm{pair}}$	Pair-state
Commutative sum	12	0.487	0.034	0.000	0.000
Affine recurrent	12	0.498	0.187	0.226	0.450

Appendix

Table 29: Coefficient-randomized online operator stress test. Entries are mean future-action changes across 12 opaque operators and 48 replicate streams per operator under the realized slot draw.

n

counts operators and does not define the inferential sample size. Pair-state is the terminal-state distance between aligned and pair-preserving cells, averaged over contexts. Action entries are proportions; Pair-state is a continuous distance.

Readout	$D_{A}^{\rm pair}$	State	$n_{A}$	$n_{S}$	$D_{A}^{\rm pair}$	State	$n_{A}$	$n_{S}$
	Commutative				Recurrent
Coordinate	0.000	0.000	0	0	0.189	0.518	12	12
Orthogonal	0.000	0.000	0	0	0.215	0.518	12	12
Mixed	0.000	0.000	0	0	0.211	0.518	12	12

Appendix

Table 30: Pair-preserving responses under independently generated state dimensions and future readouts. Each entry pools twelve operators across 48 replicate streams under the realized slot draw; the operator count is a calibration count, not an inference sample size. Pair action is the fraction of future choices changed, Pair state is the terminal-state Euclidean distance, and

n_{A}

and

n_{S}

count operators with nonzero action and state responses, respectively.

	Draw A				Draw B
Writer law	State	Pair	Value	Rekey	State	Pair	Value	Rekey
Nonlinear commutative	0.000	0.000	0.030	0.465	0.000	0.000	0.031	0.465
Nonlinear recurrent	0.439	0.218	0.180	0.510	0.441	0.221	0.185	0.510

Appendix

Table 31: Nonlinear state-coordinate checks under complete-pair transport. Each writer law uses 12 operator instances, reused across draws with the same 48 streams, nine outer maps, and six future strata; Draw B uses an independently sampled within-block permutation. The State entry is mean terminal-state distance; Pair, Value, and Rekey are changed-action proportions. State distances below

10^{-9}

are displayed as zero.

Draw	Target property	Total	Correct	Accuracy
A	Pair-preserving	16	16	1.000
A	Pair-displacing	16	15	0.938
B	Pair-preserving	16	16	1.000
B	Pair-displacing	16	16	1.000
A+B	All challenge writers	64	63	0.984

Appendix

Table 32: Family-blind calibration of the complete-pair law. The decoder classifies a writer as pair-displacing when its mean pair-action response is at least

0.050

; this threshold is fixed before coefficients, readouts, and hidden assignments are generated. Each draw contains 16 pair-preserving and 16 pair-displacing writers. Total is the denominator of the Correct count; accuracy is a proportion.

Target relation	$n$	Pair action	Pair state	Calibration accuracy
Pair-preserving	16	0.000	0.000	1.000
Pair-displacing	16	0.161	0.470	0.938
All challenge writers	32	0.081	0.235	0.969

Appendix

Table 33: Family-blind calibration of the construction-defined pair law on four held-out writer laws. The decoder uses the mean direct pair-action signature and a threshold fixed before the hidden assignment; pair state is a diagnostic, not a ranking criterion. Pair action and calibration accuracy are proportions; Pair-state distance is a continuous diagnostic;

n

is the number of writers.

Threshold	Accuracy	Specificity	Sensitivity
0.025	1.000	1.000	1.000
0.050	0.969	1.000	0.938
0.075	0.906	1.000	0.813
0.100	0.906	1.000	0.813
0.125	0.844	1.000	0.688
0.150	0.781	1.000	0.563

Appendix

Table 34: Threshold sensitivity for the fixed blind challenge. Each row re-evaluates the same 32 operator-level signatures; no operator, law, or readout is refit. Specificity and sensitivity are computed against the construction-defined pair relation.

Contrast	Utility	Action	Oracle
OCRR $-$ value null	0.019	0.027	$-0.055$
OCRR $-$ time placebo	0.028	0.015	$-0.063$
Pair placebo $-$ value null	0.021	0.027	$-0.060$
Value null $-$ time placebo	0.008	$-0.012$	$-0.008$

Appendix

Table 35: Dense continuous-state interactions on held-out streams. Each comparison uses the same 48 replicate streams and nine paired derangements. Utility is identity minus replay; action and executor-relative oracle entries are normalized map-minus-identity differences. Entries are fixed-draw calibration point estimates.

	Dense				Cross-namespace
Readout	Estimate	Lower	Upper	$p$	Estimate	Lower	Upper	$p$
$U$	0.019	0.010	0.030	$<0.001$	0.021	0.012	0.030	$<0.001$
$A$	0.027	0.013	0.043	NR	0.019	0.009	0.030	NR
$O$	$-0.055$	$-0.079$	$-0.034$	NR	$-0.069$	$-0.091$	$-0.048$	NR

Appendix

Table 36: Uncertainty for continuous-writer pairing interactions. Estimate is the point estimate, while Lower and Upper are separate 95% replicate-cluster bootstrap interval endpoints; utility, action, and oracle estimates and interval endpoints are normalized differences. The cluster sign-flip

p

value is reported for the utility interaction; NR means not reported.

Contrast	Utility	Action	Oracle
Fitted $-$ value null	0.039	0.018	$-0.094$
Fitted $-$ time placebo	0.039	0.019	$-0.090$
Pair placebo $-$ value null	0.039	0.018	$-0.094$

Appendix

Table 37: Interactions for a privileged fitted low-rank associative state writer on held-out streams. Utility is identity minus replay; action and oracle entries are normalized map-minus-identity differences for the named contrast.

Contrast	Readout	Estimate	Lower	Upper	$p$
Selected-only $-$ value null	Utility	0.024	0.015	0.035	$<0.001$
Selected-only $-$ value null	Action	0.003	$-0.008$	0.015	0.596
Selected-only $-$ value null	Oracle	$-0.089$	$-0.113$	$-0.065$	$<0.001$
Selected-only $-$ time placebo	Utility	0.024	0.015	0.033	$<0.001$
Selected-only $-$ time placebo	Action	0.005	$-0.007$	0.016	0.467
Selected-only $-$ time placebo	Oracle	$-0.089$	$-0.112$	$-0.066$	$<0.001$

Appendix

Table 38: Order-invariant selected-outcome-only commutative state control on held-out streams. The writer is fitted with a leave-one-out commutative selected-outcome objective and receives no counterfactual future utility during fitting. Each row is a readout-specific normalized estimate; intervals are 95% replicate-cluster bootstrap intervals with separate Lower and Upper endpoints, and

p

is the two-sided cluster sign-flip value.

Fit	Order	Utility	Minimum	Maximum	Oracle
Prefix	Arm-sorted	0.021	0.016	0.027	$-0.066$
Prefix	Chronological	$-0.008$	$-0.012$	$-0.005$	0.015
Leave-one-out	Order-invariant	0.023	0.021	0.027	$-0.078$

Appendix

Table 39: Sensitivity to the selected-only fitting objective. Each row summarizes five refits on the same disjoint training streams.

U

is the normalized utility interaction; Minimum and Maximum are the lower and upper endpoints of the observed range across refits, not confidence limits.

O

is the normalized oracle interaction; mismatch counts aligned-versus-pair-preserving action disagreements. The mismatch count holds for every refit and each of nine nonidentity maps separately, with

48\times 6\times 48=13{,}824

comparisons per map; the identity map is excluded.

Refit	Utility	Lower	Upper	Action	Oracle
R1	0.024	0.015	0.035	0.003	$-0.089$
R2	0.023	0.013	0.033	0.003	$-0.080$
R3	0.021	0.012	0.031	0.006	$-0.075$
R4	0.027	0.018	0.036	$-0.002$	$-0.071$
R5	0.021	0.012	0.030	0.004	$-0.075$

Appendix

Table 40: Refit stability of the order-invariant selected-outcome-only commutative writer. Every fit uses the leave-one-out commutative objective, selected adaptation outcomes only, and the same disjoint training and held-out evaluation streams. Utility intervals are 95% replicate-cluster bootstrap intervals with separate Lower and Upper endpoints; action and oracle entries are normalized differences in future-action and executor-relative oracle response. Pair mismatch counts compare aligned and pair-preserving future actions. The mismatch count holds for each of nine nonidentity maps separately, with

48\times 6\times 48=13{,}824

comparisons per map; the identity map is excluded.

Draw	Estimate	Lower	Upper	Estimate	Lower	Upper	Pair mismatch
	Value			Time
0	0.024	0.015	0.035	0.024	0.015	0.033	0
1	0.028	0.018	0.039	0.026	0.016	0.036	0
2	0.024	0.014	0.033	0.025	0.016	0.035	0
3	0.029	0.020	0.039	0.021	0.014	0.030	0

Appendix

Table 41: Sensitivity of the order-invariant selected-outcome-only commutative contrast to the within-block permutation draw. Four fixed realizations of the same blockwise law use the same fitted writer and evaluation streams. Value and time are the value-null and time-placebo interactions, respectively, reported as normalized estimates with separate 95% replicate-cluster Lower and Upper endpoints. Pair-preserving action mismatch counts are shown in the last column. The mismatch count holds for each of nine nonidentity maps separately, with

48\times 6\times 48=13{,}824

comparisons per map; the identity map is excluded.

Contrast	Utility	Lower	Upper	Action
Value null	0.001	$-0.001$	0.003	0.001
Time placebo	0.005	0.001	0.009	$-0.012$
Pair minus value	0.000	$-0.003$	0.002	$-0.005$

Appendix

Table 42: Learned recurrent state-writer boundary check for a reference fit. The writer is fit only to selected adaptation outcomes on disjoint training blocks and is frozen before evaluation on disjoint streams. Entries are normalized future-utility interaction estimates with 95% replicate-cluster Lower and Upper endpoints; Action is the corresponding interaction in the normalized future-action fraction. The nonlinear recurrent transition imposes no commutativity.

Refit	Estimate	Lower	Upper	Estimate	Lower	Upper
	Value			Time
R1	0.001	$-0.001$	0.003	0.005	0.001	0.009
R2	0.000	$-0.004$	0.004	0.001	$-0.003$	0.005
R3	0.001	$-0.002$	0.003	0.000	$-0.001$	0.002
R4	0.003	$-0.001$	0.007	0.002	$-0.001$	0.006
R5	$-0.003$	$-0.006$	0.001	$-0.003$	$-0.007$	0.001

Appendix

Table 43: Refit sensitivity of the learned recurrent boundary check. Each row contains one refit, with separate Value and Time estimates and their 95% replicate-cluster Lower and Upper endpoints; Value and Time denote the corresponding normalized utility interactions.

Fit	Utility	Action	Oracle
Fit 1	0.123	0.534	$-0.508$
Fit 2	0.125	0.552	$-0.521$
Fit 3	0.124	0.552	$-0.519$
Fit 4	0.124	0.547	$-0.514$
Fit 5	0.125	0.561	$-0.516$
Mean	0.124	0.549	$-0.516$

Appendix

Table 44: Direct pair-transport response of the independently learned writer. Each row is one frozen fit, evaluated on the same 48 disjoint episodes and nine derangements.

U

A

, and

O

are aligned-minus-pair future utility, future-action response, and executor-relative oracle response, respectively, all reported as normalized differences. The final row is the arithmetic mean across fits.

Contrast	Metric	Estimate	Lower	Upper	$p$
Policy-disjoint $-$ value null	Utility	0.022	0.013	0.031	$<0.001$
Policy-disjoint $-$ value null	Action	$-0.014$	$-0.029$	0.001	0.082
Policy-disjoint $-$ value null	Oracle	$-0.064$	$-0.085$	$-0.044$	$<0.001$
Policy-disjoint $-$ time placebo	Utility	0.018	0.011	0.026	$<0.001$
Policy-disjoint $-$ time placebo	Action	$-0.023$	$-0.037$	$-0.009$	0.002
Policy-disjoint $-$ time placebo	Oracle	$-0.065$	$-0.082$	$-0.048$	$<0.001$

Appendix

Table 45: Policy-disjoint order-invariant selected-outcome-only commutative control. The writer is fitted on selected outcomes generated by Generic memory and evaluated on the fixed OCRR trace; no counterfactual future utility enters the fit. Each row is one normalized interaction estimate with separate 95% replicate-cluster Lower and Upper endpoints, and

p

is the two-sided cluster sign-flip value.

Contrast	Metric	Estimate	Lower	Upper	$p$
Reverse $-$ value null	Utility	0.063	0.053	0.073	$<0.001$
Reverse $-$ value null	Action	0.023	0.012	0.034	$<0.001$
Reverse $-$ value null	Oracle	$-0.214$	$-0.231$	$-0.196$	$<0.001$
Reverse $-$ time placebo	Utility	0.054	0.044	0.064	$<0.001$
Reverse $-$ time placebo	Action	0.030	0.019	0.044	$<0.001$
Reverse $-$ time placebo	Oracle	$-0.200$	$-0.217$	$-0.182$	$<0.001$

Appendix

Table 46: Reverse cross-policy order-invariant selected-outcome-only commutative control. The writer is fitted on selected outcomes generated by OCRR and evaluated on the fixed Generic memory trace; no counterfactual future utility enters the fit. Each row is one normalized interaction estimate with separate 95% replicate-cluster Lower and Upper endpoints, and

p

is the two-sided cluster sign-flip value.

State cell	Utility	Action	Oracle
Selected-only fit	0.025	0.013	$-0.094$
Pair-preserving cell	0.025	0.013	$-0.094$

Appendix

Table 47: Independent replicate structural check for the order-invariant selected-only writer. Utility, action, and oracle entries are normalized differences. Both rows use the same 48 evaluation replicate streams and nine paired derangements; the pair-preserving row equals the aligned row by the declared commutative update law, so the repeated numbers are the invariance result.

Fit	Utility	Action	Oracle
Canonical	0.025	0.013	$-0.094$
S1	$-0.106$	0.002	0.107
S2	$-0.029$	$-0.042$	0.026
S3	$-0.044$	0.022	0.062
S4	$-0.042$	$-0.010$	0.054
S5	$-0.115$	$-0.047$	0.103

Appendix

Table 48: Training-label permutation calibration for the order-invariant selected-outcome-only writer. The canonical row uses the producer labels in the fitting trace. Rows S1–S5 independently permute those labels within each of 192 training blocks, preserve the selected-utility sequence and block label multiset, and evaluate the frozen fit on the canonical held-out labels.

U

A

, and

O

are normalized utility, action, and executor-relative oracle interactions, respectively; mismatch is the pair-preserving action mismatch count. The five shuffled rows are fit-variation summaries and do not add inference units. The mismatch count holds for each of nine nonidentity maps separately, with

48\times 6\times 48=13{,}824

comparisons per map; the identity map is excluded.

Condition-level outcomes
Condition	Split	Tasks ( $n$ )	Utility	Oracle gap	Cost	Utility per cost
No update	adaptation	9216	0.544	0.222	10.000	0.054
No update	future	13824	0.461	0.158	10.000	0.046
Static predictor	adaptation	9216	0.437	0.329	10.000	0.044
Static predictor	future	13824	0.467	0.153	10.000	0.047
Generic memory	adaptation	9216	0.555	0.211	10.000	0.056

Appendix

Table 49: Condition-level outcomes and secondary diagnostics from the primary matrix. The upper panel reports means over selected tasks for adaptation and future splits. Tasks (

n

) is the number of selected or future tasks; Utility, Oracle gap, Cost, and Utility per cost are reported on their stated scales, with Cost denoting effective cost and Utility per cost dividing Utility by Cost. The lower panel reports calibration mean absolute error (MAE) and Failure rate. Oracle gap, MAE, and Failure rate are lower-is-better diagnostics; Utility and Utility per cost are future-outcome summaries.

Secondary comparison	Difference	Lower	Upper	Sign-flip $p$	Tasks	Reps.
OCRR– Selected	0.006	$-0.006$	0.017	0.324	13824	48
OCRR– UCB1	0.136	0.122	0.150	$<0.001$	13824	48
OCRR– Replay	0.029	0.021	0.037	$<0.001$	13824	48
Selected – Static	$-0.004$	$-0.011$	0.003	0.245	13824	48

Appendix

Table 50: Secondary full-matrix future-utility contrasts. Each estimate is the left condition minus the right condition on the normalized future-utility scale. The 95% interval is split into Lower and Upper endpoints; task and replicate counts are reported separately. The row shorthands Selected , UCB1 , Replay , and Static denote Selected static , Contextual upper-confidence bound , Permutation replay , and Static predictor , respectively. These are secondary condition and mechanism contrasts.

ID	Map	OCRR– Permutation replay	Positive strata
1	ACMR	$0.223$	4
2	ARMC	$0.218$	4
3	AMCR	$0.223$	4
4	RCMA	$0.268$	4
5	RMCA	$0.268$	4
6	RMAC	$0.263$	4

Appendix

Table 51: Changed-substrate fixed-label replay. The displayed values are point estimates for the changed substrate; map strings are permutations of source labels C, A, R, and M, listed in that order. OCRR– Permutation replay is the normalized pooled future-utility difference; positive strata is an integer count of the four family–context strata with a positive estimate. The maps reuse the same replicate streams and are fixed-label robustness variants, not independent samples.

Task family	$\widehat{\Gamma}_{U}$	$\widehat{\Gamma}_{A}$	$\widehat{\Gamma}_{O}$	Pair changes	$\widehat{\Gamma}_{U}$	$\widehat{\Gamma}_{A}$	$\widehat{\Gamma}_{O}$	Pair changes
	Low				High
Hypothesis	0.009	0.028	$-0.087$	0	0.001	0.009	$-0.005$	0
Validation	0.030	0.069	$-0.069$	0	0.010	0.111	$-0.036$	0

Appendix

Table 52: Changed-substrate transport by task family and noise level. Entries are aligned-minus-value interactions from the fitted selected-outcome writer. Utility is normalized; action and oracle interactions are differences of proportions. The Pair changes column counts action mismatches under complete-pair transport across all nine maps. Each stratum has 24 evaluation streams and 48 future tasks per stream, giving 10,368 compared actions.

Figure 6: Transfer and action sensitivity across controlled strata. Panel A compares the primary OCRR and no-update future-utility levels; panel B keeps the replicate stream visible for the same transfer contrast; panel C shows the independent changed-substrate utility checks; and panel D reports the fraction of future choices changed by replay. Replicate streams remain the sampling units throughout.

Data	Context	OCRR	No update	$\boldsymbol{\Delta U_{\mathrm{O-N}}}$ ( $10^{-3}$ )
				Estimate	Lower	Upper
Breast cancer	IID	$0.834$	$0.834$	$-0.240$	$-0.660$	$0.084$
Breast cancer	Shift	$0.755$	$0.755$	$-0.007$	$-0.021$	$0.000$
Wine quality	IID	$0.541$	$0.544$	$-2.780$	$-5.243$	$-0.487$
Wine quality	Shift	$0.552$	$0.557$	$-4.705$	$-7.793$	$-1.927$

Appendix

Table 53: Public-data endpoint-check stratum estimates. OCRR and No update are normalized utility ratios;

\Delta U_{\mathrm{O-N}}

is the O-minus- No update utility difference in

10^{-3}

normalized utility units. The estimate, lower, and upper columns give the estimate and 95% cluster-bootstrap interval over the 48 replicate streams; each stratum contains 24 future tasks per stream.

Comparison	Metric	Estimate	Lower	Upper	$n_{\rm streams}$
OCRR $-$ No update	$U$	$-1.933$	$-2.774$	$-1.165$	48
OCRR $-$ Shuffled outcome	$U$	$5.666$	$3.416$	$8.063$	48
OCRR $-$ Extra sampling	$U/c$	$18.702$	$18.660$	$18.743$	48

Appendix

Table 54: Pooled public-data executor contrasts. Metrics are future utility

U

and utility per effective cost

U/c

. Contrasts use

10^{-3}

units for the stated metric. Estimate is the mean paired contrast; Lower and Upper delimit its 95% cluster-bootstrap interval over 48 replicate streams and 4,608 future tasks per condition.

Condition	Utility	Regret	Utility/cost
Extra sampling	$0.666$	$0.024$	$0.009$
Generic memory	$0.667$	$0.023$	$0.028$
Generic skill	$0.655$	$0.035$	$0.027$
No update	$0.673$	$0.017$	$0.028$
OCRR	$0.671$	$0.019$	$0.028$
Shuffled outcome	$0.665$	$0.025$	$0.028$

Appendix

Table 55: Public-data executor condition means. Utility, regret, and utility/cost are normalized continuous quantities; utility/cost divides the held-out utility by the realized effective sampling cost.

		Fold I			Fold II
Cell	Metric	Estimate	Lower	Upper	Estimate	Lower	Upper
Rekey	$A$	$0.753$	$0.750$	$0.757$	$0.620$	$0.607$	$0.631$
Rekey	$\Delta U_{\mathrm{C-A}}$	$-0.602$	$-1.194$	$-0.023$	$0.870$	$-0.016$	$1.714$
Rekey	$\Delta O_{\mathrm{C-A}}$	$-0.082$	$-0.099$	$-0.066$	$0.027$	$0.005$	$0.048$
Key-slot	$A$	$0.243$	$0.191$	$0.295$	$0.240$	$0.188$	$0.292$
Key-slot	$\Delta U_{\mathrm{C-A}}$	$-0.476$	$-0.854$	$-0.123$	$0.285$	$-0.303$	$0.819$

Appendix

Table 56: Cross-fitted persistent-agent replay on public measured outcomes.

A

is the changed-action proportion;

\Delta U_{\mathrm{C-A}}

and

\Delta O_{\mathrm{C-A}}

are cell-minus-aligned contrasts in

10^{-3}

normalized utility units and proportion units, respectively. Estimate is the point estimate; Lower and Upper delimit its 95% replicate-cluster bootstrap interval. Fold I trains on replicates 0–23 and evaluates 24–47; Fold II swaps these sets.

Readout	Keys	$\Delta U_{\rm end}$	$\Delta O_{\rm end}$	$A_{\rm rekey}$	$D_{A}^{\rm value}$	$D_{A}^{\rm pair}$	$D_{A}^{\rm logT}$	$A_{\rm traj}$
Luna	Arm	$-2.448$	$-0.214$	0.865	0.115	0.016	0.016	0.987
Luna	Opaque	$-2.504$	$-0.218$	0.866	0.139	0.042	0.023	0.936
Sol	Arm	$-2.418$	$-0.212$	0.996	0.325	0.010	0.007	0.997
Sol	Opaque	$-2.347$	$-0.211$	0.998	0.347	0.007	0.009	0.997
Terra	Arm	$-2.343$	$-0.211$	0.984	0.247	0.017	0.000	0.998
Terra	Opaque	$-2.413$	$-0.213$	0.971	0.254	0.021	0.023	0.995

Appendix

Table 57: Typed and dynamic replay profiles for three GPT-5.6 deployments. The six cells share the measured-outcome trace, future tasks, and 48 replicate streams, with four blocks per stream and 24 future decisions per block. Arm denotes readable keys and Opaque denotes token-matched opaque keys. Endpoint contrasts subtract the fixed mixed-action policy from the memory-based policy.

A_{\rm rekey}

averages nine derangements;

D_{A}^{q}

uses the identity map.

A_{\rm traj}

is mapped-versus-identity action disagreement at the declared trajectory map, with state updates in both trajectories. Utility is in

10^{-3}

normalized units; action rates and oracle differences use proportion units.

Endpoint utility contrast $\Delta U_{\rm end}$ ( $10^{-3}$ units)
	Arm			Opaque
Readout	Estimate	Lower	Upper	Estimate	Lower	Upper
GPT-5.6 Luna	$-2.448$	$-3.270$	$-1.635$	$-2.504$	$-3.304$	$-1.704$
GPT-5.6 Sol	$-2.418$	$-3.261$	$-1.580$	$-2.347$	$-3.176$	$-1.528$
GPT-5.6 Terra	$-2.343$	$-3.172$	$-1.525$	$-2.413$	$-3.257$	$-1.574$

Appendix

Table 58: Uncertainty and trajectory readouts for the GPT-5.6 future-readout family. The endpoint-utility panel reports the estimate and 95% interval in

10^{-3}

normalized units. Endpoint contrasts subtract the fixed mixed-action policy from the memory-based policy; trajectory contrasts are mapped minus identity with future state updates. The other columns report

\Delta O_{\rm end}

and

\Delta O_{\rm traj}

as executor-agreement proportions,

A_{\rm traj}

as an action proportion, and

\Delta U_{\rm traj}

10^{-3}

normalized utility units.

		$A_{\rm rekey}$			$D_{A}^{\rm value}$			$D_{A}^{\rm pair}$			$D_{A}^{\rm logT}$
Readout	Keys	Est.	Low.	Up.	Est.	Low.	Up.	Est.	Low.	Up.	Est.	Low.	Up.
Luna	Arm	$0.865$	$0.836$	$0.894$	$0.115$	$0.069$	$0.165$	$0.016$	$0.005$	$0.028$	$0.016$	$0.002$	$0.033$
Luna	Opaque	$0.866$	$0.838$	$0.895$	$0.139$	$0.092$	$0.193$	$0.042$	$0.017$	$0.069$	$0.023$	$0.009$	$0.040$
Sol	Arm	$0.996$	$0.992$	$1.000$	$0.325$	$0.241$	$0.411$	$0.010$	$0.000$	$0.026$	$0.007$	$0.000$	$0.019$
Sol	Opaque	$0.998$	$0.995$	$1.000$	$0.347$	$0.262$	$0.436$	$0.007$	$0.000$	$0.019$	$0.009$	$0.000$	$0.023$
Terra	Arm	$0.984$	$0.976$	$0.991$	$0.247$	$0.175$	$0.323$	$0.017$	$0.000$	$0.040$	$0.000$	$0.000$	$0.000$

Appendix

Table 59: 95% replicate-cluster bootstrap intervals for typed action responses in the GPT-5.6 future-readout family over 48 streams. Each row is one readout–key pair: Arm denotes readable producer keys and Opaque denotes the token-matched opaque keys. The four metric groups give the point estimate and 95% replicate-cluster Lower and Upper endpoints for

A_{\rm rekey}

D_{A}^{\rm value}

D_{A}^{\rm pair}

, and

D_{A}^{\rm logT}

; all quantities are action proportions.

	Arm					Opaque
Readout	$r$ (95% interval)			Point summaries		$r$ (95% interval)			Point summaries
	Est.	Low.	Up.	$\rho$	$p$	Est.	Low.	Up.	$\rho$	$p$
GPT-5.6 Luna	$0.739$	$0.589$	$0.865$	$0.785$	$<0.001$	$0.725$	$0.585$	$0.839$	$0.804$	$<0.001$
GPT-5.6 Sol	$0.749$	$0.604$	$0.862$	$0.802$	$<0.001$	$0.748$	$0.603$	$0.861$	$0.811$	$<0.001$
GPT-5.6 Terra	$0.745$	$0.602$	$0.862$	$0.827$	$<0.001$	$0.748$	$0.610$	$0.860$	$0.813$	$<0.001$

Appendix

Table 60: Secondary cross-readout association on the measured-outcome bridge. For each namespace, Pearson

r

is accompanied by a 95% complete-stream bootstrap interval, while Spearman

\rho

and permutation

p

are point summaries on their native scales.

	Original			Shared-trace			Between-run
Cell	Estimate	L	U	Estimate	L	U	Estimate	L	U
Aligned	0.000	0.000	0.000	0.000	0.000	0.000	0.010	0.000	0.026
Value	0.321	0.240	0.405	0.325	0.243	0.411	0.041	0.013	0.078
Pair	0.005	0.000	0.016	0.010	0.000	0.026	0.005	0.000	0.016
Logged T	0.003	0.000	0.010	0.007	0.000	0.019	0.000	0.000	0.000
Rekey	0.996	0.993	0.999	0.996	0.992	1.000	0.009	0.003	0.016

Appendix

Table 61: Post hoc comparison of two logged Sol/Arm executions at matched full-history inputs. Original and Shared-trace report within-run intervention responses; Between-run reports same-condition output disagreement. Each direct condition uses 4,608 choices across 48 streams; Rekey averages nine maps on those choices. L and U are 95% percentile bounds from 20,000 stream-bootstrap draws. Checkpoint provenance is described in the text.

	Aligned			Value
Rule	Estimate	Lower	Upper	Estimate	Lower	Upper
Mean	0.991	0.977	1.000	0.952	0.918	0.979
Sum	0.983	0.960	1.000	0.658	0.568	0.746
Count	0.983	0.960	1.000	0.658	0.568	0.746
Latest	0.988	0.972	1.000	0.663	0.576	0.750
Best	0.972	0.941	0.995	0.699	0.623	0.778

Appendix

Table 62: Post hoc reference-rule agreement with Sol/Arm choices. Each condition contains 4,608 choices from 48 streams. Lower and Upper give 95% bootstrap bounds. Agreement measures reproduction of model choices, not task accuracy.

		Aligned			Value
Trace	Rule	Estimate	Lower	Upper	Estimate	Lower	Upper
1	Mean	0.998	0.995	1.000	0.957	0.929	0.982
1	Sum	0.976	0.953	0.995	0.751	0.658	0.839
1	Count	0.976	0.953	0.995	0.751	0.658	0.839
1	Latest	0.997	0.990	1.000	0.761	0.673	0.846
1	Best	0.965	0.934	0.990	0.807	0.724	0.882

Appendix

Table 63: Fixed-rule agreement on three additional Sol/Arm trace sets. Each condition contains 4,608 choices nested in 48 streams. Lower and Upper give 95% paired stream-bootstrap bounds. Rules and tie handling are unchanged from the shared-trace comparison.

		Aligned			Value
Trace	Rule	Estimate	Lower	Upper	Estimate	Lower	Upper
1	Mean	-0.003	-0.008	0.000	0.007	-0.133	0.166
1	Sum	-0.130	-0.414	0.029	0.212	-0.431	0.844
1	Count	-0.130	-0.414	0.029	0.212	-0.431	0.844
1	Latest	-0.020	-0.060	0.000	0.322	-0.287	0.922
1	Best	-0.130	-0.420	0.044	-0.079	-0.645	0.475

Appendix

Table 64: Reference-minus-model evaluator utility on the same future tasks, in

10^{-3}

normalized units. Lower and Upper give 95% paired stream-bootstrap bounds. These retrospective comparisons do not evaluate a deployed replacement policy.

Statistic	Winning set	Blocks	Streams	Estimate	Lower	Upper
Mean	Changed	72	35	0.828	0.723	0.919
Mean	Stable	120	47	0.007	0.000	0.021
Sum	Stable	192	48	0.325	0.243	0.412
Mean, two keys	Changed	72	35	0.828	0.721	0.919
Mean, two keys	Stable	72	38	0.009	0.000	0.026

Appendix

Table 65: Post hoc Sol/Arm value response by historical winning-set change. Each block contributes 24 paired future choices. Estimates weight the available replicate streams equally. Lower and Upper are 95% stream-bootstrap bounds. No block changes its sum winner, so no sum-changed stratum is estimated. The last two rows exclude blocks with only one observed key.

Trace ID	Namespace	$\Delta U_{\rm end}$	$\Delta O_{\rm end}$	$A_{\rm rekey}$	$D_{A}^{\rm value}$	$D_{A}^{\rm pair}$	$D_{A}^{\rm logT}$	$A_{\rm traj}$
1	Semantic alias	$-12.491$	$-0.089$	0.998	0.248	0.002	0.000	0.996
1	Opaque single-token	$-12.469$	$-0.089$	0.997	0.253	0.005	0.002	0.997
2	Semantic alias	$-5.830$	$-0.025$	0.999	0.340	0.005	0.000	0.997
2	Opaque single-token	$-5.909$	$-0.026$	0.997	0.359	0.010	0.005	0.998
3	Semantic alias	$-5.822$	$-0.047$	0.997	0.455	0.009	0.009	0.992
3	Opaque single-token	$-5.851$	$-0.048$	0.997	0.458	0.016	0.009	0.992

Appendix

Table 66: Adaptation-trace comparison for the Sol readout. Numbered rows report one trace–namespace combination; the final rows average the three traces within each namespace. Typed responses use fixed states, whereas

A_{\rm traj}

uses future state updates. Metric definitions are given in Table 57 . Endpoint contrasts compare the memory-based and fixed mixed-action policies. Utility is in

10^{-3}

normalized units; oracle differences and action rates use proportion units. Each trace has matched future tasks across namespaces and uses 48 streams, four blocks per stream, and 24 future decisions per block. The three traces use independently drawn within-block task orders under the same Sol readout.

	$A$			$\Delta U$			$\Delta O$
Readout	Est.	Low.	Up.	Est.	Low.	Up.	Est.	Low.	Up.
Rekey ( $A_{\rm rekey}$ )	$0.270$	$0.242$	$0.298$	$-0.121$	$-0.448$	$0.197$	$-0.003$	$-0.022$	$0.016$
Value ( $D_{A}^{\rm value}$ )	$0.264$	$0.210$	$0.319$	$0.280$	$-0.171$	$0.738$	$-0.005$	$-0.029$	$0.019$
Pair ( $D_{A}^{\rm pair}$ )	$0.245$	$0.198$	$0.293$	$-0.416$	$-0.916$	$0.061$	$-0.008$	$-0.033$	$0.015$
Logged T ( $D_{A}^{\rm logT}$ )	$0.280$	$0.229$	$0.331$	$-0.268$	$-0.799$	$0.239$	$0.018$	$-0.009$	$0.045$
Trajectory	$0.135$	$0.122$	$0.150$	$0.040$	$-0.328$	$0.409$	$0.002$	$-0.008$	$0.011$

Appendix

Table 67: Same-estimand empty-ledger null on the first Sol trace.

A

is the changed-action proportion;

\Delta U

and

\Delta O

are cell-minus-aligned contrasts in

10^{-3}

normalized utility units and proportion units, respectively. Estimate is the point estimate; Lower and Upper delimit its 95% replicate-cluster bootstrap interval. Each row is a readout; the three metric groups give Estimate, Lower, and Upper.

Namespace	$\Delta U$			$\Delta O$	$A_{\rm rk}$			$D_{A}^{\rm v}$			$D_{A}^{\rm p}$
	Est.	Low.	Up.	Est.	Est.	Low.	Up.	Est.	Low.	Up.	Est.	Low.	Up.
Action	$-3.738$	$-4.620$	$-2.862$	$-0.248$	$0.946$	$0.927$	$0.964$	$0.246$	$0.197$	$0.296$	$0.154$	$0.120$	$0.191$
Alias	$-3.311$	$-4.168$	$-2.445$	$-0.200$	$0.878$	$0.847$	$0.908$	$0.410$	$0.369$	$0.452$	$0.327$	$0.282$	$0.375$
Opaque	$-2.415$	$-3.096$	$-1.741$	$-0.197$	$0.850$	$0.809$	$0.889$	$0.305$	$0.268$	$0.345$	$0.361$	$0.319$	$0.401$
Token-matched	$-1.075$	$-1.614$	$-0.525$	$-0.085$	$0.769$	$0.724$	$0.813$	$0.355$	$0.309$	$0.401$	$0.358$	$0.311$	$0.405$

Appendix

Table 68: Frozen Qwen3-8B namespace control under the focused cross-model profile. Each row uses the same selected adaptation trace, 192 family–context blocks, and 48 replicate streams. The endpoint panel reports the aligned memory policy minus the fixed mixed-action policy:

\Delta U_{\rm end}

is in

10^{-3}

normalized utility units and

\Delta O_{\rm end}

is the oracle-match difference. The three action panels report the pooled estimate and 95% replicate-cluster interval for the canonical rekey map (

A_{\rm rk}

), value reassignment (

D_{A}^{\rm v}

), and complete-pair transport (

D_{A}^{\rm p}

	$A$			$\Delta U_{\mathrm{C-A}}$			$\Delta O_{\mathrm{C-A}}$
Cell	Est.	Low.	Up.	Est.	Low.	Up.	Est.	Low.	Up.
Rekey	$1.000$	$1.000$	$1.000$	$-7.540$	$-8.790$	$-6.260$	$-0.074$	$-0.110$	$-0.040$
Key-slot	$0.734$	$0.677$	$0.792$	$-7.420$	$-9.650$	$-5.190$	$-0.081$	$-0.117$	$-0.045$
Value	$0.771$	$0.703$	$0.833$	$-6.020$	$-7.990$	$-4.120$	$-0.060$	$-0.101$	$-0.018$
Pair	$0.000$	$0.000$	$0.000$	$0.000$	$0.000$	$0.000$	$0.000$	$0.000$	$0.000$

Appendix

Table 69: Pooled uncertainty for UCB1 applied within family–context strata.

A

is the action proportion;

\Delta U_{\mathrm{C-A}}

and

\Delta O_{\mathrm{C-A}}

are cell-minus-aligned contrasts in

10^{-3}

normalized utility units and executor-agreement proportions, respectively. Point estimates and 95% bootstrap interval endpoints are pooled over 48 replicate streams and four public-data strata. Each row is a cell; the three metric groups give Estimate, Lower, and Upper.

		IID			Shift
Data	Cell	$A$	$\Delta U_{\mathrm{C-A}}$	$\Delta O_{\mathrm{C-A}}$	$A$	$\Delta U_{\mathrm{C-A}}$	$\Delta O_{\mathrm{C-A}}$
Breast cancer	Rekey	$1.000$	$-0.015$	$-0.057$	$1.000$	$0.002$	$0.090$
Breast cancer	Time	$0.000$	$0.000$	$0.000$	$0.000$	$0.000$	$0.000$
Breast cancer	Value	$0.000$	$0.000$	$0.000$	$0.000$	$0.000$	$0.000$
Breast cancer	Pair	$0.000$	$0.000$	$0.000$	$0.000$	$0.000$	$0.000$
Wine quality	Rekey	$1.000$	$-0.006$	$-0.049$	$1.000$	$-0.006$	$-0.044$

Appendix

Table 70: Public measured-outcome replay for the commutative count–sum ledger by stratum. Each stratum contains 1,152 future decisions across 48 replicate streams.

A

is the action proportion;

\Delta U_{\mathrm{C-A}}

and

\Delta O_{\mathrm{C-A}}

are cell-minus-aligned contrasts in normalized utility units and executor-agreement proportions, respectively.

	$A$			$\Delta U_{\mathrm{C-A}}$			$\Delta O_{\mathrm{C-A}}$
Cell	Est.	Low.	Up.	Est.	Low.	Up.	Est.	Low.	Up.
Rekey	$1.000$	$1.000$	$1.000$	$-0.006$	$-0.008$	$-0.005$	$-0.015$	$-0.061$	$0.030$
Key-slot	$0.432$	$0.391$	$0.469$	$-0.004$	$-0.006$	$-0.003$	$-0.027$	$-0.044$	$-0.010$
Value	$0.453$	$0.417$	$0.479$	$-0.005$	$-0.007$	$-0.004$	$-0.033$	$-0.050$	$-0.016$
Pair	$0.000$	$0.000$	$0.000$	$0.000$	$0.000$	$0.000$	$0.000$	$0.000$	$0.000$

Appendix

Table 71: Cluster uncertainty for the pooled public measured-outcome replay of the commutative count–sum ledger.

A

is the action proportion;

\Delta U_{\mathrm{C-A}}

and

\Delta O_{\mathrm{C-A}}

are cell-minus-aligned contrasts in normalized utility units and proportion units, respectively. Estimate is the point estimate; Lower and Upper delimit its 95% cluster-bootstrap interval over 48 replicate streams.

Stratum	$U$ range		$O$ range
	Minimum	Maximum	Minimum	Maximum
Pooled: primary	$0.275$	$0.320$	$-0.424$	$-0.391$
Source: low noise	$0.556$	$0.675$	$-0.578$	$-0.466$
Source: high noise	$0.623$	$0.700$	$-0.793$	$-0.705$
Temporal: low noise	$0.250$	$0.254$	$-0.664$	$-0.659$
Temporal: high noise	$0.091$	$0.144$	$-0.425$	$-0.342$

Appendix

Table 72: Primary-substrate sensitivity across five fixed placebo draws, each pooling the nine paired fixed-point-free map interventions over 48 replicate clusters.

U

and

O

are descriptive sensitivity ranges on their native fraction-difference scales; Minimum and Maximum give the range endpoints.

Time-preserving placebo interaction
Family	Context	Metric	Estimate	Lower	Upper
Pooled	Both	$U$	$0.327$	$0.316$	$0.338$
Pooled	Both	$O$	$-0.980$	$-1.010$	$-0.948$
Hypothesis	Low noise	$U$	$0.245$	$0.227$	$0.263$
Hypothesis	Low noise	$O$	$-1.231$	$-1.249$	$-1.211$
Hypothesis	High noise	$U$	$0.178$	$0.160$	$0.195$

Appendix

Table 73: Changed-substrate map-family sensitivity.

U

is the identity-minus-replay future-utility interaction and

O

is the difference between two executor-relative oracle-match changes on the native fraction-difference scale. As a difference of two proportion changes,

O

lies in

[-2,2]

and can have magnitude greater than one. The upper block reports point estimates with 95% cluster-bootstrap intervals; the lower block reports descriptive sensitivity ranges using Minimum and Maximum. All rows use the same 48 replicate clusters and are secondary structural diagnostics.

Contrast	Estimate	Lower	Upper
Pooled primary	1.000	1.000	1.000

Appendix

Table 74: Primary assignment-minus-renaming contrast. The percentile interval uses 10,000 complete-stream resamples within the three fixed 16-stream map strata. Every observed stream has the same contrast, producing the degenerate conditional bootstrap interval.

Comparison	A–D	W–Z
Consistent renaming (00–11)	0.000	0.000
Reassigned renaming (10–01)	0.000	0.000
Assignment (00–10)	1.000	1.000
Assignment (11–01)	1.000	1.000
Within cell 00	0.000	0.000
Within cell 01	0.000	0.000

Appendix

Table 75: Raw cross-call and within-cell disagreement for the joint history/menu control. Cross-call values average all four comparisons of two independent repeats; within-cell values compare the two repeats. Each entry averages 192 tasks in 48 streams.

	A–D				W–Z
Cell	$U$	$O$	$\Delta U$	$\Delta O$	$U$	$O$	$\Delta U$	$\Delta O$
00	0.669	0.219	0.000	0.000	0.669	0.219	0.000	0.000
01	0.664	0.281	$-0.005$	0.063	0.664	0.281	$-0.005$	0.063
10	0.664	0.281	$-0.005$	0.063	0.664	0.281	$-0.005$	0.063
11	0.669	0.219	0.000	0.000	0.669	0.219	0.000	0.000

Appendix

Table 76: Utility and oracle readouts for the joint history/menu control. Each namespace uses the same 192 frozen future tasks.

\Delta U

and

\Delta O

subtract cell 00; the evaluator and its tie rule are fixed.

Family	$n_{\rm op}$	$A_{\rm rekey}$	$D_{A}^{\rm value}$	$D_{A}^{\rm pair}$
Value–order	4	0.000	0.162	0.162
Key–value	2	0.667	0.021	0.000
Key–order	2	0.665	0.160	0.142

Appendix

Table 77: Held-out composite families, excluded from construction of the canonical-family rule. Responses follow Table 2 ;

n_{\rm op}

counts writers. Classification correctness was not evaluated.

Cell	Action	$\Delta U$	$\Delta O$	Action	$\Delta U$	$\Delta O$
	Fold I			Fold II
Rekey	0.753	$-0.602$	$-0.082$	0.620	0.870	0.027
Key-slot	0.243	$-0.476$	$-0.009$	0.240	0.285	0.003
Value	0.000	0.000	0.000	0.003	0.012	0.000
Pair	0.306	$-0.786$	$-0.027$	0.257	0.105	0.008

Appendix

Table 78: Measured-outcome replay. Fold I trains on streams 0–23 and evaluates on 24–47; Fold II reverses this split (24 evaluation streams each). Action is disagreement;

\Delta U

and

\Delta O

subtract aligned values. Normalized utility units are

10^{-3}

; action and oracle entries are proportions. Intervals: Table 56 .

Condition	$N_{S}$	$\Delta U$	$\|\Delta U\|$	$\|\Delta U\|\mid S$	Harm	Tie	Gain
Measured: rekey	48	0.134	15.088	22.115	0.376	0.250	0.375
Measured: key-slot	45	$-0.096$	6.100	25.812	0.433	0.152	0.416
Measured: pair	47	$-0.341$	7.227	25.784	0.455	0.127	0.418
Astra: reassignment	48	$-4.722$	21.477	21.477	0.375	0.260	0.365

Appendix

Table 79: Retrospective utility decomposition. Utility columns use

10^{-3}

units;

\Delta U

subtracts aligned utility. The first two utility columns average within each stream, then equally over 48 streams. The conditional absolute change and sign proportions first average over switched pairs within each stream, then over the

N_{S}

streams containing a switch. Measured rows pool both evaluation folds. The Astra row compares cells 10 and 00 with outcome values present.

Study	Input verification	Repeat control	Future outcomes
Joint ledger	All selected calls	Within condition	Archived tasks
Memory pipeline	All calls	Within condition	New task pools
Sol/Arm archive	Aligned, value, pair	Unavailable	Archived tasks
Other GPT-5.6 archives	Limited reconstruction	Unavailable	Archived tasks

Appendix

Table 80: Verification scope of the joint, memory, and archival interface evidence. New runs check server-accepted inputs, output schemas, and runtime metadata. The joint matrix includes replacements for 14 capacity failures; original and replacement attempts are retained. Archival reconstruction has the scope stated in Appendix J.2 .

	Shared		Trace 1		Trace 2		Trace 3
Rule	A	V	A	V	A	V	A	V
Mean	0.991	0.952	0.998	0.957	1.000	0.939	0.990	0.984
Sum	0.983	0.658	0.976	0.751	0.984	0.670	0.974	0.568
Count	0.983	0.658	0.976	0.751	0.984	0.670	0.974	0.557
Latest	0.988	0.663	0.997	0.761	0.990	0.665	0.969	0.542
Best	0.972	0.699	0.965	0.807	0.974	0.740	0.953	0.641

Appendix

Table 81: Post hoc Sol/Arm reference agreement. A and V denote aligned and value conditions. Shared uses the original histories; traces 1–3 use independently ordered histories on the same future tasks. Each estimate averages 48 streams. Intervals: Appendix J.5 .

Comparison	A–D	W–Z	Pooled
Consistent renaming (00–11)	0.000	0.000	0.000
Reassigned renaming (10–01)	0.000	0.000	0.000
Assignment (00–10)	1.000	1.000	1.000
Assignment (11–01)	1.000	1.000	1.000
Assignment minus renaming	1.000	1.000	1.000

Appendix

Table 82: Joint history/menu control with GPT-6 Astra. Comparisons report

T_{\mathrm{gr}}

; the last row gives mean assignment minus mean renaming. Within each namespace, responses are averaged over four tasks in each of 48 streams, using two fresh calls per cell. Namespaces have equal weight in the pooled values.

Comparator	Estimate	Lower	Upper
FIFO	3.042	0.092	6.153
Endpoint-selected binned mean	-0.292	-1.079	0.209
No memory	4.580	0.970	8.219

Appendix

Table 83: Audit-selected minus comparator utility on the equal-mixture test, in

10^{-3}

units. Lower and Upper are individual 97.5% percentile-bootstrap limits from 20,000 paired draws of 48 streams. The first two comparisons form the prespecified family with a Bonferroni 95% coverage target; bootstrap coverage is approximate. The no-memory comparison is descriptive.

Memory	Stored summaries	Retrieved text
FIFO	192	192
Binned mean (audit)	0	0
Binned mean (endpoint)	0	0
No memory	192	0

Appendix

Table 84: Changed memory artifacts after complete-event reordering. Each count has denominator 192 test blocks. Stored summaries are compared as a sorted multiset of displayed fields at six-decimal precision; undisplayed state and slot order are excluded. Retrieved text is compared exactly. No-memory retains an unused FIFO sidecar but exposes no retrieved text to the policy.

Regimen	Fit	Dev. excess BCE	Mapped aligned target acc.	Pair replay target acc.	Pair action	Lower	Upper
Ordinary	1	0.471	0.367	0.343	0.670	0.637	0.704
Ordinary	2	0.670	0.262	0.237	0.736	0.708	0.764
Ordinary	3	0.404	0.536	0.500	0.557	0.515	0.597
Ordinary	4	0.583	0.422	0.394	0.613	0.579	0.647
Ordinary	5	0.605	0.280	0.256	0.740	0.712	0.766
Permutation aug.	1	0.133	0.810	0.833	0.186	0.141	0.234

Appendix

Table 85: All completed learned-control fits. Fit indices 1–5 correspond respectively to model seeds 20260951, 20260952, 20260953, 20260954, and 20260955. Target accuracies use the mapped-aligned reference and the arbitrary complete-pair slot replay, respectively. Pair action is the mapped-aligned versus pair-slot action-change proportion; its Lower and Upper columns are 95% episode-bootstrap limits (96 held-out episodes; nine maps paired within episode). Excess BCE is binary cross-entropy less the soft-target entropy.

Metric	Unit	Estimate	Lower	Upper
Pair action change	proportion	-0.279	-0.300	-0.259
Mapped aligned target acc.	proportion	0.091	0.068	0.114
Pair replay target acc.	proportion	0.114	0.093	0.135
Aligned–replay utility	$10^{-3}$ normalized utility	0.555	-0.361	1.531
Replay–aligned oracle agreement	proportion	-0.002	-0.006	0.002

Appendix

Table 86: Permutation-augmented minus ordinary contrasts. The first three rows report the primary pair-slot readouts; the last two report secondary consequences. Intervals use a joint 4,096-draw bootstrap of the same 96 episode IDs across the five fixed seed pairs, with maps averaged within episode. Utility is in

10^{-3}

units; all other metrics are proportions.

Choice	Condition	$T_{\rm gr}$	Lower	Upper	Cross	Within	Aligned
First	Value reassigned	0.708	0.625	0.792	0.990	0.250	0.312
First	Pair transport	0.031	-0.031	0.104	0.292	0.208	0.312
First	Consistent renaming	-0.042	-0.099	0.026	0.323	0.417	0.312
Second	Value reassigned	0.542	0.438	0.646	1.000	0.438	0.479
Second	Pair transport	0.042	-0.052	0.141	0.542	0.521	0.479
Second	Consistent renaming	-0.052	-0.120	0.010	0.490	0.604	0.479

Appendix

Table 87: Action responses relative to aligned histories, with descriptive 95% intervals. Cross averages all four cross-repeat disagreements; Within and Aligned give each condition’s repeat disagreement. Each estimate averages the same 48 paired tasks. Later choices follow the preceding experiment feedback.

Choice	Estimate	Lower	Upper
First	0.677	0.568	0.776
Second	0.500	0.391	0.609
Third	0.500	0.391	0.604
Submit	0.875	0.812	0.932

Appendix

Table 88: Value-minus-pair response gaps,

T_{\rm gr}(\mathrm{value},\mathrm{aligned})-T_{\rm gr}(\mathrm{pair},\mathrm{aligned})

, with descriptive 95% intervals. This compares two responses to the same aligned reference.

Policy	Condition	Estimate	Lower	Upper
Agent	Aligned	0.618	0.598	0.639
Agent	Value reassigned	0.359	0.303	0.415
Agent	Pair transport	0.617	0.597	0.639
Agent	Consistent renaming	0.619	0.599	0.640
Random search	Aligned	0.610	0.588	0.632
Random search	Value reassigned	0.443	0.379	0.506

Appendix

Table 89: Final-test utility with descriptive 95% intervals. Agent estimates first average the two repeats within each task. References use their frozen choices on the same test pools.

Contrast	Estimate	Lower	Upper	Level
Pair transport minus aligned	0.000	-0.002	0.001	0.975
Value reassigned minus aligned	-0.259	-0.330	-0.190	0.975
Consistent renaming minus aligned	0.001	-0.001	0.003	0.950

Appendix

Table 90: Paired final-utility contrasts. The two primary contrasts use individual 97.5% bootstrap intervals, a Bonferroni adjustment for two comparisons; the renaming interval is descriptive.

Reference	Condition	Estimate	Lower	Upper
Random search	Aligned	-0.008	-0.028	0.014
Random search	Value reassigned	0.084	0.036	0.137
Random search	Pair transport	-0.008	-0.028	0.015
Random search	Consistent renaming	-0.009	-0.029	0.013
Initial incumbent	Aligned	-0.024	-0.039	-0.011
Initial incumbent	Value reassigned	-0.017	-0.035	-0.003

Appendix

Table 91: Reference-minus-agent utility under the same history condition, with descriptive 95% intervals. Random search has the same three-experiment allowance; the initial incumbent makes no new experimental calls. Both references use no model calls.

Condition	Distinct	Gap	Lower	Upper
Aligned	3.708	0.027	0.009	0.046
Value reassigned	3.417	0.264	0.208	0.321
Pair transport	3.583	0.027	0.009	0.046
Consistent renaming	3.896	0.027	0.008	0.045

Appendix

Table 92: Reference-minus-agent utility under the same history condition, with descriptive 95% intervals. Random search has the same three-experiment allowance; the initial incumbent makes no new experimental calls. Both references use no model calls.

Readout	Condition	Estimate	Lower	Upper
First action	Value reassigned	0.604	0.438	0.771
First action	Pair transport	0.042	0.000	0.125
First action	Consistent renaming	0.083	0.021	0.167
Final action	Value reassigned	0.167	0.042	0.312
Final action	Pair transport	0.000	0.000	0.000
Final action	Consistent renaming	0.000	0.000	0.000

Appendix

Table 93: Code-debugging replay readouts relative to aligned histories. Estimates are task-level means over 24 tasks; intervals are descriptive 95% bootstrap limits from 10,000 resamples of the 24 task values. First and Final are action-disagreement proportions; Hidden utility is the held-out test-score difference.

Figure 7: Cell-level joint black-box responses. Points are estimates and horizontal bars are 95% stream-bootstrap intervals over 48 streams. Rows use O/S for OPAQUE/SEMANTIC, the four history/menu cells, and the four replay forms. Panel A reports

T_{\mathrm{gr}}

against Full; panel B reports replay-minus-Full future utility.

Figure 9: Reference-rule agreement and utility. Each row is one form/namespace/cell combination: F, V, P, K, and U denote Full, Value, Pair, Key-slot, and Utility-masked; O and S denote OPAQUE and SEMANTIC. Colored points are the five prespecified reference rules and horizontal bars are 95% stream-bootstrap intervals over 48 streams. Undefined rules for Utility-masked histories are left blank. The figure is a compact display of the complete cell-level matrix; exact numeric values and joins remain in the reproducibility archive.

Group	Rule pair	Freq.	Nom. B	Nom. S	$\rho_{01}$		$\rho_{02}$		$\rho_{03}$
					B	S	B	S	B	S
g01	Mean–Sum	unbalanced	20	10	6	4	9	4	5	2
g02	Mean–Count	unbalanced	20	6	4	1	4	2	12	3
g03	Mean–Latest record	balanced	19	6	4	1	5	2	10	3
g04	Mean–Best	balanced	19	6	5	2	4	1	10	3
g05	Sum–Count	unbalanced	19	9	10	4	6	3	3	2

Appendix

Table 94: Shared metadata for the ten designed rule-disagreement groups. B and S denote block and stream counts; the six map columns report each quantity separately.

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Traces Agentic Evaluations Large Language Model Evaluation Surprisal

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When evaluator-derived step rewards are pooled or compared across scoring channels, their sign is treated as transportable. Yet the same frozen transition can change sign with the scoring channel. Process rewards vary agent states, while evaluator audits vary scoring configurations; neither first difference isolates their interaction. We define Agent Step Value (ASV) as channel-indexed target-margin gain and identify the missing state-by-channel interaction by replaying complete faces. Of 1,100 PubMed open question-answering transitions, 1,004 were complete across four cyclic layouts. Their mean update is positive under direct scoring (+0.163 [0.102, 0.218]) and negative with an externally generated view (-0.160 [-0.244, -0.079]), giving an interaction of -0.323 [-0.418, -0.232]. Across paired transitions, 507/1,004 cross zero in one direction or the other. Matched templates isolate a generated-minus-quote interaction of -1.121 [-1.534, -0.703]. Its direction remains negative after the readout and evaluator-stack changes, and quote yields a higher paired area under the receiver operating characteristic curve (AUC) for stored success at all three bridge vertices. Because the two views preserve the same task information conditional on the retained state, a representation-invariance null predicts equal responses and success rankings across them. ASV provides a transport audit for evaluator-derived step measurements; causal actor credit lies outside its estimand.

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