RoutePrism: Tracing Construction Order Effects in Agent Memory

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

cs.AISep 28, 2026

RoutePrism: Tracing Construction Order Effects in Agent Memory

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

Processing the same records in a different order can discard different evidence, yet endpoint accuracy alone cannot reveal what changed or whether it mattered. We introduce RoutePrism, a diagnostic protocol that builds memory twice from the same source pool in two processing orders, then traces which sources, compiled contexts, and answers differ. Because record content, timestamps, policy, and the answer model all stay fixed, any observed difference is localized to the memory construction step. A matched four-condition intervention tests whether a record displaced by reordering actually carried task-relevant evidence: restoring that single record recovers over 60 percentage points of lost accuracy, while substituting a non-supporting record of equal length does not. We evaluate the protocol on PersonaMem-32K (63 primary queries, 29 users) and 470 LongMemEval-S questions with histories spanning 38 to 62 sessions, replicating the core intervention across five answer models. Survivor selection, defined as the choice of which record a cluster retains, drives most source-level changes, while different memory policies (compaction, bounded recency, MemoChat-style summarization, A-MEM) produce distinct failure signatures at the source, context, and metadata layers.

Figures & tables

Figure 1: RoutePrism overview. Given a question and its source pool, we build memory in two processing orders, record which sources and contexts differ, and test whether the displaced evidence matters via a four-condition support-restoration intervention. The protocol isolates construction-order effects from answer-model noise.

Experiment	Policy or interface	Benchmark	Answer model	Queries	Users
Route diagnostics	Focal, Recent-3	PersonaMem	Luna	63	29
Support restoration	Focal	PersonaMem	Luna	33	21
Support restoration	Recent-3	PersonaMem	Luna	36	18
Mechanism localization	Focal schedules	PersonaMem	Luna	63	29
Policy interfaces	Lexical, cross-fitted	PersonaMem	Luna	589	37
Policy interfaces	MemoChat, A-MEM	PersonaMem	Luna	63	29

Table 1: Experiment overview. Queries and Users give each experiment’s analysis units; NR means the benchmark supplies no user identifier, and NA denotes a source-only measurement without an answer model. Best Matching 25 (BM25) is the lexical retriever for LongMemEval-S. Extended answer-bearing rows report Luna estimates except for model comparisons; the complete Qwen3-8B collection is retained, and its LongMemEval answers receive the same masked Terra judge.

		$D_{\mathrm{res}}$			$\Delta_{\mathrm{rep}}$
Policy	$J$	Estimate	Lower	Upper	Estimate	Lower	Upper
Focal	0.057	0.529	0.361	0.690	0.444	0.261	0.612
Recent-3	0.166	0.493	0.376	0.604	0.028	-0.183	0.240

Table 2: Primary exact-token route diagnostics. Each row uses 63 query pairs from 29 equally weighted users with one padding; the x control and full direct profiles are in Appendix I.3. Each route combines one formal and two fresh answers. Lower and Upper are 95% user-bootstrap limits.

Figure 2: Support restoration (a–c) and state reuse (d). $S^{+}$ , Res., $S^{-}$ , and Pl. denote support present, rescue, support absent, and matched non-support replacement. Contrasts compare against $S^{-}$ . Panel (d) uses repeated answers, with $H_{\mathrm{in}}=H_{\mathrm{within}}$ . The full route profiles are in Appendix I.3 .

Policy	Q	U	Pres.	Abs.	Res.	Repl.	Q	U	Pres.	Abs.	Res.	Repl.
	Primary						All eligible
Focal	33	21	0.875	0.210	0.881	0.280	78	33	0.894	0.191	0.879	0.239
Recent-3	36	18	0.940	0.269	0.917	0.167	71	28	0.868	0.225	0.927	0.109

Table 3: PersonaMem whole-record restoration. Primary is the semantic-consensus set; All eligible contains every fact-recall pair passing the structural gate. Pres., Abs., Res., and Repl. denote support present, support absent, restored support, and matched non-support replacement. In the contrast panel, R–A is restored minus absent and R–P is restored minus replacement. LongMemEval-S is reported in Section 4.5 . Estimates and 95% bootstrap limits weight users equally; full intervals appear in Tables 26 , 50 , 51 , and 66 .

Operation	$H$	$\Delta$	Changed	$H$	$\Delta$	Changed	$H$	$\Delta$	Changed
	Replay			Half-swap			Odd-even
Both operations	0.603	0.390	63	0.350	0.011	63	0.425	0.182	43
Survivor selection	0.558	0.347	63	0.367	0.028	63	0.420	0.202	41
Clustering only	0.103	0.000	4	0.135	-0.003	2	0.115	0.080	2

Table 4: Mechanism localization by schedule using single-draw

H

and

\Delta

. Estimates weight users equally; CIs are in Table 32 . Changed counts pairs with different exposed source sets; the denominator is 63 in every row.

	Retained sessions			Exposed sessions
Policy	Overlap	Recall F	Recall R	Overlap	Recall F	Recall R
Recent-8	0.000	0.215	0.146	0.000	0.209	0.140
Recent-16	0.000	0.381	0.319	0.000	0.350	0.295
Recent-32	0.349	0.688	0.619	0.287	0.598	0.539
Focal	0.438	0.157	0.113	0.227	0.146	0.106

Table 7: LongMemEval-S retention and exposure over 470 questions. Overlap is source-set Jaccard; recall is the fraction of published evidence sessions. F/R denote import order; intervals and source-order controls are in Appendix O .

Condition	Luna			Qwen3-8B
	Estimate	Lower	Upper	Estimate	Lower	Upper
Present	1.000	1.000	1.000	0.875	0.750	1.000
Absent	0.000	0.000	0.000	0.000	0.000	0.000
Restored	1.000	1.000	1.000	0.917	0.792	1.000
Replacement	0.042	0.000	0.125	0.042	0.000	0.125

Table 8: LongMemEval-S four-condition answer accuracy on 24 single-session-user questions. Both answer models are scored by the same masked Terra max judge. Lower and Upper are 95% question-bootstrap limits.

Model	$H_{\mathrm{focal}}$	$\Delta_{\mathrm{focal}}$	Focal $R$ – $A$	Focal $R$ – $P$	Recent $R$ – $A$	Recent $R$ – $P$
Astra	0.581	0.442	0.808	0.756	0.671	0.819
Sol	0.559	0.399	0.764	0.683	0.685	0.759
Terra	0.558	0.376	0.774	0.681	0.681	0.810
Luna	0.614	0.437	0.671	0.601	0.648	0.750
Qwen3-8B	0.338	0.175	0.214	0.143	0.194	0.167

Table 9: Core cross-model replication on fixed PersonaMem inputs.

H

and

\Delta

use the focal 63-pair route trace;

R

–

A

(rescue minus absent) and

R

–

P

(rescue minus replacement) use the support restoration sets. All entries are equal-user point estimates; 95% intervals are in Appendix I.12 .

Appendix figures & tables60 assets

Supplementary material from the paper’s appendix.

Appendix

					Label counts
Read	Rule	Model	Queries	Users	Admissible	Ambiguous	Inadmissible
Record pass A	Single	Independent	146	37	66	59	21
Record pass B	Single	Independent	146	37	115	23	8
Admissible intersection	Two reads	Independent	59	29	NA	NA	NA
Benchmark fact recall	Taxonomy	Benchmark	146	37	NA	NA	NA

Appendix

Table 10: Semantic sensitivity under independent selection rules. Panel A reports screen counts; panels B and C report route coordinates with 95% bootstrap limits, using equal weight for users. Route coordinates use the retained answer traces. NA denotes not applicable.

Condition	Correctness		Answer relation
	Correct	Accuracy	Same as present	Change from absent
Support present	8	1.000	8	5
Support absent	3	0.375	3	0
Support rescue	8	1.000	8	5
Replacement without direct support	4	0.500	4	1

Appendix

Table 11: Matched support rescue for two support-loss pairs from the cross-fitted policy. Each condition has eight answer draws; source count and full-prompt token count are matched within each pair.

Reading specification			Label counts
Read	Rule	Model	Admissible	Ambiguous	Inadmissible
Pass A	Single read	Luna max	70	8	68
Pass B	Single read	Luna max	77	12	57
Third context	Single read	Luna max	25	2	119
Strict plurality	Majority	L/L/L	64	10	72
Third model	Single read	Terra max	58	4	84

Appendix

Table 12: Readings across contexts and models. Every reading sees the same 146 complete source pools under a rubric that withholds outcome information. Labels are reported as admissible, ambiguous, and inadmissible counts; L denotes Luna max, T denotes Terra max, and S denotes Sol max.

Readers	Rule	Queries	Users	Estimate	Lower	Upper	Estimate	Lower	Upper
				$H_{\times}$			$D_{\mathrm{res}}$
L/L/T	Majority	70	31	0.594	0.470	0.713	0.469	0.339	0.602
L/L/T	Unanimity	48	26	0.529	0.380	0.678	0.433	0.288	0.577
L/L/S	Majority	69	32	0.599	0.478	0.715	0.463	0.332	0.598
L/L/S	Unanimity	50	27	0.585	0.441	0.725	0.474	0.319	0.623

Appendix

Table 13: Sensitivity of the semantic gate across models. Route quantities use the retained Luna traces; intervals are 95% user-bootstrap intervals. The consensus from two Luna readings is the prespecified primary semantic stratum; L, T, and S denote Luna, Terra, and Sol max readings.

	$D_{\mathrm{res}}$			$\Delta_{\mathrm{rep}}$
Variant	Estimate	Lower	Upper	Estimate	Lower	Upper
A	0.524	0.361	0.686	0.439	0.254	0.611
B	0.507	0.361	0.649	0.345	0.144	0.534

Appendix

Table 14: Focal estimates after excluding identical-option queries. Each row contains 61 pairs from 29 users and combines one formal answer with two fresh draws per route. A and B use the original padding variants. Lower and Upper are 95% percentile limits from 10,000 user-bootstrap resamples.

Stratum	Queries	Users	Estimate	Lower	Upper	Estimate	Lower	Upper
			$H_{\times}$			$H_{\mathrm{within}}$
All targets	34	20	0.555	0.394	0.715	0.107	0.040	0.185
Support present	18	13	0.712	0.538	0.865	0.135	0.048	0.240
Support absent	16	11	0.409	0.182	0.636	0.057	0.000	0.136

Appendix

Table 15: Multiple-question consequences of fixed states under overall and support-constrained strata. Estimates average padding variants before assigning equal weight to users; Lower and Upper columns give 95% bootstrap limits. Targets in the support-present stratum differ in direct support across the paired states; targets in the support-absent stratum expose no direct support under either route.

	Coverage			Changed pairs
Policy	Users	Targets	Multi	$\Delta S$	$\Delta C$
MemoChat	20	34	8	2	68

Appendix

Table 16: Persistent MemoChat continuation. State reuse reports users, targets, users with at least two targets (Multi), changed source lineage (

\Delta S

), and changed context (

\Delta C

). Profile estimates give equal weight to users; Lower and Upper columns give 95% bootstrap limits for target–padding-group summaries, with users as the resampling unit.

Threshold	Survivor rule	Change	Forward	Reverse	Uniform
0.025	Last arrival	0.806	0.105	0.635	0.304
0.025	First arrival	0.806	0.635	0.070	0.301
0.025	Largest source position	0.019	0.105	0.070	0.099
0.055	Last arrival	0.815	0.116	0.635	0.316
0.055	First arrival	0.810	0.635	0.116	0.319
0.055	Largest source position	0.040	0.116	0.116	0.118

Appendix

Table 17: Exhaustive survivor analysis on 63 queries from 29 users. Change is the probability of a survivor-set difference from forward construction under uniform permutations. Forward, Reverse, and Uniform give direct-support retention under the respective arrival distributions. All entries weight users equally.

Condition	$H$			$\Delta$
	Estimate	Lower	Upper	Estimate	Lower	Upper
Raw	0.149	0.115	0.184	$-0.023$	$-0.044$	$-0.002$
Canonical	0.166	0.128	0.208	0.016	$-0.018$	0.048
Arrival route	0.509	0.449	0.569	0.127	0.074	0.183
Preserved	0.150	0.121	0.181	$-0.007$	$-0.041$	0.027
Gated	0.160	0.125	0.200	$-0.020$	$-0.057$	0.014

Appendix

Table 18: Complete policy and provenance condition estimates. Lower and Upper columns give 95% bootstrap limits with equal weight for users; retained-state and length diagnostics are in Table 28 .

	$\Gamma_{H}$			$\Gamma_{\Delta}$
Comparison	Estimate	Lower	Upper	Estimate	Lower	Upper
Exchangeable (storage permutation)	0.528	0.426	0.624	0.302	0.192	0.414
Omnibus (reversal diagnostic)	0.343	0.275	0.411	0.111	0.045	0.179

Appendix

Table 19: Primary paired contrasts and diagnostics at the answer boundary. Accuracy contrasts are gated minus preserved. Lower and Upper columns give 95% bootstrap limits with equal weight for users.

Stratum	Queries	Users	Estimate	Lower	Upper	Estimate	Lower	Upper
			$\Gamma_{H}$			$\Gamma_{\Delta}$
Exchangeable	146	37	0.528	0.426	0.624	0.302	0.192	0.414
Residual	205	37	0.317	0.229	0.410	0.102	0.017	0.185

Appendix

Table 20: Semantic-stratum summaries. Panel A reports storage-policy contrasts

\Gamma_{H}

and

\Gamma_{\Delta}

for exchangeable and residual queries. Panel B reports raw reversal coordinates

H,\Delta

and chronology-gated provenance contrasts

\Gamma_{H}^{\mathrm{prov}},\Gamma_{\Delta}^{\mathrm{prov}}

for the same 238 temporal queries from 33 users; the superscript

\mathrm{prov}

denotes gated minus preserved. Lower and Upper give 95% user-bootstrap limits. Estimates weight users equally; raw temporal reversal is retained as a chronology diagnostic.

			Label counts
Audit quantity	Queries	Users	Admissible	Ambiguous	Inadmissible
Complete pool	146	37	NA	NA	NA
Pass A	146	37	70	8	68
Pass B	146	37	77	12	57
Unanimous admissible	63	29	63	NA	NA

Appendix

Table 21: Semantic sensitivity audit over complete pools. Panel A reports the outcome-blind screen, Panel B reports inter-reader agreement, and Panel C reports storage-policy contrasts

\Gamma_{H}

and

\Gamma_{\Delta}

on the retained intersection. Lower and upper columns are 95% bootstrap limits with equal weight for users. NA means not applicable; NR means not reported.

Reading A	Reading B
	Admissible	Ambiguous	Inadmissible
Admissible	63	2	5
Ambiguous	7	1	0
Inadmissible	7	9	52

Appendix

Table 22: Confusion matrix for two independent readings of complete pools. Rows are reading A labels and columns are reading B labels; the unanimous-admissible cell defines the retained sensitivity subset.

Mask	Queries	Users	Estimate	Lower	Upper	Estimate	Lower	Upper
			$D_{\mathrm{res}}$			$\Delta_{\mathrm{rep}}$
A admissible	70	31	0.496	0.370	0.632	0.441	0.259	0.605
B admissible	77	33	0.484	0.347	0.619	0.351	0.172	0.518
Consensus	63	29	0.459	0.322	0.598	0.403	0.213	0.580

Appendix

Table 23: Sensitivity of the canonicalized two-draw route profile to the fixed semantic screen. The

H_{\mathrm{eq}}

panel reports the equal-user-weighted rate of answer changes with unchanged correctness, where

H_{\mathrm{eq},q}=\mathbf{1}[a_{q}^{(f)}\neq a_{q}^{(r)}\ \land\ c_{q}^{(f)}=c_{q}^{(r)}]

. Lower and upper columns give 95% bootstrap limits with equal weight for users.

				$H$			$\Delta$
Stratum	Support	Queries	Users	Estimate	Lower	Upper	Estimate	Lower	Upper
Consensus	Changed	39	26	0.724	0.571	0.865	0.583	0.349	0.792
Consensus	Preserved	24	16	0.284	0.112	0.479	0.125	0.000	0.281
Coverage	Changed	92	37	0.720	0.628	0.813	0.494	0.354	0.631
Coverage	Preserved	54	26	0.500	0.351	0.649	0.056	$-0.028$	0.163
Consensus	Difference	NA	13	0.359	0.013	0.686	0.545	0.250	0.814

Appendix

Table 24: Answer-bearing support localization. Rows give estimates with equal weight for users; lower and upper columns are 95% bootstrap limits. Support status records whether the source set that directly supports the gold option changes. Difference reports the within-user changed-minus-preserved contrast among users represented in both groups: 13 for Consensus and 26 for Coverage. NA means not applicable.

Support present accuracy			Support removed accuracy			Present minus removed accuracy
Estimate	Lower	Upper	Estimate	Lower	Upper	Estimate	Lower	Upper
0.902	0.833	0.960	0.188	0.069	0.326	0.714	0.569	0.844

Appendix

Table 25: Controlled support intervention at the answer boundary. The support-presence estimates use 35 eligible pairs from 23 users; the identity-swap diagnostic uses 4 additional pairs from 4 users. The Lower and Upper columns give 95% bootstrap confidence limits with equal user weight; identity-swap rows are a separate diagnostic.

	Accuracy
Condition	Estimate	Lower	Upper
Support present	0.875	0.778	0.952
Support absent	0.210	0.087	0.349
Support rescue	0.881	0.790	0.952
Support placebo	0.280	0.141	0.440

Appendix

Table 26: Route-support rescue estimates for 33 eligible pairs from 21 users with equal selected-source counts. Lower and upper columns give 95% bootstrap limits with equal weight for users.

Condition	$\Gamma_{H}$			$\Gamma_{\Delta}$
	Estimate	Lower	Upper	Estimate	Lower	Upper
Overlap-IDF check	0.360	0.311	0.409	0.124	0.055	0.190
Recent window versus source	0.302	0.256	0.349	0.071	0.013	0.128
Utility buffer versus source	0.043	$-0.002$	0.089	$-0.004$	$-0.039$	0.030
Provenance gate	0.010	$-0.032$	0.052	$-0.013$	$-0.049$	0.025

Appendix

Table 27: Secondary policy contrasts on complete 589-query matrices from 37 users. The overlap check uses inverse document frequency (IDF) weighting. Each contrast subtracts the route statistic for the second representation from that for the first: compressed minus canonical-compressed (overlap-IDF identity check), bounded-recent-3 minus bounded-source-3, utility-arrival-3 minus utility-source-3, and provenance-gated minus provenance-preserved. The columns report

\Gamma_{H}

and

\Gamma_{\Delta}

for disagreement and replay-minus-forward correctness change, respectively. For every row, the Estimate, Lower, and Upper columns report the equal-user-weighted point estimate and its 95% user-clustered bootstrap limits.

Condition	Jaccard similarity $J$			Context length
	Estimate	Lower	Upper	Forward	Replay
Raw	1.000	1.000	1.000	6562	6562
Canonical	1.000	1.000	1.000	2766	2766
Arrival route	0.045	0.009	0.081	2766	4181
Preserved	1.000	1.000	1.000	6992	6992
Bounded recent (3)	0.121	0.088	0.153	6716	6967

Appendix

Table 28: Complete retained-context diagnostics on the complete 589-query matrix from 37 users. The Estimate, Lower, and Upper columns give the Jaccard similarity

J

and its 95% bootstrap confidence limits with equal user weight; length columns report character-derived context-length proxies under forward and replay order.

Path	Schedule	$\delta_{H}^{\mathrm{op}}$			$\delta_{\Delta}^{\mathrm{op}}$
		Estimate	Lower	Upper	Estimate	Lower	Upper
Both operations	Replay	0.360	0.303	0.420	0.171	0.094	0.251
Both operations	Half-swap	0.261	0.202	0.327	0.132	0.054	0.211
Both operations	Odd-even	0.203	0.129	0.279	0.077	$-0.001$	0.162
Survivor selection	Replay	0.312	0.255	0.370	0.151	0.081	0.223
Survivor selection	Half-swap	0.238	0.175	0.309	0.099	0.032	0.167

Appendix

Table 29: Operation-versus-canonical contrasts

\delta_{H}^{\mathrm{op}}

and

\delta_{\Delta}^{\mathrm{op}}

by schedule on the complete 589-query matrix from 37 users. The Lower and Upper columns give 95% bootstrap confidence limits with equal user weight.

	Replay		Half-swap		Odd-even
Path	$J$	$C_{\mathrm{chg}}$	$J$	$C_{\mathrm{chg}}$	$J$	$C_{\mathrm{chg}}$
Survivor selection	0.045	1.000	0.054	1.000	0.414	0.622
Clustering only	0.973	0.054	0.986	0.027	0.986	0.027

Appendix

Table 30: State-layer diagnostics for the operation matrix on the complete 589-query matrix from 37 users. Survivor selection varies representatives with arrival order under a fixed partition; clustering only varies clustering, with representatives fixed to source order. Entries give equal-user-weighted estimates over 37 users;

J

is source-set overlap and

C_{\mathrm{chg}}

is the fraction of paired serialized contexts that differ, with

C_{\mathrm{chg},q}=\mathbf{1}[C_{q}^{(f)}\neq C_{q}^{(r)}]

Operation	Schedule	$\delta_{H}^{\mathrm{op}}$			$\delta_{\Delta}^{\mathrm{op}}$
		Estimate	Lower	Upper	Estimate	Lower	Upper
Survivor selection	Replay	0.531	0.382	0.679	0.356	0.149	0.553
Survivor selection	Half-swap	0.310	0.164	0.466	0.037	$-0.138$	0.198
Survivor selection	Odd-even	0.355	0.180	0.531	0.210	0.021	0.399
Clustering only	Replay	0.056	$-0.037$	0.172	0.013	$-0.097$	0.117
Clustering only	Half-swap	0.019	$-0.092$	0.129	0.010	$-0.106$	0.121

Appendix

Table 31: Operation-versus-canonical contrasts on the primary semantic stratum of 63 queries from 29 users. Lower and upper columns give 95% bootstrap limits with equal weight for users.

Path	Schedule	$H$			$\Delta$			Changed
		Estimate	Lower	Upper	Estimate	Lower	Upper
Both	Replay	0.603	0.460	0.740	0.390	0.183	0.583	63
Both	Half-swap	0.350	0.210	0.496	0.011	$-0.161$	0.180	63
Both	Odd-even	0.425	0.278	0.578	0.182	0.005	0.357	43
Survivor	Replay	0.558	0.407	0.706	0.347	0.140	0.540	63
Survivor	Half-swap	0.367	0.231	0.511	0.028	$-0.149$	0.197	63

Appendix

Table 32: Coordinates for each operation on 63 queries from 29 users. Both denotes the two operations following arrival order; Survivor denotes survivor selection following arrival order; and Cluster denotes clustering following arrival order with survivor choice fixed to source order. Changed is an integer count of pairs with different exposed source sets; the denominator is 63 in every row. Entries weight users equally; lower and upper columns are 95% bootstrap limits.

Question	Fixed object			Interpretation
	User	Query	Evidence
Order	same	same	Source pool	Changes in exposed sources and contexts
Operation	same	same	Source pool	Contributions of clustering and survivor selection
Support	same	same	Pool and source count	Task value of the displaced support record
Answers	same	same	Prompt and context	Variation within the answer model
Reuse	same	new	Constructed state	Effects on another question from the same user

Appendix

Table 33: Objects held fixed and interpretations of the paired comparisons. Restoration changes source identities while preserving the pool and exposed source count.

Study	Comparison		Observation		Endpoint
	Fixed object	Route boundary	Observable state	State–task link
Stable-RAG	Retrieved set	Prompt order	Hidden state	Prompt and answer	Stability
SegTreeMem	Events	Build order	Segment tree	State and utility	Utility
StateAud.	Trace	Update path	Recorded state	State and repair	Repair
Faulty	Trace	Consolidation	Text state	Text and utility	Consolidation
AttriMem	Policy	Attribution	Token attribution	Score and learning	Learning

Appendix

Table 34: Comparison planes for adjacent order and memory evaluations. Columns separate the fixed object, route boundary, observable state, state–task link, and endpoint. StateAud., Selection Int., and Faulty denote StateAuditor, Selection Integrity, and Useful Memories Become Faulty, respectively.

Comparison	Estimate	Lower	Upper
Display	0.013	-0.010	0.040
Construction, native layout	0.089	0.008	0.195
Construction, reversed layout	0.029	0.000	0.072
Construction, mean layouts	0.059	0.016	0.112
Construction minus display	0.046	0.004	0.101

Appendix

Table 35: Fresh MemoChat residual contrasts. Every row uses 63 queries and 29 users; Lower and Upper are 95% limits. The final row is a paired difference, computed before bootstrap resampling.

Policy	Queries	Users	Prompt pairs	Identical
Focal	33	21	66	62
Recent-3	36	18	36	0

Appendix

Table 36: Exact full-prompt identity between Present and Restored. Prompt pairs counts query–padding combinations: two per focal query and one per recent-policy query. Identical counts equal prompt texts; repeated answer draws do not add prompt pairs.

		$D_{\mathrm{res}}$			$\Delta_{\mathrm{rep}}$
Trace	$m$	Estimate	Lower	Upper	Estimate	Lower	Upper
F-EA	2	0.517	0.346	0.683	0.426	0.241	0.606
F-EB	2	0.538	0.393	0.686	0.327	0.112	0.533
M-C	6	0.039	0.004	0.092	0.038	-0.017	0.112

Appendix

Table 37: Fresh-answer estimates for 63 queries from 29 users in every row.

m

is the number of fresh draws per route and prompt. F-EA/F-EB and R-EA/R-EB denote focal/recent traces with padding A/B; A and B retain the original padding variants. Lower and Upper are 95% intervals from 10,000 user-bootstrap resamples with seed 2026091011.

	Direct profile			Repeated answers
Trace	$J$	$H_{1}$	$\Delta_{1}$	$H_{\times}$	$H_{\mathrm{within}}$	$D_{\mathrm{res}}$	$\Delta_{\mathrm{rep}}$
F-EA	0.057	0.631	0.480	0.630	0.101	0.529	0.444
F-EB	0.057	0.528	0.394	0.593	0.080	0.513	0.349
R-EA	0.166	0.564	0.071	0.586	0.093	0.493	0.028
R-EB	0.166	0.534	$-0.017$	0.527	0.144	0.383	$-0.002$

Appendix

Table 38: Profiles for exact-token traces F-E (focal) and R-E (Recent-3). A and B denote padding with one and x , respectively.

H_{1}

and

\Delta_{1}

use one formal answer per route; repeated estimates combine that answer with two fresh draws per route. Estimates weight users equally. Every row contains 63 query pairs from 29 users.

$H$			$\Delta$
Estimate	Lower	Upper	Estimate	Lower	Upper
0.538	0.387	0.683	0.336	0.138	0.528

Appendix

Table 39: Exact-token matching on the primary semantic stratum of 63 queries from 29 users. Estimates give equal weight to users; lower and upper columns give 95% user-bootstrap limits.

Padding	$H$			$\Delta$
	Estimate	Lower	Upper	Estimate	Lower	Upper
F-EA	0.631	0.484	0.772	0.480	0.286	0.657
F-EB	0.528	0.380	0.670	0.394	0.214	0.564

Appendix

Table 40: Directly retained equal token route trace with canonical display. Lower and upper columns give 95% bootstrap limits with equal weight for users; both padding rows contain 63 query pairs from 29 users, and all 63 pairs have different exposed source sets.

	$H_{\times}$			$H_{\mathrm{within}}$			$D_{\mathrm{res}}$
Trace	Estimate	Lower	Upper	Estimate	Lower	Upper	Estimate	Lower	Upper
F-EA	0.630	0.497	0.754	0.101	0.039	0.175	0.529	0.361	0.690
F-EB	0.593	0.459	0.720	0.080	0.034	0.137	0.513	0.374	0.652

Appendix

Table 41: Repeated-answer estimands for focal exact-token trace F-E (one formal and two fresh answers per route). Lower and upper columns give 95% bootstrap limits with equal weight for users.

Figure 3: Single-draw route profiles for the focal compactor, bounded recent policy, and MemoChat. Panels (a)–(c) show source change, $H_{1}$ , and $\Delta_{1}$ ; panel (d) shows correctness transitions, with C denoting correct and I incorrect. Focal and Recent combine the two padding variants within users. Dots denote user means; boxes show the median and interquartile range, and whiskers extend to observations within 1.5 interquartile ranges.

	Forward correct		Forward incorrect
Padding	Replay correct	Replay incorrect	Replay correct	Replay incorrect
Matched A	8	2	29	24
Matched B	7	2	27	27

Appendix

Table 42: Correctness transitions in the directly retained equal token trace with canonical display. Column groups fix forward correctness; subcolumns give replay correctness.

Schedule	$\Gamma_{H}$			$\Gamma_{\Delta}$
	Estimate	Lower	Upper	Estimate	Lower	Upper
Replay	$-0.017$	$-0.055$	0.020	$-0.034$	$-0.068$	$-0.003$
Half-swap	$-0.007$	$-0.044$	0.029	$-0.047$	$-0.080$	$-0.015$
Odd-even	0.000	$-0.032$	0.037	$-0.049$	$-0.077$	$-0.020$

Appendix

Table 43: Policy contrasts on users held out from fitting. Lower and upper columns give 95% bootstrap limits with equal weight for users.

Case	Coverage		State change			Task
	Pools	Users	Visible	Support	Loss	Answer
All audited	146	37	15	9	2	1
Visible change	15	3	15	9	2	1
Direct support change	9	3	9	9	2	1
Support loss	2	2	2	2	2	1

Appendix

Table 44: Support-layer localization for the cross-fit policy on held-out users. Counts use the same 146 query cards and support labels collected without outcome information.

Policy	Changed fraction	Estimate	Lower	Upper
Arrival route	0.068	0.014	$-0.006$	0.039
Source stable	0.000	$-0.003$	$-0.013$	0.007
Arrival minus source	0.068	0.017	$-0.004$	0.043

Appendix

Table 45: Repeated answer route decomposition. Lower and upper columns give 95% bootstrap limits with equal weight for users.

Subset	$H$			$\Delta$
	Estimate	Lower	Upper	Estimate	Lower	Upper
All queries	0.145	0.111	0.181	$-0.029$	$-0.057$	$-0.002$
Selection changed (40)	0.301	0.118	0.400	$-0.092$	$-0.200$	0.000
Selection unchanged (549)	0.125	0.093	0.158	$-0.023$	$-0.050$	0.003

Appendix

Table 46: Canonical serialization route contrasts. Lower and upper columns give 95% bootstrap limits with equal weight for users.

$H_{\times}^{(m)}$			$H_{\mathrm{within}}^{(m)}$
Estimate	Lower	Upper	Estimate	Lower	Upper
0.368	0.144	0.533	0.139	0.088	0.200

Appendix

Table 47: Fresh answer extension on the 40 canonical pairs whose selected source sets differ. Lower and upper columns give 95% bootstrap limits with equal weight for users.

Model	$H_{\mathrm{focal}}$	$\Delta_{\mathrm{focal}}$	Focal $R$ – $A$	Focal $R$ – $P$	Recent $R$ – $A$	Recent $R$ – $P$
Astra	0.581	0.442	0.808	0.756	0.671	0.819
Sol	0.559	0.399	0.764	0.683	0.685	0.759
Terra	0.558	0.376	0.774	0.681	0.681	0.810
Luna	0.614	0.437	0.671	0.601	0.648	0.750
Qwen3-8B	0.338	0.175	0.214	0.143	0.194	0.167

Appendix

Table 48: Core answer-model replication on fixed PersonaMem inputs.

R

–

A

is rescue minus absent and

R

–

P

is rescue minus matched non-support replacement. Entries are equal-user point estimates.

	$\Delta_{\mathrm{focal}}$		Focal $R$ – $A$		Focal $R$ – $P$		Recent $R$ – $A$		Recent $R$ – $P$
Model	Lower	Upper	Lower	Upper	Lower	Upper	Lower	Upper	Lower	Upper
Astra	0.260	0.614	0.649	0.948	0.593	0.897	0.509	0.819	0.704	0.926
Sol	0.218	0.570	0.607	0.903	0.524	0.829	0.551	0.810	0.653	0.861
Terra	0.182	0.557	0.619	0.917	0.524	0.823	0.537	0.815	0.690	0.917
Luna	0.265	0.598	0.500	0.821	0.440	0.754	0.519	0.773	0.639	0.856
Qwen3-8B	0.043	0.319	0.071	0.381	-0.071	0.341	0.083	0.333	0.042	0.319

Appendix

Table 49: 95% user-bootstrap intervals for the core cross-model replication. Point estimates are in Table 48 ; each entry here reports Lower and Upper only.

R

–

A

and

R

–

P

use the definitions in that table.

Support present			Support absent			Restoration			Replacement
Estimate	Lower	Upper	Estimate	Lower	Upper	Estimate	Lower	Upper	Estimate	Lower	Upper
0.940	0.866	1.000	0.269	0.144	0.407	0.917	0.833	0.981	0.167	0.074	0.273

Appendix

Table 50: Bounded-recent-3 support restoration on 36 pairs from 18 users. Each condition has three fresh answers per pair. Lower and Upper are 95% user-bootstrap limits; estimates give users equal weight. Replacement inserts an independent record without direct support.

Scope	Queries	Users	Estimate	Lower	Upper	Estimate	Lower	Upper	Estimate	Lower	Upper	Estimate	Lower	Upper
			Present			Absent			Restored			Replacement
Primary	33	21	0.875	0.778	0.952	0.210	0.087	0.349	0.881	0.790	0.952	0.280	0.141	0.440
All eligible	78	33	0.894	0.831	0.948	0.191	0.113	0.279	0.879	0.800	0.942	0.239	0.134	0.354
Outside primary	45	27	0.906	0.832	0.968	0.150	0.074	0.234	0.881	0.785	0.955	0.149	0.058	0.260

Appendix

Table 51: Expanded PersonaMem restoration accuracies. Primary reproduces the frozen semantic-consensus analysis; All eligible includes every structurally eligible fact-recall query; Outside primary contains the added queries only. Estimates and Lower/Upper are 95% user-bootstrap limits.

	Changed pairs
Policy	Source changes	Context changes	Queries
MemoChat	1	63	63

Appendix

Table 52: Direct MemoChat route trace on the semantic consensus stratum. This table is separate from the all-pool coverage matrix; estimates weight users equally, the Lower and Upper columns give 95% bootstrap limits, and Queries gives the denominator for all change counts.

$H_{\times}$			$H_{\mathrm{within}}$
Estimate	Lower	Upper	Estimate	Lower	Upper
0.106	0.042	0.186	0.069	0.030	0.114

Appendix

Table 53: Repeated answer decomposition for the MemoChat route pair. The Lower and Upper columns give 95% bootstrap limits with equal user weight.

	Changed pairs
Policy	Signature changes	Source changes	Context changes	Queries
A-MEM	63	0	0	63

Appendix

Table 54: Independent A-MEM boundary check. The Lower and Upper columns are 95% bootstrap limits with equal user weight.

Trace	Experiment	Model	Queries	Users	$m$
F-C	Focal canonical repeat	Luna	63	29	2
F-E	Focal exact matched routes	Luna	63	29	3
R-E	Recent-3 exact matched routes	Luna	63	29	3
F-S	Focal restoration	Luna	33	21	2
R-S	Recent-3 restoration	Luna	36	18	3
F-S+	Focal restoration, all eligible	Luna	78	33	2

Appendix

Table 55: Index of principal answer experiments.

m

counts answers per route or condition and padding variant. Exact focal routes combine one formal and two fresh draws; MemoChat combines one original and six fresh draws. F-S+ and R-S+ include all structurally eligible PersonaMem restoration pairs. A-MEM uses the corrected query-specific matrix. Mechanism and streaming rows describe the full retained coverage; their primary analyses use the specified semantic subsets. NR means not reported; LongMemEval supplies no user identifiers. Luna is the reporting model for extended rows unless a model comparison is shown.

			Source set		Answer		Correctness
Policy	Pairs	Changed	Miss	Extra	Miss	Extra	Miss	Extra
Focal	126	126	0	0	59	0	66	0
MemoChat	63	63	62	0	59	0	60	0
A-MEM	63	0	0	0	0	6	0	5

Appendix

Table 56: Simpler readouts compared with complete-prompt identity. All rows use 63 queries and 29 users. Pairs counts query–padding comparisons (two variants for Focal); Changed counts different prompts. Miss and Extra are counts with the definitions above. Answers use the original single-draw matrices.

Subset	Queries	Users	Estimate	Lower	Upper	Estimate	Lower	Upper
			$D_{\mathrm{res}}$			$\Delta_{\mathrm{rep}}$
Target preserved	43	25	0.483	0.294	0.671	0.442	0.238	0.633
Strict	23	17	0.353	0.118	0.588	0.284	0.020	0.529

Appendix

Table 57: Historical target-visible task-preservation sensitivity, retained for archival transparency and excluded from the conclusion evidence. Queries and Users give the denominators. Lower and Upper are 95% user-bootstrap limits. The strict subset also satisfies all three outcome-blind semantic readings. A and B are the two matched padding controls.

Setting / subset	Queries	Users	Estimate	Lower	Upper	Estimate	Lower	Upper
			$D_{\mathrm{res}}$			$\Delta_{\mathrm{rep}}$
Focal A / Gold	62	29	0.518	0.346	0.682	0.444	0.261	0.612
Focal A / Strict	24	18	0.431	0.222	0.653	0.361	0.102	0.602
Focal B / Gold	62	29	0.502	0.359	0.646	0.338	0.141	0.529
Focal B / Strict	24	18	0.454	0.241	0.667	0.356	0.093	0.611
State reuse / Gold	33	19	0.419	0.232	0.610	0.400	0.197	0.599

Appendix

Table 58: Repeated-answer sensitivity under the new gold-visible reading. Gold and Strict are defined above. A and B denote the original matched padding controls. State reuse retains 33 of 34 target queries under Gold and 14 under Strict. Estimates give equal weight to users; Lower and Upper are 95% user-bootstrap limits.

Setting / subset	Queries	Users	Estimate	Lower	Upper	Estimate	Lower	Upper
			Present			Absent
Compactor / Gold	32	21	0.857	0.734	0.952	0.210	0.087	0.349
Compactor / Strict	12	10	0.975	0.925	1.000	0.275	0.100	0.475
Recent / Gold	36	18	0.940	0.866	1.000	0.269	0.144	0.407
Recent / Strict	19	15	0.900	0.733	1.000	0.306	0.100	0.544

Appendix

Table 59: Restoration accuracies on the new task-preservation intersections. The same Queries and Users apply to both panels. Present, Absent, Restored, and Replacement denote the four matched conditions; Replacement supplies no directly supporting source. Lower and Upper are 95% user-bootstrap limits.

Setting	Queries	Users	Estimate	Lower	Upper	Estimate	Lower	Upper	Estimate	Lower	Upper
			$R-A$			$R-N$			$R-P$
Focal / Gold	32	21	0.659	0.480	0.813	0.583	0.409	0.750	0.012	-0.036	0.071
Focal / Strict	12	10	0.700	0.500	0.875	0.825	0.600	1.000	0.000	0.000	0.000
Recent / Gold	36	18	0.648	0.519	0.773	0.750	0.639	0.856	-0.023	-0.051	0.000
Recent / Strict	19	15	0.594	0.361	0.811	0.706	0.500	0.889	0.000	0.000	0.000

Appendix

Table 60: Paired restoration accuracy contrasts for Table 59 . Focal denotes the compactor. R denotes Restored, A Absent, N non-support Replacement, and P Present. Lower and Upper are 95% user-bootstrap limits; all differences are computed within the same users.

Setting / subset	Queries	Users	Estimate	Lower	Upper	Estimate	Lower	Upper
			$H$			$\Delta$
Arrival / Gold	62	29	0.124	0.055	0.203	-0.015	-0.088	0.054
Arrival / Strict	24	18	0.083	0.000	0.222	-0.083	-0.222	0.000
Source / Gold	62	29	0.063	0.000	0.138	0.017	-0.052	0.086
Source / Strict	24	18	0.000	0.000	0.000	0.000	0.000	0.000

Appendix

Table 61: Cross-fitted reversal-route sensitivity under the new reading. Arrival and Source denote the arrival-order policy and source-order comparator. Lower and Upper are 95% user-bootstrap limits.

	Forward			Reverse			Reverse minus forward
Dataset	Estimate	Lower	Upper	Estimate	Lower	Upper	Estimate	Lower	Upper
PersonaMem	0.069	0.013	0.151	0.450	0.343	0.559	0.381	0.227	0.528
LongMemEval-S	0.146	0.118	0.175	0.106	0.083	0.132	-0.039	-0.071	-0.007

Appendix

Table 62: Exposed support under common focal construction and BM25 top-three retrieval. Lower and Upper are 95% bootstrap limits. PersonaMem uses 63 queries and 29 users; LongMemEval-S uses 470 queries.

	Source overlap			Evidence recall F			Evidence recall R
Policy	Estimate	Lower	Upper	Estimate	Lower	Upper	Estimate	Lower	Upper
Recent-8	0.000	0.000	0.000	0.215	0.185	0.245	0.146	0.122	0.170
Recent-16	0.000	0.000	0.000	0.381	0.345	0.416	0.319	0.287	0.352
Recent-32	0.349	0.340	0.358	0.688	0.655	0.721	0.619	0.584	0.654
Source-order-8	1.000	1.000	1.000	0.215	0.185	0.245	0.215	0.185	0.245
Source-order-16	1.000	1.000	1.000	0.381	0.345	0.416	0.381	0.345	0.416

Appendix

Table 63: Retained sessions on 470 LongMemEval-S questions. Source-order fixes ingestion to original source indices. Lower and Upper are 95% query-bootstrap limits; F and R denote import order.

	Source overlap			Evidence recall F			Evidence recall R
Policy	Estimate	Lower	Upper	Estimate	Lower	Upper	Estimate	Lower	Upper
Recent-8	0.000	0.000	0.000	0.209	0.180	0.239	0.140	0.117	0.164
Recent-16	0.000	0.000	0.000	0.350	0.316	0.385	0.295	0.264	0.327
Recent-32	0.287	0.266	0.309	0.598	0.563	0.633	0.539	0.503	0.575
Source-order-8	1.000	1.000	1.000	0.209	0.180	0.239	0.209	0.180	0.239
Source-order-16	1.000	1.000	1.000	0.350	0.316	0.385	0.350	0.316	0.385

Appendix

Table 64: Exposed sessions under the shared BM25 top-three adapter. Definitions and denominator follow Table 63 .

	Recall R minus F			All-covered F			All-covered R
Policy	Estimate	Lower	Upper	Estimate	Lower	Upper	Estimate	Lower	Upper
Recent-8	-0.070	-0.110	-0.029	0.096	0.070	0.123	0.040	0.023	0.060
Recent-16	-0.055	-0.112	0.003	0.185	0.151	0.221	0.134	0.104	0.166
Recent-32	-0.059	-0.115	-0.003	0.415	0.372	0.460	0.360	0.317	0.404
Source-order-8	0.000	0.000	0.000	0.096	0.070	0.123	0.096	0.070	0.123
Source-order-16	0.000	0.000	0.000	0.185	0.151	0.221	0.185	0.151	0.221

Appendix

Table 65: Paired exposure-recall change and complete evidence coverage on the same questions. All-covered requires every published evidence session; it measures exposure, not answer correctness.

Condition or contrast	Luna			Qwen3-8B
	Estimate	Lower	Upper	Estimate	Lower	Upper
Present	1.000	1.000	1.000	0.875	0.750	1.000
Absent	0.000	0.000	0.000	0.000	0.000	0.000
Restored	1.000	1.000	1.000	0.917	0.792	1.000
Replacement	0.042	0.000	0.125	0.042	0.000	0.125
Present minus Absent	1.000	1.000	1.000	0.875	0.750	1.000

Appendix

Table 66: LongMemEval four-condition answer accuracy and paired contrasts, 24 questions. Luna and Qwen3-8B answers are scored by the same masked Terra max judge. Lower and Upper are 95% question-bootstrap limits.

		Forward			Reverse			Reverse minus forward
Task	Queries	Estimate	Lower	Upper	Estimate	Lower	Upper	Estimate	Lower	Upper
User	64	0.266	0.156	0.375	0.109	0.047	0.188	-0.156	-0.297	-0.016
Assistant	56	0.286	0.179	0.411	0.232	0.125	0.339	-0.054	-0.214	0.107
Preference	30	0.267	0.133	0.433	0.067	0.000	0.167	-0.200	-0.367	-0.067
Multi-session	121	0.058	0.017	0.099	0.017	0.000	0.041	-0.041	-0.083	0.000
Temporal	127	0.126	0.071	0.189	0.071	0.031	0.118	-0.055	-0.126	0.016

Appendix

Table 67: Recent-8/BM25 answer accuracy on LongMemEval-S for Luna. Lower and Upper give 95% question-bootstrap limits.

	Forward			Reverse			Reverse minus forward
Answer model	Estimate	Lower	Upper	Estimate	Lower	Upper	Estimate	Lower	Upper
Luna	0.206	0.170	0.245	0.081	0.057	0.106	-0.126	-0.170	-0.083
Qwen3-8B	0.204	0.168	0.243	0.089	0.064	0.115	-0.115	-0.157	-0.072

Appendix

Table 68: Overall Recent-8/BM25 answer comparison on 470 LongMemEval-S questions. Both answer models use the same masked Terra max judge; Lower and Upper give 95% question-bootstrap limits.

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