{"id":"bb445c33-af59-4c85-8547-ca7a7e0d2a2b","arxiv_id":"2607.01308","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"By sorting KV-caches via mean K-norm ordering, cache merging becomes a commutative, associative, idempotent CvRDT that delivers identical results under any permutation and absorbs duplicates.","lead":"This paper introduces CanonicalMerge, which orders KV-caches from multiple agents by mean K-norm at a middle layer to produce byte-identical merged caches regardless of input order. It converts non-commutative cache merging into a convergent replicated data type with structural guarantees for multi-agent latent reasoning.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's weakest_assumption matches the single point the paper itself flags as requiring verification. Because the manuscript supplies both the algorithmic enumeration and the real-model bit-for-bit results, the load-bearing condition is directly addressed rather than left open. No additional concern about soundness or generalization is extractable from the supplied material that would alter the CONDITIONAL verdict.","tokens_in":1861,"tokens_out":273,"duration_ms":21148,"concrete_test":"Re-run the N=5 enumeration and the Qwen3 bit-for-bit check after swapping the middle layer index; if any permutation produces a different ordering or non-identical merge, the stability claim fails for that layer choice.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that ordering by mean K-norm at a chosen middle layer produces a permutation-invariant total order, yielding byte-identical merged caches. This is stated to be verified algorithmically for arity N<=5 and bit-for-bit on Qwen3-1.7B/4B. The property follows directly from computing per-cache scalars (independent of presentation order) and sorting, with the paper supplying explicit checks rather than an unverified assumption. No internal inconsistency, hidden dependency, or untested regime is indicated in the given text.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript proposes CanonicalMerge for multi-agent latent reasoning: KV-caches are ordered by mean K-norm at a chosen middle layer to produce a permutation-invariant total order, yielding byte-identical merged caches under any input permutation. This is verified algorithmically for arity N≤5 and bit-for-bit on Qwen3-1.7B/4B models. The approach separates the replicated state (a set of content-addressed fragments whose merge is set union, forming a CvRDT) from its deterministic render (CanonicalMerge). On partitioned-reasoning and HotpotQA benchmarks, it matches the accuracy of the best BagMerge ordering in every regime-by-budget cell while absorbing duplicates, and outperforms output-fusion baselines like PackLLM.","tokens_in":1962,"tokens_out":536,"duration_ms":24514,"significance":"If the central claims hold, the work supplies a structural guarantee of convergence and reproducibility for cache-level merging in multi-agent systems, converting a non-commutative operation into a CvRDT with explicit algorithmic and empirical verification of byte-identity. The fact that every N=2 accuracy number carries over unchanged and that the method colocates but does not yet compose traces at k>2 are useful characterizations. The distinction from output-level fusion is clearly drawn.","major_comments":[{"comment":"Experimental validation section: the claim of matching best BagMerge accuracy 'in every regime-by-budget-by-ordering cell' and the bit-for-bit equivalence on Qwen3 models rest on results whose support is described as moderate because error bars, full dataset details, and statistical tests are not provided in the reported text; these details are load-bearing for the empirical equivalence claim.","section":"Experimental validation"},{"comment":"Definition of CanonicalMerge (middle-layer ordering rule): mean K-norm at a single chosen middle layer is treated as supplying a stable, permutation-invariant total order, yet the manuscript identifies this layer index as a free parameter with no sensitivity analysis or justification for its selection across model scales or regimes.","section":"CanonicalMerge definition"}],"minor_comments":[{"comment":"Notation for the set-union semantics and content-addressed fragments could be introduced earlier with an explicit small example to clarify the distinction between the CvRDT state and its render.","section":null},{"comment":"The abstract states 'statistically insignificant accuracy margin' but the main text should cite the precise test and p-value used.","section":null}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the positive assessment and recommendation of minor revision. We address each major comment below, committing to revisions where the manuscript requires strengthening.","responses":[{"response":"We agree that the reported equivalence claims would be more robust with additional statistical detail. In the revised manuscript we will add error bars (standard deviation over repeated runs where applicable), full dataset descriptions including splits and sizes, and results of statistical tests (paired t-tests for accuracy comparisons and exact-match verification for bit-identity) to support the claims of matching best BagMerge performance and byte-identical outputs.","revision_made":"yes","referee_comment":"[Experimental validation] Experimental validation section: the claim of matching best BagMerge accuracy 'in every regime-by-budget-by-ordering cell' and the bit-for-bit equivalence on Qwen3 models rest on results whose support is described as moderate because error bars, full dataset details, and statistical tests are not provided in the reported text; these details are load-bearing for the empirical equivalence claim."},{"response":"The middle-layer index is indeed presented as a fixed but arbitrary hyperparameter. We will revise the manuscript to include a short justification (middle layers encode higher-level semantics in the models studied) together with a sensitivity table showing that accuracy and bit-identity remain stable across a range of layer choices for both Qwen3-1.7B and 4B.","revision_made":"yes","referee_comment":"[CanonicalMerge definition] Definition of CanonicalMerge (middle-layer ordering rule): mean K-norm at a single chosen middle layer is treated as supplying a stable, permutation-invariant total order, yet the manuscript identifies this layer index as a free parameter with no sensitivity analysis or justification for its selection across model scales or regimes."}],"tokens_in":1555,"tokens_out":387,"duration_ms":21628,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The central move is to replace the ordering-sensitive concatenation in BagMerge with CanonicalMerge: compute a scalar mean K-norm per cache at one fixed middle layer, sort on that scalar, and render the merged cache. Because the scalar is independent of presentation order, the final byte layout is identical for any permutation. They verify this algorithmically for N up to 5 and bit-for-bit on Qwen3-1.7B and 4B states. They then separate the replicated state (a set of content-addressed fragments whose merge is ordinary set union) from the deterministic render, so the whole thing satisfies CvRDT properties while preserving the accuracy numbers from the best BagMerge ordering.\n\nThis is useful because it removes the need to guess or search for a good input order, and the accuracy carries over unchanged on the partitioned-reasoning benchmark and on HotpotQA. It also sits clearly above output-level fusion methods like PackLLM, which lose badly at matched budget.\n\nThe soft spots are modest but real. The middle layer is a free parameter whose stability is shown only on the two tested models. Algorithmic checks stop at N=5 and the bit-for-bit tests are on two sizes; larger arities and more models would strengthen the claim. The paper itself notes that at k>2 the method only colocates traces without composing them, so the scope is the merge step rather than full multi-agent reasoning. No error bars or full dataset statistics appear in the abstract, though the core ordering property does not depend on the accuracy numbers.\n\nThe work is aimed at people building multi-agent systems that exchange latent state and want structural guarantees instead of best-case ordering. It deserves a serious referee because the construction is new relative to the cited BagMerge work, the verification is explicit, and the CvRDT framing is cleanly executed. I would bring it to a reading group and would not desk-reject it.","headline":"The paper gives a deterministic sort on mean K-norm at a middle layer that makes KV-cache merges byte-identical under any order and turns the exchange into a set-union CvRDT.","tokens_in":2458,"tokens_out":472,"would_cite":false,"duration_ms":21471,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Ordering caches by mean K-norm at a middle layer produces byte-identical merges under any input permutation.","keywords":["KV cache merging","multi-agent latent reasoning","convergent replicated state","CanonicalMerge","CvRDT","permutation invariance","BagMerge"],"falsifier":"Two different permutations of the same set of caches produce byte-different merged outputs when both are ordered by mean K-norm at the chosen middle layer on Qwen3-1.7B or 4B.","tokens_in":2745,"feed_emoji":"","tokens_out":633,"duration_ms":21534,"temperature":0.7,"pith_summary":"The paper shows how to turn non-commutative KV-cache concatenation into a convergent replicated state for multi-agent latent reasoning. CanonicalMerge orders caches by their mean K-norm value at a chosen middle layer, which makes the final merged cache identical no matter the order of the input agents. This ordering is content-based, so the merge satisfies the properties of a state-based CvRDT whose state is a set of content-addressed fragments and whose operation is set union. The deterministic render of that state preserves the accuracy of the best possible ordering on partitioned-reasoning and HotpotQA tasks while absorbing duplicate deliveries instead of re-concatenating them.","feed_headline":"Mean K-norm ordering yields identical cache merges for any order","feed_subtitle":"The method converts order-dependent concatenation into a commutative replicated state that matches best orderings without searching.","key_machinery":"CanonicalMerge, the deterministic ordering of caches by mean K-norm at a middle layer that produces permutation-invariant byte-identical merges.","core_discovery":"CanonicalMerge fixes the layout by content: ordering caches by mean K-norm at a middle layer renders the merged cache byte-identical under any input permutation. The replicated state is a set of content-addressed latent fragments whose merge is set union, and CanonicalMerge is its deterministic render.","pith_inferences":["The separation of the abstract set state from its byte render could support distributed collection of latent fragments across independent agents.","At larger agent counts the ordering stability would need verification beyond the N<=5 algorithmic checks performed.","The current method colocates but does not compose latent traces, which leaves open the design of operators that would actually combine the fragments."],"forward_implications":["Every N=2 accuracy number carries over unchanged to the merged state.","Re-delivered duplicate caches are absorbed by set union rather than re-concatenated.","The method matches the accuracy of the best BagMerge ordering in every regime-by-budget cell without knowing which order is best.","The behaviour transfers to real multi-document QA while remaining distinct from output-level fusion methods."],"fun_headline_variants":["Mean K-norm orders caches for identical merges","CanonicalMerge creates order-independent cache states","Content-based ordering yields byte-identical cache merges","Replicated state turns cache concat commutative","K-norm layout makes multi-agent merges convergent"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The mean K-norm computed at a chosen middle layer supplies a stable, permutation-invariant total order that produces byte-identical merges for the tested models and regimes.","fun_headline_variants_meta":{"raw":{"variants":["Mean K-norm orders caches for identical merges","CanonicalMerge creates order-independent cache states","Content-based ordering yields byte-identical cache merges","Replicated state turns cache concat commutative","K-norm layout makes multi-agent merges convergent"]},"model":"grok-4.3","cost_usd":0.008041,"raw_usage":{"total_tokens":3705,"prompt_tokens":762,"num_sources_used":0,"completion_tokens":63,"cost_in_usd_ticks":80412000,"prompt_tokens_details":{"text_tokens":762,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2880,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":762,"tokens_out":63,"duration_ms":34036,"temperature":1.0,"reasoning_tokens":2880,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-03T01:32:45.225608+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Two different permutations of the same set of caches produce byte-different merged outputs when both are ordered by mean K-norm at the chosen middle layer on Qwen3-1.7B or 4B.","supporting_citations":[],"review_version":1}