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REVIEW 4 major objections 5 minor 32 references

Decentralized Causal Discovery using Judo Calculus

T0 review · 4 major / 5 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read This paper claims that causal discovery can be decentralized: learn one graph per regime, then keep only edges that survive across regimes — a rule it derives from sheaf-theoretic 'local truth' and validates with faster, more accurate exper

desk verdict The topos packaging is a coat of paint over stability selection, and the load-bearing sheaf derivation is mathematically wrong; the experiments are internally inconsistent, so I would not trust this as a result. read the letter →

arxiv 2510.23942 v2 pith:KKXR3NBL submitted 2025-10-27 cs.AI

Sridhar Mahadevan This is my paper · ORCID
classification cs.AI MSC 03G3018F20
keywords causaldiscoveryintuitionisticlogictoposofsheavesLawvere–Tierneytopologyregimeheterogeneityj-stabilitydo-calculuslocaltruth
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper is trying to establish that causal discovery can be made 'j-stable': instead of learning one global graph from pooled data, learn local graphs on regimes (age, country, dose, cell line, etc.) and glue them by keeping edges that appear on every regime or on all-but-k regimes. It formalizes this as 'judo calculus' — j-stable causal inference in a topos of sheaves, where a Lawvere–Tierney modal operator j picks the relevant regimes and truth is treated as local rather than global. If correct, this would turn one hard pooled problem into many small parallel problems and improve precision by filtering out regime-idiosyncratic edges. The paper reports better F1/SHD and lower wall-clock time than pooled baselines on synthetic, biology, and economics datasets.

What carries the argument

The central object is the Lawvere–Tierney modal operator j acting on the subobject classifier of a sheaf topos Sh_J(C); it selects which regimes are relevant and defines j-stability as truth on a cover that glues across overlapping charts. Operationally, the carrying identity is Disc_j(U) = ∧_i Disc_j(V_i): the global j-stable graph is the edgewise intersection of per-regime graphs. The paper also uses nerve invariants (f0, f1, f2 of the skeleton) as regularizers in its score-based variants.

What would settle it

Find a 3-variable counterexample to the identity Disc_j(U)=∧_i Disc_j(V_i): two CI theories whose pointwise least I-maps intersect to a graph that is not the least I-map of the intersection theory. If such graphs exist, the cover-glueing identity fails. Empirically, generate a synthetic DAG with a spurious edge present in every regime with the same sign; the intersection aggregator will retain it, contradicting the claimed false-positive control.

Watch

Extended reading notes

Core claim

The paper proposes that causal claims be treated as local truths: a claim (e.g., 'X causes Y' or a conditional independence) must be proven on a j-cover of regimes — a family of charts chosen by a Lawvere–Tierney modal operator j — and then glued into a j-stable statement. It defines j-stable intervention probabilities as monotone aggregations over regimes, three judo rules as local counterparts of the classical do-calculus rules, and 'sheafified' versions of score-based, constraint-based, and gradient-based discovery in which per-regime graphs are computed independently and aggregated by a support threshold (intersection or k-of-E). The claimed result is that this decentralized procedure ma

Load-bearing premise

The entire derivation rests on the claim that the 'least I-map' functor Ψ preserves meets (edgewise intersections), asserted in the appendix's universal-property proof; left adjoints preserve joins, not meets, so if this step fails the intersection aggregation has no theoretical support. The paper also assumes without demonstration that true edges recur across regimes while spurious edges do not.

Editorial extensions

If this is right

  • Running discovery independently on each regime and keeping edges that appear on every chart (or all-but-k) filters out regime-idiosyncratic edges, improving precision and structural Hamming distance on the paper's synthetic and Sachs benchmarks.
  • The method's map-reduce structure turns one pooled run into E independent per-regime runs plus a cheap Boolean fold, so wall-clock time drops roughly with the number of workers on CPU benchmarks.
  • The j-backdoor rule allows evaluation of regime-local adjustment formulas aggregated over the cover, yielding do-queries certified on the chosen regimes without committing to a single global model.
  • Support thresholds (π) can be selected by validation log-likelihood on held-out regimes, giving a tuning rule that the paper shows lands on a plateau where j-stable variants dominate pooled baselines.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the meet-preservation gap in the proof is repaired, the same aggregation can serve as a privacy-preserving distributed discovery protocol, since only per-regime adjacency matrices need to be shared.
  • The paper's own bagging analogy implies the method's advantage depends on true edges having higher recurrence rates than false edges across regimes; datasets with heavily overlapping regime-specific mechanisms would be a harder test.
  • A natural stress test is to construct regimes where a spurious edge appears consistently with the same sign in every chart; the intersection aggregator would keep it, exposing where sign-aware or orientation-aware gluing is needed.
  • The 'all-but-k' aggregator can be read as a robust-to-one-region rule; for policy or medical settings, k should encode minority-group protections rather than being chosen purely by validation likelihood.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes 'judo calculus,' an intuitionistic, sheaf-theoretic framework for decentralized causal discovery. The central claim is that causal claims can be certified locally on a cover of regimes and glued via a j-stability rule, yielding algorithms that learn per-regime graphs and aggregate them by intersection or support thresholds. The paper describes j-stable variants of GES, ψ-FCI, and DCDI, and reports experiments on synthetic and real data claiming improved structural accuracy and computational efficiency over pooled baselines. The theoretical development is mostly relegated to the appendix and to companion papers; the operational core is the support-aggregation rule formalized in Section 4.

Significance. If the central claim were established, the idea of decomposing causal discovery into independent per-regime subproblems and gluing the results would be valuable both computationally and statistically, and the paper's template for 'sheafifying' standard algorithms (GES, FCI, DCDI) is potentially useful. The paper also makes a serious attempt to connect a topos-theoretic modal logic to a concrete algorithmic pipeline, which is unusual and potentially generative. However, the formal derivation in Appendix A.5 that underwrites the intersection/support aggregation contains a fundamental error, and the experimental evidence is internally inconsistent and largely preliminary, with no released code. As it stands, the paper does not establish its advertised formal theory or its empirical claims.

major comments (4)
  1. [Appendix A.5, 'Universality and gluing' theorem] The cover-calculus identity Disc_j(U) = ∧_i Disc_j(V_i) is the theoretical justification for the intersection/support aggregation used throughout the paper. The proof claims 'Ψ is left adjoint in a poset and preserves existing meets.' Two errors: (1) The claimed adjunction Ψ ⊣ Φ fails already for V={X,Y}: with S={X⊥Y} and G=X→Y, Ψ(S) is the empty graph, so Ψ(S) ≤ G but S ⊄ Φ(G), violating the bi-implication. (2) Even if Ψ were a left adjoint, left adjoints preserve joins, not meets; the stated identity requires meet preservation. Without this identity, the formal link from the sheaf-theoretic framework to the operational intersection aggregation is broken.
  2. [Tables 6, 7, and 8, Section 5.2] The same condition (α=0.005, synthetic DAG) is reported with contradictory results. Table 7 gives pooled F1=0.286/SHD=10 and j-stable intersection F1=0.333/SHD=4, while Table 6 gives pooled F1=0.167/SHD=20 and j-stable intersection F1=0.250/SHD=6; Table 8 repeats the Table 6 numbers. The pooled SHD differs by a factor of two between tables. This internal inconsistency makes the empirical comparison unreliable and prevents verification of the claimed improvement.
  3. [Table 9, Section 5.3] The reported j-stable GES result is a perfect F1=1.00 and SHD=0 on a single synthetic graph, with no variance, no multiple seeds, and no cross-validation. This is anecdotal. The accompanying text claims that 'j-stable GES removes spurious edges and exactly matches the true undirected skeleton,' but no evidence of replication or robustness is provided. The empirical case for the method cannot rest on one perfect run.
  4. [Section 4, 'Why this realizes j-stability'; Section 5.1] The paper defines j-stability operationally as support aggregation and then presents the aggregation as justified by the theory, but the theoretical derivation in A.5 does not go through (see above). In addition, the key premise in §5.1 that 'true edges recur across regimes while spurious edges do not' is asserted without formal statement or empirical verification; the diagnostic promised in §4.1 (separation of true vs. false edge support distributions) is never reported. The argument is thus circular relative to the failed derivation: the operational rule is stipulated to be the content of j-stability, and the experiments then validate that same rule.
minor comments (5)
  1. [Global] There are many typos and inconsistent notations: 'leke Moerdijk' instead of 'le Moerdijk' in several places; 'Intutionistic' in the reference to the companion paper; the method is called both 'PSI-FCI' and 'ψ-FCI'; 'CausalLearn' is referenced without a URL or version.
  2. [Section 4.1 / Table 5] Table 5 is a template with dotted entries, not a results table. It should either be filled or removed.
  3. [Section 5.2] The default experimental settings state R=10 regimes, but Tables 6–8 describe a '3-regime dataset.' The relationship between these settings and the reported tables is unclear.
  4. [Section 3.17 and A.16] The aggregator axioms (A1)–(A4) are introduced in A.16 but referenced earlier in §3.17 as 'matching the KJ boxed modality' before the modality is defined. Numbered cross-references such as '§2.16' do not match the actual section numbering.
  5. [Appendix A.13] The transition from j-stability to do-calculus is left as 'a detailed translation... can be added in an appendix.' As written, the paper's central claim to formalize j-do-calculus is supported only by a promissory note.

Circularity Check

3 steps flagged · score 5.0 of 10

j-stability is defined to be the support/intersection aggregator, so the 'cover calculus' theorem restates the algorithm's rule; formal j-do-calculus details are deferred to self-cited companion papers, and the empirical rationale is stability selection relabeled in sheaf language.

  1. self definitional [Appendix A.5 ('Cover calculus (gluing)') and Section 4 ('Why this realizes j-stability')]
    "Because Ψ is left adjoint in a poset and preserves existing meets, Discj(U)= Ψ(∩_i CIj(V_i)) = ∧_i Ψ(CIj(V_i)) = ∧_i Discj(V_i). ... Algorithmic reading (what our code computes): ... Graph route: output ∧_i Ĝ_i (edgewise intersection)."

    The theorem's conclusion is exactly the operational rule implemented in the paper: j-stable discovery over a cover is edgewise intersection/support aggregation. The only derivation step is the assertion that Ψ preserves meets, which is precisely the property needed to make Disc_j = Ψ∘CI_j commute with the cover meet; no independent argument establishes it. Section 4 already defines the implemented j-stable graph as 'Intersection A∩ certifies edges that hold on all charts (cover-wise truth), hence correspond to forced edges under j,' so the formal 'prediction' is the definition restated as a theorem.

  2. renaming known result [Section 5.1 'Why j-stable discovery works: an ensemble view (bagging & boosting)']
    "Bagging in disguise. For each regime e∈E we fit a base learner A to get a directed graph A(e)... We bag these hypotheses via the frequency map Fij = 1/|E| Σ_e h(e)ij ∈[0,1]... The π-stable skeleton keeps {i,j} if max(Fi→j,Fj→i)≥π; we orient by a tiny margin rule Mij≥δ..."

    The paper's own account of why the method works is that it is bagging/stability selection over per-regime graphs. The 'j-stability' formalism is stipulated to be this same frequency-threshold/support aggregation, so the empirical explanation (true edges recur, spurious edges flicker) is the known stability-selection assumption, not a consequence of the sheaf axioms. The topos terminology renames the aggregator rather than deriving or predicting it.

1 more flagged steps
  1. self citation load bearing [Section 2.4 'The j-stable do-operator (practical form)']
    "We refer the reader to our previous paper for a more rigorous categorical framework for j-do-calculus [Mahadevan, 2025b]. ... Formal details appear in the companion theory paper."

    The paper's headline formalism — j-do-calculus / 'judo calculus' — is not fully defined in this text; its 'more rigorous' categorical semantics are explicitly delegated to a companion paper by the same author. Since the abstract claims judo calculus is 'formally defined' here, the central theoretical premise rests on a self-citation to unverified companion work, even though the operational support-threshold algorithm is implemented and benchmarked independently.

full rationale

The central circularity is that the theory's key derived object — j-stable discovery over a cover — is stipulated to be exactly the operational support/intersection aggregator. Appendix A.5's cover calculus concludes Disc_j(U) = ∧_i Disc_j(V_i), and the paper's own 'algorithmic reading' identifies this with the code's edgewise intersection; Section 4 then equates j-stability with 'holds on all charts.' Thus the claimed derivation of the k-of-E/intersection aggregation reduces to its definition, with the asserted meet-preservation of Ψ doing all the work. The empirical results are not logically forced — they are real benchmark comparisons — so the paper is not fully circular; but the topos-theoretic contribution is largely a relabeling of stability selection/bagging, as the paper itself says in §5.1. In addition, formal j-do-calculus semantics are deferred to self-cited companion papers. Score 5 reflects partial circularity: one central predicted rule reduces by construction, but the experimental efficiency/accuracy claims retain independent empirical content.

Assumptions & free parameters 10 free parameters · 6 assumptions · 3 invented entities

The framework introduces a layer of categorical vocabulary on top of a simple ensemble aggregation. Free parameters are numerous and mostly tuned by validation or set to default ranges. The central derivation relies on a questionable preservation-of-meets step, and the new constructs (P_J, π-stable skeleton, empirical sheafification) are defined inside the paper with no external falsifiable handles.

free parameters (10)
  • stability threshold π = π ∈ {0.3, 0.6} defaults; selected by validation likelihood
    Controls how many regimes must contain an edge for it to be kept; central to j-stable aggregation (§2.1, §5.1).
  • sparsity/top-K or τ for DCDI = top-2 parents per node (PISA), top-K to match edge budget
    Post-processing of weighted adjacency to binary graph; affects all DCDI comparisons (§4.5, §5.4).
  • λtop, λ△ = λtop ∈ [0.05, 0.3], λ△ ∈ [0.01, 0.2]
    Hyperparameters of the CGES/TCES score (§3.4).
  • λj, λsheaf = λj ∈ [0.05, 0.2], λsheaf ∈ [0.02, 0.1]; λj ∈ [10^-2, 10^-1] for DCDI
    Weights for j-stability and sheaf penalties (§3.8, §3.16).
  • CI significance α = swept {0.005, 0.01, 0.02} for ψ-FCI
    Threshold for conditional independence tests; results are reported per α (§4.5, Tables 6-8).
  • aggregator Agg = Fisher/Stouffer/mean/Tippett
    Choice of how to combine per-regime p-values or logits; the paper gives axioms but does not fix a unique aggregator (§3.17, A.15).
  • all-but-k tolerance k = k=1 and k=E-1 used
    Controls conservativeness of gluing; results vary with k (§4, Table 7).
  • orientation margin δ = small, unspecified
    Net-preference rule for orienting edges; no concrete value is given (§5.1).
  • UMAP k-NN k and overlap threshold q = k ∈ [10, 30], q ∈ (0,1]
    Used in the empirical sheafification appendix, not in the main experimental tables (§B.6-B.7).
  • number of charts K and edge threshold τβ in interference demo = τβ = 0.2, K unspecified
    Operational test of j-stability in the interference example (§2.1).
assumptions (6)
  • standard math The category of (co)presheaves on a small category forms a topos; Grothendieck topologies correspond to Lawvere-Tierney topologies
    Used throughout Appendix A to justify sheaf semantics (Mac Lane & Moerdijk).
  • domain assumption Causal claims can be interpreted as truth in the internal logic of a sheaf topos over a site of regimes; local truth on a J-cover glues to global truth
    The core modeling commitment of judo calculus; not established by data (§2, A.7-A.8).
  • domain assumption True edges reappear consistently across regimes while spurious edges flicker; perfect interventions cut all incoming edges of the target
    The ensemble/bagging explanation for why intersection aggregation works (§5.1, §5.2).
  • domain assumption Per-chart learners are consistent, and local edge errors are independent with per-edge FP/FN rates < 1/2
    Needed for the all-but-k consistency claim (Appendix A.4, Proposition 4).
  • ad hoc to paper Ψ, the left adjoint to d-separation, preserves meets (intersections)
    Asserted in Appendix A.5 to derive the cover calculus; left adjoints in posets preserve joins, not meets, so this premise is false as stated.
  • ad hoc to paper Aggregators satisfying axioms (A1)-(A4) suffice for finite-sample J-soundness
    The soundness theorem is conditional on these axioms; they are chosen so that the desired conclusion goes through (§A.16).
invented entities (3)
  • j-stable intervention probability P_J
    purpose: Define do-queries certified on a cover via a monotone aggregator of regime-specific interventional probabilities
    A definition (§2.4); it reduces to classical Pearl when the cover has one regime and Agg is the identity, so it provides no external falsifiable handle.
  • π-stable skeleton / edge frequency map F
    purpose: Operationalize j-stability by keeping edges whose per-regime support exceeds π
    Constructed from per-regime graph outputs; no independent evidence beyond the paper's own thresholds (§5.1).
  • Empirical sheafification bCI_J_P
    purpose: Build J-stable CI sets from UMAP-section-weighted per-regime graphs
    Introduced in Appendix B.6; depends on UMAP embeddings and thresholds, and is not validated beyond its own definitions.

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Pith. "Pith review of Decentralized Causal Discovery using Judo Calculus." pith.science (2026). https://pith.science/paper/KKXR3NBL

@misc{pith2026251023942,
  author       = {Pith},
  title        = {Pith review of: Decentralized Causal Discovery using Judo Calculus},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KKXR3NBL}},
  note         = {Machine review of arXiv:2510.23942}
}
read the original abstract

We describe a theory and implementation of an intuitionistic decentralized framework for causal discovery using judo calculus, which is formally defined as j-stable causal inference using j-do-calculus in a topos of sheaves. In real-world applications -- from biology to medicine and social science -- causal effects depend on regime (age, country, dose, genotype, or lab protocol). Our proposed judo calculus formalizes this context dependence formally as local truth: a causal claim is proven true on a cover of regimes, not everywhere at once. The Lawvere-Tierney modal operator j chooses which regimes are relevant; j-stability means the claim holds constructively and consistently across that family. We describe an algorithmic and implementation framework for judo calculus, combining it with standard score-based, constraint-based, and gradient-based causal discovery methods. We describe experimental results on a range of domains, from synthetic to real-world datasets from biology and economics. Our experimental results show the computational efficiency gained by the decentralized nature of sheaf-theoretic causal discovery, as well as improved performance over classical causal discovery methods.

Figures

Figures reproduced from arXiv: 2510.23942 by the authors.

Figure 1
Figure 1. Interference with overlapping covers. Edge frequencies f(E1→ Y), f(E2→ Y) by cover (left); per￾chart coefficients on intersections (right). Local claims are j-stable on each cover and persist on intersections. 2.2 Computational and Statistical Efficiency of j-Stable Discovery Another significant advantage of judo calculus is its highly decentralized characteristic. As we observed frequently during our experiments, w… view at source ↗
Figure 2
Figure 2. Computational advantages of j-stable discovery. Left: Per-iteration wall-clock (seconds per 10k iterations) is on par with or lower than vanilla across d∈ {10, 20, 40}; the aggregation+π step adds negligible overhead. Right: Seed ensembles are highly parallel: wall-clock for 10 seeds drops substantially with 4 workers at d=40 [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 4
Figure 4. j-stable DCDI scales significantly better than regular DCDI on a synthetic DAG benchmark used originally in [Brouillard, 2020]. 2.4 The j-stable do-operator (practical form) We introduce a “practical" form of judo calculus in this section. We refer the reader to our previous paper for a more rigorous categorical framework for j-do-calculus [Mahadevan, 2025b]. Let J be a cover (the family of comparable regimes releva… view at source ↗
Figures from the paper (18 more)
Figure 5
Figure 5. Figure 5: 10 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 5
Figure 5. Figure 5: The Three Rules of Judo Calculus. Remark. The premises “· | (·, J)” are certified by the π-stable structure (and margins) on the cover. Formal details appear in the companion theory paper. Example (PISA ESCS). Let J be the set of OECD countries with comparable SES meas…
Figure 6
Figure 6. Figure 6: j-stability. Cells are (env, variable) mechanisms. Red cells are intervened (free). Colored blocks in a column are non-intervened and thus tied (penalized to agree). 3.3 TCM Primer: Nerve Invariants on the Skeleton One simple but elegant categorical trick is to map a c…
Figure 7
Figure 7. Figure 7: Pipeline: PSI–FCI vs. j-stable PSI–FCI on synthetic data. Regimes e ∈ {e0,e1,e2} act as a J-cover {Ve→U} of the ambient stage U. Per-env FCI yields local skeletons A (e) (truth on each chart). Aggregation by intersection keeps the edges forced on every chart (A ∩ ij = …
Figure 8
Figure 8. Figure 8: Comparison of regular ψ-FCI (pooled) with the j-stable variant on a synthetic DAG. α Method F1 SHD Time (s) 0.005 j-stable 0.25 6 1.799 0.005 pooled 0.167 20 1.065 0.01 j-stable 0.25 6 1.075 0.01 pooled 0.167 20 1.087 0.02 j-stable 0.25 6 1.093 0.02 pooled 0.154 22 1.0…
Figure 9
Figure 9. Figure 9: Results on Synthetic DAG comparing j-stable DCDI against the standard DCDI. Boxplots over 10 random graphs (whiskers 1.5×IQR). j-stable DCDI yields substantially lower SHD and tighter dispersion than vanilla DCDI in both directed and skeleton space (median 6.0 vs 22.5)…
Figure 10
Figure 10. Figure 10: Results on Synthetic DAG comparing j-stable DCDI against the standard DCDI. Boxplots over 20 random graphs (whiskers 1.5×IQR). j-stable DCDI yields substantially lower SHD and tighter dispersion than vanilla DCDI in both directed and skeleton space (median 6.0 vs 22.5…
Figure 11
Figure 11. Figure 11: Comparison of GES, CGES, and TC-GES on Sachs dataset. [PITH_FULL_IMAGE:figures/full_fig_p032_11.png]
Figure 12
Figure 12. Figure 12: TCES decisions on sheaf metrics for Sachs data. [PITH_FULL_IMAGE:figures/full_fig_p033_12.png]
Figure 13
Figure 13. Figure 13: DCDI results for PISA dataset. A Appendix: Theory of j-Stable Causal Discovery For readers who are familiar with category theory, we now give a detailed theoretical overview of our intutionistic causal discovery framework based on judo calculus. Background material to…
Figure 14
Figure 14. Figure 14: Adjunction between Topos Causal Models and statistical independence categories. The left adjoint [PITH_FULL_IMAGE:figures/full_fig_p037_14.png]
Figure 15
Figure 15. Figure 15: Naturality of the realization isomorphism [PITH_FULL_IMAGE:figures/full_fig_p037_15.png]
Figure 16
Figure 16. Figure 16: Commuting triangle connecting the adjunction [PITH_FULL_IMAGE:figures/full_fig_p038_16.png]
Figure 17
Figure 17. Figure 17: Adjunction triangle connecting conditional-independence syntax, categorical causal models, and [PITH_FULL_IMAGE:figures/full_fig_p038_17.png]
Figure 18
Figure 18. Figure 18: Diagrammatic view of functorial causal discovery. Learning new conditional independences or [PITH_FULL_IMAGE:figures/full_fig_p039_18.png]
Figure 19
Figure 19. Figure 19: External Grothendieck topology J and internal Lawvere–Tierney topology j both induce subtopoi embedded in the presheaf topos [C op , Set]. A.3 Lawvere-Tierney Topologies on a Topos In the original paper defining TCM [Mahadevan, 2025a], the category of sheaves defining…
Figure 20
Figure 20. Figure 20: Universal property of causal discovery. D-separation functor. Define the monotone map Φ : DAGV −→ CIV, Φ(G) = the (semi-graphoid) closure of CIs entailed by d-separation in G. Left adjoint (least I-map). For S ∈ CIV, put Ψ(S) := ^ { G ∈ DAGV | S ⊆ Φ(G) }, i.e. the gre…
Figure 21
Figure 21. Figure 21: Coend calculus for J-stability. B Appendix: Implementation details B.1 Experimental Plots For each node i, we report: (i) cover size |Si | and cover type (e.g., “no direct interventions on i”), (ii) the aggregator agg and α, (iii) the combined Pi and accept/reject for…

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Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.