Pith Number

pith:MP2GWTEH

pith:2026:MP2GWTEHNFOTOZC7NTK4JZOEXW

not attested not anchored not stored refs resolved

Causal Learning with the Invariance Principle

Francesco Locatello, Francesco Montagna

Assuming acyclicity and invariance, only two auxiliary environments suffice to identify the causal graph for arbitrary nonlinear mechanisms.

arxiv:2605.13589 v1 · 2026-05-13 · stat.ML · cs.LG

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\pithnumber{MP2GWTEHNFOTOZC7NTK4JZOEXW}

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

assuming that the causal relations are acyclic and invariant across multiple environments, only two auxiliary environments are sufficient to infer the causal graph for arbitrary nonlinear mechanisms

C2weakest assumption

the causal relations are acyclic and invariant across multiple environments

C3one line summary

Two auxiliary environments suffice to identify causal graphs and functional mechanisms in structural causal models under acyclicity and invariance assumptions, enabling correct counterfactual inference.

References

97 extracted · 97 resolved · 0 Pith anchors

[1] Acemoglu, Daron and Johnson, Simon and Robinson, James A. , title =. American Economic Review , volume =

[2] Card, David and Krueger, Alan B. , title =. American Economic Review , volume =

[3] Forty-second International Conference on Machine Learning , year=

[4] The Thirteenth International Conference on Learning Representations , year=

[5] The Fourteenth International Conference on Learning Representations , year=

Receipt and verification

First computed	2026-05-18T02:44:23.098718Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63f46b4c87695d37645f6cd5c4e5c4bdad5cd745a9e6bd7f1e1972ff63c8b5b7

Aliases

arxiv: 2605.13589 · arxiv_version: 2605.13589v1 · doi: 10.48550/arxiv.2605.13589 · pith_short_12: MP2GWTEHNFOT · pith_short_16: MP2GWTEHNFOTOZC7 · pith_short_8: MP2GWTEH

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MP2GWTEHNFOTOZC7NTK4JZOEXW \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 63f46b4c87695d37645f6cd5c4e5c4bdad5cd745a9e6bd7f1e1972ff63c8b5b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37d49d77e2c72a33a39b2fda827741e629d1b36841c09b0cbd9a6bf08dfe9943",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-13T14:25:04Z",
    "title_canon_sha256": "c414f7cde36d5f4c67635fb740b2e817e00bb6a108141474b652f85f3428e8bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13589",
    "kind": "arxiv",
    "version": 1
  }
}