Pith Number

pith:K5KGEY4B

pith:2026:K5KGEY4BIIFBETG46Q5QXYO2Y5

not attested not anchored not stored refs pending

A Distributional Perspective on Pearl's Causal Hierarchy: From Marginal to Joint and Individualized Potential Outcomes

Linbo Wang, Peng Wu

arxiv:2601.20405 v2 · 2026-01-28 · stat.OT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K5KGEY4BIIFBETG46Q5QXYO2Y5}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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.

Receipt and verification

First computed	2026-07-29T01:25:34.150469Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5754626381420a124cdcf43b0be1dac76b926caa13acff345ce8358501959411

Aliases

arxiv: 2601.20405 · arxiv_version: 2601.20405v2 · doi: 10.48550/arxiv.2601.20405 · pith_short_12: K5KGEY4BIIFB · pith_short_16: K5KGEY4BIIFBETG4 · pith_short_8: K5KGEY4B

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/K5KGEY4BIIFBETG46Q5QXYO2Y5 \
  | 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: 5754626381420a124cdcf43b0be1dac76b926caa13acff345ce8358501959411

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fec4e68b2417fe7c6467c4c556502836e7a535555fdf11f4167dc25572504e30",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.OT",
    "submitted_at": "2026-01-28T09:09:50Z",
    "title_canon_sha256": "f67e598e01820f0a77b3d99b55d256a83d559236c66c06fb73d1a65c01c67674"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.20405",
    "kind": "arxiv",
    "version": 2
  }
}