Pith Number

pith:WTYD7Y3C

pith:2024:WTYD7Y3CRFY2BY6WSDOSTNTWVS

not attested not anchored not stored refs pending

Bounds on the Distribution of a Sum of Two Random Variables: Revisiting a problem of Kolmogorov with application to Individual Treatment Effects

Thomas S. Richardson, Zhehao Zhang

arxiv:2405.08806 v2 · 2024-05-14 · math.ST · econ.EM · math.PR · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WTYD7Y3CRFY2BY6WSDOSTNTWVS}

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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.

Cited by

1 paper in Pith

Individual Treatment Effect: Prediction Intervals and Sharp Bounds

Receipt and verification

First computed	2026-07-05T10:39:18.359556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4f03fe3628971a0e3d690dd29b676ac88e20d73c90a7c790ebbabcd8ccd49b7

Aliases

arxiv: 2405.08806 · arxiv_version: 2405.08806v2 · doi: 10.48550/arxiv.2405.08806 · pith_short_12: WTYD7Y3CRFY2 · pith_short_16: WTYD7Y3CRFY2BY6W · pith_short_8: WTYD7Y3C

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/WTYD7Y3CRFY2BY6WSDOSTNTWVS \
  | 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: b4f03fe3628971a0e3d690dd29b676ac88e20d73c90a7c790ebbabcd8ccd49b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d544de9952d55c5b8c5168c817190e2f98f4d8bb77ccbe106a3d0f5b98284bb7",
    "cross_cats_sorted": [
      "econ.EM",
      "math.PR",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2024-05-14T17:53:08Z",
    "title_canon_sha256": "3936bf939faf1429d77631b58ce0baa07f179882d7225fa43dd74e450e4daf63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2405.08806",
    "kind": "arxiv",
    "version": 2
  }
}