Pith Number

pith:DBPTK7RY

pith:2026:DBPTK7RYWUJ6DTRDWZ2GK3WZRT

not attested not anchored not stored refs pending

Multivariable Mendelian randomization with weak instruments: a comparison of Bayesian and frequentist methods

Andrew J. Grant, Ashish Patel, Stephen Burgess

arxiv:2606.26638 v1 · 2026-06-25 · stat.ME

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DBPTK7RYWUJ6DTRDWZ2GK3WZRT}

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	2026-06-26T01:15:36.835954Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

185f357e38b513e1ce23b674656ed98ccb0da9ec7bcdccda4471f34f726f069d

Aliases

arxiv: 2606.26638 · arxiv_version: 2606.26638v1 · doi: 10.48550/arxiv.2606.26638 · pith_short_12: DBPTK7RYWUJ6 · pith_short_16: DBPTK7RYWUJ6DTRD · pith_short_8: DBPTK7RY

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/DBPTK7RYWUJ6DTRDWZ2GK3WZRT \
  | 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: 185f357e38b513e1ce23b674656ed98ccb0da9ec7bcdccda4471f34f726f069d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94b3bbe329f246e9a8a0011e97116ac0ff27313557d12f2e43762aa671d18d53",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-06-25T06:04:56Z",
    "title_canon_sha256": "b19a88c39779153ccd340ea843fb65eb6e5474d22ac01bb18cd78672ab13a7c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.26638",
    "kind": "arxiv",
    "version": 1
  }
}