Pith Number

pith:4XPD3GXQ

pith:2026:4XPD3GXQ63WLJLDP3GHOA3F5N7

not attested not anchored not stored refs pending

The Value of Depth in Message Passing on Sparse Graphs: A Kesten-Stigum Dichotomy

Aseem Raj Baranwal

arxiv:2607.16676 v1 · 2026-07-18 · math.ST · cs.LG · math.PR · stat.ML · 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{4XPD3GXQ63WLJLDP3GHOA3F5N7}

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	2026-07-21T01:20:21.430759Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5de3d9af0f6ecb4ac6fd98ee06cbd6ffbfcad389b908ab9d64871ff681c806d

Aliases

arxiv: 2607.16676 · arxiv_version: 2607.16676v1 · doi: 10.48550/arxiv.2607.16676 · pith_short_12: 4XPD3GXQ63WL · pith_short_16: 4XPD3GXQ63WLJLDP · pith_short_8: 4XPD3GXQ

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/4XPD3GXQ63WLJLDP3GHOA3F5N7 \
  | 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: e5de3d9af0f6ecb4ac6fd98ee06cbd6ffbfcad389b908ab9d64871ff681c806d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "176b3a36071bb9021dd735aef1f82a898680e5fc930fe1448b4c6ab3690f4f2e",
    "cross_cats_sorted": [
      "cs.LG",
      "math.PR",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-07-18T07:11:45Z",
    "title_canon_sha256": "0923b3a016ece23cecea71e451ec47a5247a1c767d6ae6ccc7062bd6ff3dd152"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.16676",
    "kind": "arxiv",
    "version": 1
  }
}