Pith Number

pith:VQ4ZZ3MM

pith:2026:VQ4ZZ3MMF5A3YTFYFLWN2TXBVC

not attested not anchored not stored refs pending

Spatial depth characterizes probability measures

Alberto Gonz\'alez-Sanz, Dimitri Konen

arxiv:2607.04375 v1 · 2026-07-05 · math.ST · 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{VQ4ZZ3MMF5A3YTFYFLWN2TXBVC}

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	2026-07-07T02:19:15.404526Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac399ced8c2f41bc4cb82aecdd4ee1a8aae11fb61e7365b7226f6d074411b426

Aliases

arxiv: 2607.04375 · arxiv_version: 2607.04375v1 · doi: 10.48550/arxiv.2607.04375 · pith_short_12: VQ4ZZ3MMF5A3 · pith_short_16: VQ4ZZ3MMF5A3YTFY · pith_short_8: VQ4ZZ3MM

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/VQ4ZZ3MMF5A3YTFYFLWN2TXBVC \
  | 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: ac399ced8c2f41bc4cb82aecdd4ee1a8aae11fb61e7365b7226f6d074411b426

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d23a5ae6c81e8ace7d7d46861335ff47484ee99161ebb5adb176d296351dc3fb",
    "cross_cats_sorted": [
      "math.PR",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2026-07-05T16:08:23Z",
    "title_canon_sha256": "474c864d27008bb74ee6537defd9339f5a820c5102585d9a8f7e3d2f454dbf1f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.04375",
    "kind": "arxiv",
    "version": 1
  }
}