Pith Number

pith:3D4VF2AG

pith:2026:3D4VF2AGU6P6OPWGGOOPLSLMJ5

not attested not anchored not stored refs pending

Gaussian rigidity for infinite exchangeable sequences

Qi Zhou, Yushu Zheng

arxiv:2606.25976 v1 · 2026-06-24 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3D4VF2AGU6P6OPWGGOOPLSLMJ5}

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	2026-06-25T01:18:44.841209Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8f952e806a79fe73ec6339cf5c96c4f5dd1a5e7db9f1101be9d49140cab302c

Aliases

arxiv: 2606.25976 · arxiv_version: 2606.25976v1 · doi: 10.48550/arxiv.2606.25976 · pith_short_12: 3D4VF2AGU6P6 · pith_short_16: 3D4VF2AGU6P6OPWG · pith_short_8: 3D4VF2AG

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/3D4VF2AGU6P6OPWGGOOPLSLMJ5 \
  | 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: d8f952e806a79fe73ec6339cf5c96c4f5dd1a5e7db9f1101be9d49140cab302c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4883dc0ba13c6361fcf6b03bc0b7506ddaca100d6ae59cd4b4fcc91011d22097",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-24T15:47:15Z",
    "title_canon_sha256": "91f93ee0706f764fe5c75be260bc12fefdc4200180e116b14695476594ab440e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.25976",
    "kind": "arxiv",
    "version": 1
  }
}