Pith Number

pith:R3UFCKXU

pith:2026:R3UFCKXUDOJHIHQR2U32GZFUSP

not attested not anchored not stored refs pending

Counting Triangles of Graphs via Randomized Trace Estimation with Incomplete Matrix-Vector Products

Lior Horesh, Shashanka Ubaru, Soumyadip Ghosh, Tomasz Nowicki, Vasileios Kalantzis, Yingdong Lu

arxiv:2606.22629 v1 · 2026-06-21 · math.NA · cs.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R3UFCKXUDOJHIHQR2U32GZFUSP}

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	2026-06-23T02:13:43.517354Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ee8512af41b92741e11d537a364b493ee8642eed1491818f3290d1797dacbf3

Aliases

arxiv: 2606.22629 · arxiv_version: 2606.22629v1 · doi: 10.48550/arxiv.2606.22629 · pith_short_12: R3UFCKXUDOJH · pith_short_16: R3UFCKXUDOJHIHQR · pith_short_8: R3UFCKXU

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/R3UFCKXUDOJHIHQR2U32GZFUSP \
  | 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: 8ee8512af41b92741e11d537a364b493ee8642eed1491818f3290d1797dacbf3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "beaad28311b5f3536cee9dc8b996bbb7f7502e51bd5a580e40e813d2f0ada9c9",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-06-21T18:31:29Z",
    "title_canon_sha256": "d45cef4dd29bad27d8fca86a6f1516e769ca185b66d047c2e74ee13e56dc7f8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.22629",
    "kind": "arxiv",
    "version": 1
  }
}