Pith Number

pith:QAEM3YZ4

pith:2013:QAEM3YZ4JA5GVQ7WKOIPQJ5RAZ

not attested not anchored not stored refs pending

Subtraction-free complexity, cluster transformations, and spanning trees

Dima Grigoriev, Gleb Koshevoy, Sergey Fomin

arxiv:1307.8425 v4 · 2013-07-31 · math.CO · cs.CC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QAEM3YZ4JA5GVQ7WKOIPQJ5RAZ}

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	2026-05-18T02:41:42.252966Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8008cde33c483a6ac3f65390f827b1064a4c400025849b8be5b53bb5335000b3

Aliases

arxiv: 1307.8425 · arxiv_version: 1307.8425v4 · doi: 10.48550/arxiv.1307.8425 · pith_short_12: QAEM3YZ4JA5G · pith_short_16: QAEM3YZ4JA5GVQ7W · pith_short_8: QAEM3YZ4

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/QAEM3YZ4JA5GVQ7WKOIPQJ5RAZ \
  | 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: 8008cde33c483a6ac3f65390f827b1064a4c400025849b8be5b53bb5335000b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5f36cb82d33eef663fda885428ae7d088e37cced9f66dbd7d74572922f3606f",
    "cross_cats_sorted": [
      "cs.CC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-07-31T18:59:00Z",
    "title_canon_sha256": "6bec5d80fe4917e3e5b7413c69e11ad5158c157df4fce674efc867ed69ce8b09"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.8425",
    "kind": "arxiv",
    "version": 4
  }
}