Pith Number

pith:2LS33LVK

pith:2015:2LS33LVKYMWUUSFYP4YPYESHXA

not attested not anchored not stored refs pending

Groebner-Shirshov bases for pre-associative algebras

Pavel Kolesnikov

arxiv:1509.06860 v1 · 2015-09-23 · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2LS33LVKYMWUUSFYP4YPYESHXA}

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	2026-05-18T00:02:02.449487Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d2e5bdaeaac32d4a48b87f30fc1247b80755be64c50cc3a9b86c87e1e26f5a1e

Aliases

arxiv: 1509.06860 · arxiv_version: 1509.06860v1 · doi: 10.48550/arxiv.1509.06860 · pith_short_12: 2LS33LVKYMWU · pith_short_16: 2LS33LVKYMWUUSFY · pith_short_8: 2LS33LVK

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/2LS33LVKYMWUUSFYP4YPYESHXA \
  | 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: d2e5bdaeaac32d4a48b87f30fc1247b80755be64c50cc3a9b86c87e1e26f5a1e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc4cfa19916aaeaf7dd40e1b64893634c4728901e452ffd7d8e6b580e52428e9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2015-09-23T06:55:57Z",
    "title_canon_sha256": "893080491e8d7b421ec4f5b2e9c2556a47a129f869b1888351ab3c8f4c478630"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.06860",
    "kind": "arxiv",
    "version": 1
  }
}