Pith Number

pith:7CVQCEKG

pith:2016:7CVQCEKGJZ74QUFO6Z5I6GEQSO

not attested not anchored not stored refs pending

Lower Bounds on Words Separation: Are There Short Identities in Transformation Semigroups?

Andrei A. Bulatov, Arseny M. Shur, Konstantin Startsev, Olga Karpova

arxiv:1609.03199 v1 · 2016-09-11 · math.CO · cs.FL · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7CVQCEKGJZ74QUFO6Z5I6GEQSO}

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	2026-05-18T01:04:47.544188Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8ab0111464e7fc850aef67a8f1890938b11ed5b6e480458698565d5f3767508

Aliases

arxiv: 1609.03199 · arxiv_version: 1609.03199v1 · doi: 10.48550/arxiv.1609.03199 · pith_short_12: 7CVQCEKGJZ74 · pith_short_16: 7CVQCEKGJZ74QUFO · pith_short_8: 7CVQCEKG

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/7CVQCEKGJZ74QUFO6Z5I6GEQSO \
  | 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: f8ab0111464e7fc850aef67a8f1890938b11ed5b6e480458698565d5f3767508

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4424a6a6fb582f2b0986d308d5fd237bed7d11d4ff62836114c5896c242fc94",
    "cross_cats_sorted": [
      "cs.FL",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-09-11T19:22:58Z",
    "title_canon_sha256": "8fa9b8734db0646c588dc7992d6cb1d2728e4b599d2a954bd19a7ec03ea6e379"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.03199",
    "kind": "arxiv",
    "version": 1
  }
}