Pith Number

pith:FA3OIEYZ

pith:2011:FA3OIEYZI7AXQNPGOUHCNQCGGF

not attested not anchored not stored refs pending

The Rank and Hanna Neumann Property of Some Submonoids of a Free Monoid

K. V. Krishna, Shubh Narayan Singh

arxiv:1112.4250 v1 · 2011-12-19 · cs.FL · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FA3OIEYZI7AXQNPGOUHCNQCGGF}

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	2026-05-18T03:35:26.257408Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2836e4131947c17835e6750e26c046316b5dd23b747a0f7663cb4bfe75ae170a

Aliases

arxiv: 1112.4250 · arxiv_version: 1112.4250v1 · doi: 10.48550/arxiv.1112.4250 · pith_short_12: FA3OIEYZI7AX · pith_short_16: FA3OIEYZI7AXQNPG · pith_short_8: FA3OIEYZ

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/FA3OIEYZI7AXQNPGOUHCNQCGGF \
  | 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: 2836e4131947c17835e6750e26c046316b5dd23b747a0f7663cb4bfe75ae170a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "30d39f6225865acbf85e5b99228886fe5c22616ba3ef44d17f4d0f05b656cf20",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.FL",
    "submitted_at": "2011-12-19T07:11:41Z",
    "title_canon_sha256": "de8174be70dd9c609716185b98819c29f996bfefc48438e2b08a5de3460e285a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4250",
    "kind": "arxiv",
    "version": 1
  }
}