Pith Number

pith:REVOYCXR

pith:2012:REVOYCXRWIGLRZC2HIP6QCWYUC

not attested not anchored not stored refs pending

Rank gradient and cost of Artin groups and their relatives

Aditi Kar, Nikolay Nikolov

arxiv:1210.2873 v4 · 2012-10-10 · 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{REVOYCXRWIGLRZC2HIP6QCWYUC}

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	2026-05-18T02:52:42.276874Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

892aec0af1b20cb8e45a3a1fe80ad8a0a0a9878e8ef5be865476ef663962f3aa

Aliases

arxiv: 1210.2873 · arxiv_version: 1210.2873v4 · doi: 10.48550/arxiv.1210.2873 · pith_short_12: REVOYCXRWIGL · pith_short_16: REVOYCXRWIGLRZC2 · pith_short_8: REVOYCXR

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/REVOYCXRWIGLRZC2HIP6QCWYUC \
  | 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: 892aec0af1b20cb8e45a3a1fe80ad8a0a0a9878e8ef5be865476ef663962f3aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4fc255c2a5a809c68a265d3cf419c3cdfba64e491f6008730fab690b9b5d43f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-10-10T11:14:44Z",
    "title_canon_sha256": "8f852ffebf27a85e34410503ad5905d54d26723aca5583f22894a5a24ef3d533"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.2873",
    "kind": "arxiv",
    "version": 4
  }
}