Pith Number

pith:C37AM7F7

pith:2010:C37AM7F73DYHWI2SKBLYWTQ7NB

not attested not anchored not stored refs pending

Relative hyperbolicity and similar properties of one-generator one-relator relative presentations with powered unimodular relator

Anton A. Klyachko, Denis E. Lurye

arxiv:1010.4220 v3 · 2010-10-20 · 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{C37AM7F73DYHWI2SKBLYWTQ7NB}

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	2026-05-18T02:23:45.190523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

16fe067cbfd8f07b235250578b4e1f686f8c7d684621cadc499f15f4cce57969

Aliases

arxiv: 1010.4220 · arxiv_version: 1010.4220v3 · doi: 10.48550/arxiv.1010.4220 · pith_short_12: C37AM7F73DYH · pith_short_16: C37AM7F73DYHWI2S · pith_short_8: C37AM7F7

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/C37AM7F73DYHWI2SKBLYWTQ7NB \
  | 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: 16fe067cbfd8f07b235250578b4e1f686f8c7d684621cadc499f15f4cce57969

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db939bcf291aabbba5a5d0a18e8239b78f394d0fccada7e104cbd3d23d521f49",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-10-20T15:04:25Z",
    "title_canon_sha256": "1f01b4787304ac078dfda2590b852245db6cf97dea514e228790c006db87bad9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4220",
    "kind": "arxiv",
    "version": 3
  }
}