Pith Number

pith:LSOGHRL5

pith:2007:LSOGHRL5DJE2IIECDZB2LVTUMP

not attested not anchored not stored refs pending

Combination of quasiconvex subgroups of relatively hyperbolic groups

Eduardo Martinez-Pedroza

arxiv:0709.2113 v2 · 2007-09-13 · 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{LSOGHRL5DJE2IIECDZB2LVTUMP}

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	2026-05-18T01:20:49.123313Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c9c63c57d1a49a420821e43a5d67463ff0b6b7fdf30590124571dae2b408aaa

Aliases

arxiv: 0709.2113 · arxiv_version: 0709.2113v2 · doi: 10.48550/arxiv.0709.2113 · pith_short_12: LSOGHRL5DJE2 · pith_short_16: LSOGHRL5DJE2IIEC · pith_short_8: LSOGHRL5

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/LSOGHRL5DJE2IIECDZB2LVTUMP \
  | 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: 5c9c63c57d1a49a420821e43a5d67463ff0b6b7fdf30590124571dae2b408aaa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "820a3673114225286a9a861a28cd27876db938363da81b191e465dadec4f335c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2007-09-13T17:01:21Z",
    "title_canon_sha256": "89f291c2d2b4ddad22ae054ba2adea4f0b78205c67fb84d816d6fd5f1695c785"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.2113",
    "kind": "arxiv",
    "version": 2
  }
}