Pith Number

pith:CA2HA4V5

pith:2013:CA2HA4V5EAUKMXRYVF5BGLJJRX

not attested not anchored not stored refs pending

Quasi-convexity of hyperbolically embedded subgroups

Alessandro Sisto

arxiv:1310.7753 v1 · 2013-10-29 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CA2HA4V5EAUKMXRYVF5BGLJJRX}

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	2026-05-18T03:08:35.378849Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10347072bd2028a65e38a97a132d298dfb598a7db7bad6114936f3d099858fc9

Aliases

arxiv: 1310.7753 · arxiv_version: 1310.7753v1 · doi: 10.48550/arxiv.1310.7753 · pith_short_12: CA2HA4V5EAUK · pith_short_16: CA2HA4V5EAUKMXRY · pith_short_8: CA2HA4V5

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/CA2HA4V5EAUKMXRYVF5BGLJJRX \
  | 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: 10347072bd2028a65e38a97a132d298dfb598a7db7bad6114936f3d099858fc9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e706f798568961ef01c069cf41df625e908c971857a50000c7eb93e115949bc",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-10-29T11:00:03Z",
    "title_canon_sha256": "dbfab355955e719ca8b64f23d892d5560e9d24c4006419c15df4a0de8530a8e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.7753",
    "kind": "arxiv",
    "version": 1
  }
}