Pith Number

pith:XDC3IJJ4

pith:2016:XDC3IJJ4SUWUFYYP3S6G6GK6D2

not attested not anchored not stored refs pending

Cheeger isoperimetric constant of Gromov hyperbolic manifolds and graphs

\'Alvaro Mart\'inez-P\'erez, Jos\'e M. Rodr\'iguez

arxiv:1605.04394 v1 · 2016-05-14 · math.MG · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XDC3IJJ4SUWUFYYP3S6G6GK6D2}

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	2026-05-18T01:14:51.817969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8c5b4253c952d42e30fdcbc6f195e1e932d0a43eac53dc9e9ee79231db04b29

Aliases

arxiv: 1605.04394 · arxiv_version: 1605.04394v1 · doi: 10.48550/arxiv.1605.04394 · pith_short_12: XDC3IJJ4SUWU · pith_short_16: XDC3IJJ4SUWUFYYP · pith_short_8: XDC3IJJ4

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/XDC3IJJ4SUWUFYYP3S6G6GK6D2 \
  | 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: b8c5b4253c952d42e30fdcbc6f195e1e932d0a43eac53dc9e9ee79231db04b29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "409879fee2c0f6c9acdc6805c45add5c69e66e783b5479d7821852cd9666edae",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2016-05-14T08:52:56Z",
    "title_canon_sha256": "79211d9f00d8e147054386eb20da6f0474efef424e0f502d741e68ade655a2f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.04394",
    "kind": "arxiv",
    "version": 1
  }
}