Pith Number

pith:WTBFOXME

pith:2015:WTBFOXMEVR5IPS5DB4Q5JUQWUN

not attested not anchored not stored refs pending

Hyperbolicity vs. Amenability for planar graphs

Agelos Georgakopoulos, Bruno Federici

arxiv:1509.02028 v3 · 2015-09-07 · math.CO · 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{WTBFOXMEVR5IPS5DB4Q5JUQWUN}

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	2026-05-18T01:30:57.504226Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4c2575d84ac7a87cba30f21d4d216a361ccde4ed15d97c3bf96071a642584ea

Aliases

arxiv: 1509.02028 · arxiv_version: 1509.02028v3 · doi: 10.48550/arxiv.1509.02028 · pith_short_12: WTBFOXMEVR5I · pith_short_16: WTBFOXMEVR5IPS5D · pith_short_8: WTBFOXME

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/WTBFOXMEVR5IPS5DB4Q5JUQWUN \
  | 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: b4c2575d84ac7a87cba30f21d4d216a361ccde4ed15d97c3bf96071a642584ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "91201564c136b037fbd8f15bbe42fefa3c0d34408b284950b0cba58118ea0f15",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-09-07T13:20:21Z",
    "title_canon_sha256": "476f2e7cd281714ea749a0cea569b380d2d8f73cbcf16d042115c6f2de520d87"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.02028",
    "kind": "arxiv",
    "version": 3
  }
}