Pith Number

pith:TE44VYYU

pith:2015:TE44VYYUY5FUWY7OIIC5TFMFKQ

not attested not anchored not stored refs pending

The Cheeger Constant, Isoperimetric Problems, and Hyperbolic Surfaces

Brian Benson

arxiv:1509.08993 v2 · 2015-09-30 · math.DG · math.GT · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TE44VYYUY5FUWY7OIIC5TFMFKQ}

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	2026-05-18T01:23:18.570880Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9939cae314c74b4b63ee4205d99585543d81b2ad1f8366074b1a4d311988fb22

Aliases

arxiv: 1509.08993 · arxiv_version: 1509.08993v2 · doi: 10.48550/arxiv.1509.08993 · pith_short_12: TE44VYYUY5FU · pith_short_16: TE44VYYUY5FUWY7O · pith_short_8: TE44VYYU

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/TE44VYYUY5FUWY7OIIC5TFMFKQ \
  | 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: 9939cae314c74b4b63ee4205d99585543d81b2ad1f8366074b1a4d311988fb22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "495c8f5d9e1a11e257882b6a8f5e210c3ea148169d7c4cb33f0b40c04fdc0a86",
    "cross_cats_sorted": [
      "math.GT",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-09-30T02:06:45Z",
    "title_canon_sha256": "afef278788f1160385d4ac89c83816e6a6bec034a0474cdd87514dc9beb766fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.08993",
    "kind": "arxiv",
    "version": 2
  }
}