Pith Number

pith:ZTRJYAQU

pith:2010:ZTRJYAQU45C2TQGI5K4FDYBDVO

not attested not anchored not stored refs pending

Determining Edge Expansion and Other Connectivity Measures of Graphs of Bounded Genus

Viresh Patel

arxiv:1004.4484 v1 · 2010-04-26 · cs.DM · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZTRJYAQU45C2TQGI5K4FDYBDVO}

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	2026-07-04T17:27:19.183423Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cce29c0214e745a9c0c8eab851e023ababe66ec299bc06a15f9d78646ef69548

Aliases

arxiv: 1004.4484 · arxiv_version: 1004.4484v1 · doi: 10.48550/arxiv.1004.4484 · pith_short_12: ZTRJYAQU45C2 · pith_short_16: ZTRJYAQU45C2TQGI · pith_short_8: ZTRJYAQU

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/ZTRJYAQU45C2TQGI5K4FDYBDVO \
  | 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: cce29c0214e745a9c0c8eab851e023ababe66ec299bc06a15f9d78646ef69548

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c42e0be89aeb60f0ac98a47a5095afec86e6fffa6a188f8e808ba84728d4bcb",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2010-04-26T11:13:47Z",
    "title_canon_sha256": "05cfc2b50a09c64c31c3906b92c53af8efe2471eed4ad1560bf1c2a730690529"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.4484",
    "kind": "arxiv",
    "version": 1
  }
}