Pith Number

pith:TEVPKDHJ

pith:2016:TEVPKDHJYQZX5AX6GZUWIERYFR

not attested not anchored not stored refs pending

Large Fixed-Diameter Graphs are Good Expanders

Gal Shahaf, Michael Dinitz, Michael Schapira

arxiv:1611.01755 v3 · 2016-11-06 · 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{TEVPKDHJYQZX5AX6GZUWIERYFR}

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	2026-05-18T00:29:52.043309Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

992af50ce9c4337e82fe36696412382c4f4c7cfb3504172955c0c0b111929423

Aliases

arxiv: 1611.01755 · arxiv_version: 1611.01755v3 · doi: 10.48550/arxiv.1611.01755 · pith_short_12: TEVPKDHJYQZX · pith_short_16: TEVPKDHJYQZX5AX6 · pith_short_8: TEVPKDHJ

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/TEVPKDHJYQZX5AX6GZUWIERYFR \
  | 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: 992af50ce9c4337e82fe36696412382c4f4c7cfb3504172955c0c0b111929423

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9683ba71d5d6e108aaf86629ee41f0a6c14605838621ed29ec81b7a3953ffc1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-11-06T10:51:21Z",
    "title_canon_sha256": "d14dcf87116422aa8e9aef68d75331eaf7889b951b570f4d19110b15e91f7020"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.01755",
    "kind": "arxiv",
    "version": 3
  }
}