Pith Number

pith:SA4HKZRC

pith:2015:SA4HKZRCZ6Y3MWG34NHAKA6TQM

not attested not anchored not stored refs pending

Expanders are order diameter non-hyperbolic

Anton Malyshev

arxiv:1501.07904 v2 · 2015-01-30 · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SA4HKZRCZ6Y3MWG34NHAKA6TQM}

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	2026-05-18T02:26:12.360572Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9038756622cfb1b658dbe34e0503d3830a9b33760626e0662976272fa27bd63c

Aliases

arxiv: 1501.07904 · arxiv_version: 1501.07904v2 · doi: 10.48550/arxiv.1501.07904 · pith_short_12: SA4HKZRCZ6Y3 · pith_short_16: SA4HKZRCZ6Y3MWG3 · pith_short_8: SA4HKZRC

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/SA4HKZRCZ6Y3MWG34NHAKA6TQM \
  | 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: 9038756622cfb1b658dbe34e0503d3830a9b33760626e0662976272fa27bd63c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed42aebfa1bdd464b3a87fce6f1de8ade33dd06397a5c041711af697e79fbeef",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-01-30T20:34:12Z",
    "title_canon_sha256": "907630582cee5b57015a8513b56919a2569584ee75bb49efe8ae0540d506eac5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.07904",
    "kind": "arxiv",
    "version": 2
  }
}