Pith Number

pith:DRMKHHPQ

pith:2020:DRMKHHPQ7PISDEFFE2XTCIAWNM

not attested not anchored not stored refs pending

A note on the structure of expanders

Itai Benjamini, Mikolaj Fraczyk

arxiv:2010.08944 v1 · 2020-10-18 · math.CO · math.GR · 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{DRMKHHPQ7PISDEFFE2XTCIAWNM}

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	2026-07-05T01:43:46.863190Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c58a39df0fbd12190a526af3120166b3e775f13aa09e3900ba12bc9a6956641

Aliases

arxiv: 2010.08944 · arxiv_version: 2010.08944v1 · doi: 10.48550/arxiv.2010.08944 · pith_short_12: DRMKHHPQ7PIS · pith_short_16: DRMKHHPQ7PISDEFF · pith_short_8: DRMKHHPQ

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/DRMKHHPQ7PISDEFFE2XTCIAWNM \
  | 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: 1c58a39df0fbd12190a526af3120166b3e775f13aa09e3900ba12bc9a6956641

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9011b03311d9c31534a5f3ebef99ac539c5b544fedd988e9ae5a6d8562b52cb9",
    "cross_cats_sorted": [
      "math.GR",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-10-18T08:53:05Z",
    "title_canon_sha256": "bd5cfb5296dcd9ced92eb04f361f74e4686d2a3c9c0a1016ba732dedf3d90eeb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2010.08944",
    "kind": "arxiv",
    "version": 1
  }
}