Pith Number

pith:Z25C7GDU

pith:2017:Z25C7GDU7MQS3B2576A53MQHHR

not attested not anchored not stored refs pending

A Second Wave of Expanders over Finite Fields

Brendan Murphy, Giorgis Petridis

arxiv:1701.01635 v1 · 2017-01-06 · 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{Z25C7GDU7MQS3B2576A53MQHHR}

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	2026-05-18T00:53:16.350057Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ceba2f9874fb212d875dff81ddb2073c6441937bcb79a19aa178f475359ecee1

Aliases

arxiv: 1701.01635 · arxiv_version: 1701.01635v1 · doi: 10.48550/arxiv.1701.01635 · pith_short_12: Z25C7GDU7MQS · pith_short_16: Z25C7GDU7MQS3B25 · pith_short_8: Z25C7GDU

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/Z25C7GDU7MQS3B2576A53MQHHR \
  | 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: ceba2f9874fb212d875dff81ddb2073c6441937bcb79a19aa178f475359ecee1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "93d7e37b278548b0410d727ae82e0fd88b734ed91c67d1cced586c707416a9de",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-01-06T13:54:47Z",
    "title_canon_sha256": "7b06c35d33be1bce4abf535ef2b79dbd83945cb133b4f32e912409bc3a54b25e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.01635",
    "kind": "arxiv",
    "version": 1
  }
}