Pith Number

pith:AA5NUE7C

pith:2013:AA5NUE7CD2XWPSS6PRJHO4EZ7Y

not attested not anchored not stored refs pending

Expanders with respect to Hadamard spaces and random graphs

Assaf Naor, Manor Mendel

arxiv:1306.5434 v2 · 2013-06-23 · math.MG · cs.DS · math.CO · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AA5NUE7CD2XWPSS6PRJHO4EZ7Y}

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	2026-05-18T01:28:15.195617Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

003ada13e21eaf67ca5e7c52777099fe0110a6bbb7a89d488dc401f7244ebcf4

Aliases

arxiv: 1306.5434 · arxiv_version: 1306.5434v2 · doi: 10.48550/arxiv.1306.5434 · pith_short_12: AA5NUE7CD2XW · pith_short_16: AA5NUE7CD2XWPSS6 · pith_short_8: AA5NUE7C

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/AA5NUE7CD2XWPSS6PRJHO4EZ7Y \
  | 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: 003ada13e21eaf67ca5e7c52777099fe0110a6bbb7a89d488dc401f7244ebcf4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb5eecdb48d71a858be3ce400632535c1683e1dca4338406ed0ba44059261791",
    "cross_cats_sorted": [
      "cs.DS",
      "math.CO",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2013-06-23T16:29:21Z",
    "title_canon_sha256": "197ee0705c2746239696600dcc646c75017d851159c30dddbd3fe89919e3db96"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.5434",
    "kind": "arxiv",
    "version": 2
  }
}