Pith Number

pith:ICRUKJR2

pith:2008:ICRUKJR2Z76TNAVYTKXJRZZLZS

not attested not anchored not stored refs pending

Words Maps and Spectra of Random Graph Lifts

Doron Puder, Nati Linial

arxiv:0806.1993 v3 · 2008-06-12 · 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{ICRUKJR2Z76TNAVYTKXJRZZLZS}

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	2026-05-18T04:23:54.618535Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

40a345263acffd3682b89aae98e72bcc9354a3921074c1dcbe94952950c82637

Aliases

arxiv: 0806.1993 · arxiv_version: 0806.1993v3 · doi: 10.48550/arxiv.0806.1993 · pith_short_12: ICRUKJR2Z76T · pith_short_16: ICRUKJR2Z76TNAVY · pith_short_8: ICRUKJR2

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/ICRUKJR2Z76TNAVYTKXJRZZLZS \
  | 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: 40a345263acffd3682b89aae98e72bcc9354a3921074c1dcbe94952950c82637

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6691168f6dc2d5fe61bb951fb1e67ab692aa91c307a8767fbc6b5c9a68c70a45",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2008-06-12T03:25:52Z",
    "title_canon_sha256": "4716dd3ead80529c1548dc95ed71c932a14d57050597096e71ebfb984ccfffde"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0806.1993",
    "kind": "arxiv",
    "version": 3
  }
}