Pith Number

pith:B2SVSRVE

pith:2008:B2SVSRVEIVNTQW3GMFR4762LPE

not attested not anchored not stored refs pending

Expander graphs based on GRH with an application to elliptic curve cryptography

David Jao, Ramarathnam Venkatesan, Stephen D. Miller

arxiv:0811.0647 v2 · 2008-11-05 · math.NT · 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{B2SVSRVEIVNTQW3GMFR4762LPE}

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	2026-05-18T02:59:31.542384Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ea55946a4455b385b666163cffb4b79245a789e4c3f95ad77a800cd83ed1672

Aliases

arxiv: 0811.0647 · arxiv_version: 0811.0647v2 · doi: 10.48550/arxiv.0811.0647 · pith_short_12: B2SVSRVEIVNT · pith_short_16: B2SVSRVEIVNTQW3G · pith_short_8: B2SVSRVE

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/B2SVSRVEIVNTQW3GMFR4762LPE \
  | 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: 0ea55946a4455b385b666163cffb4b79245a789e4c3f95ad77a800cd83ed1672

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f9337f5809a2b6b797cbc3d6372c6ff31fa0f164d462c6f6854c32bb3e0535b",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2008-11-05T04:23:03Z",
    "title_canon_sha256": "168a719eaa5266982115dc2b0247318052b32ead7fc3b1a87161c67b42b48dc6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0811.0647",
    "kind": "arxiv",
    "version": 2
  }
}