Pith Number

pith:3HBIQ2UC

pith:2026:3HBIQ2UCKK2SNEFKMNX3QHT723

not attested not anchored not stored refs pending

Average analytic rank for the $L$-functions of the elliptic curves $y^2=x^3-dx$

Alessandro Fazzari, Chantal David, Ezra Waxman, Lucile Devin

arxiv:2608.06286 v1 · 2026-08-06 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3HBIQ2UCKK2SNEFKMNX3QHT723}

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	2026-08-07T01:41:18.166271Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9c2886a8252b52690aa636fb81e7fd6c1ac2c34f8f82f3ff11dd8341d670ded

Aliases

arxiv: 2608.06286 · arxiv_version: 2608.06286v1 · doi: 10.48550/arxiv.2608.06286 · pith_short_12: 3HBIQ2UCKK2S · pith_short_16: 3HBIQ2UCKK2SNEFK · pith_short_8: 3HBIQ2UC

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/3HBIQ2UCKK2SNEFKMNX3QHT723 \
  | 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: d9c2886a8252b52690aa636fb81e7fd6c1ac2c34f8f82f3ff11dd8341d670ded

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a32b9f2d22c980a73e15d59801eed41f88478bffd52717b2746155008a8f5d80",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-08-06T17:12:01Z",
    "title_canon_sha256": "a02f6a7c840a356e7e56f7ad347febbef23053ba71d2aea8a034fac81738a109"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.06286",
    "kind": "arxiv",
    "version": 1
  }
}