Pith Number

pith:D4QVPHVO

pith:2016:D4QVPHVOFAN22PSSCXELC6PZ3N

not attested not anchored not stored refs pending

Canonical lifts of families of elliptic curves

James Borger, Lance Gurney

arxiv:1608.05912 v1 · 2016-08-21 · math.NT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D4QVPHVOFAN22PSSCXELC6PZ3N}

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	2026-05-17T23:53:13.053456Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f21579eae281bad3e5215c8b179f9db5944362c1682800bcc52f2c587dd5a03

Aliases

arxiv: 1608.05912 · arxiv_version: 1608.05912v1 · doi: 10.48550/arxiv.1608.05912 · pith_short_12: D4QVPHVOFAN2 · pith_short_16: D4QVPHVOFAN22PSS · pith_short_8: D4QVPHVO

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/D4QVPHVOFAN22PSSCXELC6PZ3N \
  | 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: 1f21579eae281bad3e5215c8b179f9db5944362c1682800bcc52f2c587dd5a03

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b9b35e0d69dfcfb640bd9cd0429b3e56184e6930c7422d17aff279d45a03043",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-08-21T10:05:36Z",
    "title_canon_sha256": "a5e69e90140046389da394f5b0a784e3b61dcd24a6146a1eac12eee1da8dc8ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.05912",
    "kind": "arxiv",
    "version": 1
  }
}