Pith Number

pith:IMF5JODA

pith:2012:IMF5JODA2NERXZW2RMT2A3SSVQ

not attested not anchored not stored refs pending

On the average exponent of elliptic curves modulo p

P\"ar Kurlberg, Tristan Freiberg

arxiv:1203.4382 v3 · 2012-03-20 · 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{IMF5JODA2NERXZW2RMT2A3SSVQ}

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	2026-05-18T03:38:56.056427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

430bd4b860d3491be6da8b27a06e52ac2e9e02f54aacb62b113a91a4df8a91d5

Aliases

arxiv: 1203.4382 · arxiv_version: 1203.4382v3 · doi: 10.48550/arxiv.1203.4382 · pith_short_12: IMF5JODA2NER · pith_short_16: IMF5JODA2NERXZW2 · pith_short_8: IMF5JODA

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/IMF5JODA2NERXZW2RMT2A3SSVQ \
  | 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: 430bd4b860d3491be6da8b27a06e52ac2e9e02f54aacb62b113a91a4df8a91d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33a4351d1a3060c1b2d363280751542861b3aecd82c1d583ed34550003022c9c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-03-20T10:43:21Z",
    "title_canon_sha256": "06fb21a6941f9da9e0425095c487994917dfdd628deae8520ca6b542cb1edcef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.4382",
    "kind": "arxiv",
    "version": 3
  }
}