Pith Number

pith:NLQIBBRZ

pith:2011:NLQIBBRZ27UTFA6YQ3MQGDSEH4

not attested not anchored not stored refs pending

A mean value formula for elliptic curves

Hongfeng Wu, Rongquan Feng

arxiv:1107.0506 v1 · 2011-07-04 · 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{NLQIBBRZ27UTFA6YQ3MQGDSEH4}

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	2026-05-18T04:18:53.833770Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ae0808639d7e93283d886d9030e443f352dbf67abf2739d5a7178c24f4fe087

Aliases

arxiv: 1107.0506 · arxiv_version: 1107.0506v1 · doi: 10.48550/arxiv.1107.0506 · pith_short_12: NLQIBBRZ27UT · pith_short_16: NLQIBBRZ27UTFA6Y · pith_short_8: NLQIBBRZ

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/NLQIBBRZ27UTFA6YQ3MQGDSEH4 \
  | 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: 6ae0808639d7e93283d886d9030e443f352dbf67abf2739d5a7178c24f4fe087

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ecb607ad535354cc36a1f9d053905fe54381df2d753f971e0d23050f6221e6da",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-07-04T00:16:09Z",
    "title_canon_sha256": "1326d61e36f0433d3a8ba6b0a2893dd095ea1a8dce0bc0754c27054e994730d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.0506",
    "kind": "arxiv",
    "version": 1
  }
}