Pith Number

pith:N2Z4YRDV

pith:2011:N2Z4YRDVNFZEBAMXHKHWBQIZ56

not attested not anchored not stored refs pending

Second Isogeny Descents and the Birch and Swinnerton-Dyer Conjectural Formula

Brendan Creutz, Robert L. Miller

arxiv:1105.4018 v2 · 2011-05-20 · 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{N2Z4YRDVNFZEBAMXHKHWBQIZ56}

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	2026-05-18T01:24:13.048669Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6eb3cc447569724081973a8f60c119efb8b0f23f156761c45cf5cb2aafb2edda

Aliases

arxiv: 1105.4018 · arxiv_version: 1105.4018v2 · doi: 10.48550/arxiv.1105.4018 · pith_short_12: N2Z4YRDVNFZE · pith_short_16: N2Z4YRDVNFZEBAMX · pith_short_8: N2Z4YRDV

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/N2Z4YRDVNFZEBAMXHKHWBQIZ56 \
  | 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: 6eb3cc447569724081973a8f60c119efb8b0f23f156761c45cf5cb2aafb2edda

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1ca326e0bae8b2484be0abb376eeb813ee5b22fb0cfff9e943e148d36c5d6ab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-05-20T06:36:29Z",
    "title_canon_sha256": "cb98aeb3dabe2ce0dbf3471ac6dbd7b5f60b9d6f01c7d9bc7f2ec8a7e8a230dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.4018",
    "kind": "arxiv",
    "version": 2
  }
}