Pith Number

pith:NV64ZT75

pith:2010:NV64ZT75QRJOPNFN4YMG7SAHUT

not attested not anchored not stored refs pending

Complete classification of torsion of elliptic curves over quadratic cyclotomic fields

Filip Najman

arxiv:1005.0560 v1 · 2010-05-04 · 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{NV64ZT75QRJOPNFN4YMG7SAHUT}

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	2026-05-18T04:07:52.791873Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d7dcccffd8452e7b4ade6186fc807a4cce8eee3f4cbce608b0191a7aeafa648

Aliases

arxiv: 1005.0560 · arxiv_version: 1005.0560v1 · doi: 10.48550/arxiv.1005.0560 · pith_short_12: NV64ZT75QRJO · pith_short_16: NV64ZT75QRJOPNFN · pith_short_8: NV64ZT75

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/NV64ZT75QRJOPNFN4YMG7SAHUT \
  | 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: 6d7dcccffd8452e7b4ade6186fc807a4cce8eee3f4cbce608b0191a7aeafa648

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cfc8bafdc7dcc51f3bb85c6fe769b3c69ff4773dcbc4cb5df42c2faf709232a3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-05-04T15:36:08Z",
    "title_canon_sha256": "ab4d27d5adef75ea0c464b1d6e5c00ac0884cff164eba385a609e0a6c0710693"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.0560",
    "kind": "arxiv",
    "version": 1
  }
}