Pith Number

pith:ES5MMDND

pith:2018:ES5MMDND2SHL27SOH4PXDG7KHV

not attested not anchored not stored refs pending

On the degree of the $p$-torsion field of elliptic curves over $\mathbb{Q}_\ell$ for $\ell \neq p$

Alain Kraus, Nuno Freitas

arxiv:1804.07627 v1 · 2018-04-20 · 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{ES5MMDND2SHL27SOH4PXDG7KHV}

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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	2026-05-18T00:17:58.270404Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

24bac60da3d48ebd7e4e3f1f719bea3d5eeb702656d7c0c13cb8c04ef025b612

Aliases

arxiv: 1804.07627 · arxiv_version: 1804.07627v1 · doi: 10.48550/arxiv.1804.07627 · pith_short_12: ES5MMDND2SHL · pith_short_16: ES5MMDND2SHL27SO · pith_short_8: ES5MMDND

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/ES5MMDND2SHL27SOH4PXDG7KHV \
  | 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: 24bac60da3d48ebd7e4e3f1f719bea3d5eeb702656d7c0c13cb8c04ef025b612

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bba86cef44b1d56bcaa495d1e04d8c4535ac3eafc62a1a30189364574090c3ff",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-04-20T14:11:16Z",
    "title_canon_sha256": "d8e28a60197a1a32291d7cad15c71fd9073733663029d3e872a8f2f753b7b2a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.07627",
    "kind": "arxiv",
    "version": 1
  }
}