Pith Number

pith:7TEUZSRC

pith:2012:7TEUZSRCVRSWFCYNAZILRANPHL

not attested not anchored not stored refs pending

The trace of Frobenius of elliptic curves and the $p$-adic gamma function

Dermot McCarthy

arxiv:1205.5001 v4 · 2012-05-22 · 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{7TEUZSRCVRSWFCYNAZILRANPHL}

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	2026-05-18T03:29:40.709567Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fcc94cca22ac65628b0d0650b881af3acd4e8aa671b918988f1c1d1f23a7fb93

Aliases

arxiv: 1205.5001 · arxiv_version: 1205.5001v4 · doi: 10.48550/arxiv.1205.5001 · pith_short_12: 7TEUZSRCVRSW · pith_short_16: 7TEUZSRCVRSWFCYN · pith_short_8: 7TEUZSRC

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/7TEUZSRCVRSWFCYNAZILRANPHL \
  | 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: fcc94cca22ac65628b0d0650b881af3acd4e8aa671b918988f1c1d1f23a7fb93

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2edb9614962e719d0efc8afcc165a83da8d79e92ee6b85b8e58c78de872d771",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-05-22T18:33:35Z",
    "title_canon_sha256": "137468eeced5f7fbaf611b6ef3684087786aef585130200f3eaa314d153aab7c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.5001",
    "kind": "arxiv",
    "version": 4
  }
}