Pith Number

pith:PNKU5QWI

pith:2015:PNKU5QWI6HTCV2JAFPYZKD5YSF

not attested not anchored not stored refs pending

Higher descents on an elliptic curve with a rational 2-torsion point

Tom Fisher

arxiv:1509.03234 v1 · 2015-09-10 · 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{PNKU5QWI6HTCV2JAFPYZKD5YSF}

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	2026-05-18T01:33:24.974126Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b554ec2c8f1e62ae9202bf1950fb8917e63fe0cf1ef4af119a1c49d76e40464

Aliases

arxiv: 1509.03234 · arxiv_version: 1509.03234v1 · doi: 10.48550/arxiv.1509.03234 · pith_short_12: PNKU5QWI6HTC · pith_short_16: PNKU5QWI6HTCV2JA · pith_short_8: PNKU5QWI

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/PNKU5QWI6HTCV2JAFPYZKD5YSF \
  | 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: 7b554ec2c8f1e62ae9202bf1950fb8917e63fe0cf1ef4af119a1c49d76e40464

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "465c3ce2592a3b0f101bcc64602695a86b3d419eb5c20f80fe3052360040ec7b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-09-10T17:15:25Z",
    "title_canon_sha256": "75891e5f693109146a333e18fb0a7d6478a53682374509a76960bd65a7d06d6e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.03234",
    "kind": "arxiv",
    "version": 1
  }
}