Pith Number

pith:WRQAX4GE

pith:2013:WRQAX4GEP5HWFGGSUC4DTQ7ZXF

not attested not anchored not stored refs pending

Canonical heights and division polynomials

J. Steffen M\"uller, Robin de Jong

arxiv:1306.4030 v1 · 2013-06-17 · 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{WRQAX4GEP5HWFGGSUC4DTQ7ZXF}

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	2026-05-17T23:53:35.563330Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4600bf0c47f4f6298d2a0b839c3f9b96552120c1f145659a915b50d672f4284

Aliases

arxiv: 1306.4030 · arxiv_version: 1306.4030v1 · doi: 10.48550/arxiv.1306.4030 · pith_short_12: WRQAX4GEP5HW · pith_short_16: WRQAX4GEP5HWFGGS · pith_short_8: WRQAX4GE

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/WRQAX4GEP5HWFGGSUC4DTQ7ZXF \
  | 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: b4600bf0c47f4f6298d2a0b839c3f9b96552120c1f145659a915b50d672f4284

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f82b7e9abdaaa011303505fd1350b69cebacd1a5d0588b68b9a0d4349d5ddcc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-06-17T21:59:01Z",
    "title_canon_sha256": "a7b7c66054bc24591f4bf3892de94f62b52c1731a2e29e4c46b977833938dd96"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.4030",
    "kind": "arxiv",
    "version": 1
  }
}