Pith Number

pith:4UFCF7CH

pith:2012:4UFCF7CHK3Q2TLPSOS7LGTLSU5

not attested not anchored not stored refs pending

One half log discriminant and division polynomials

Robin de Jong

arxiv:1207.5387 v1 · 2012-07-23 · 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{4UFCF7CHK3Q2TLPSOS7LGTLSU5}

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	2026-05-18T03:50:23.679034Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e50a22fc4756e1a9adf274beb34d72a76a859873d17bffea825192b578d76a46

Aliases

arxiv: 1207.5387 · arxiv_version: 1207.5387v1 · doi: 10.48550/arxiv.1207.5387 · pith_short_12: 4UFCF7CHK3Q2 · pith_short_16: 4UFCF7CHK3Q2TLPS · pith_short_8: 4UFCF7CH

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/4UFCF7CHK3Q2TLPSOS7LGTLSU5 \
  | 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: e50a22fc4756e1a9adf274beb34d72a76a859873d17bffea825192b578d76a46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b3ea9072cecb6c3313d8e729d750a98a4eb9a339d645b9e7a811c64ed8219de",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-07-23T13:20:08Z",
    "title_canon_sha256": "9351f2cf88e39e44c50c6c3910852c3d73efcabb40dc0b6301dfb9f5bc485b6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.5387",
    "kind": "arxiv",
    "version": 1
  }
}