Pith Number

pith:32ZIJ3WW

pith:2016:32ZIJ3WW72VSERM2JDGRLLF7K3

not attested not anchored not stored refs pending

The geometry of efficient arithmetic on elliptic curves

David Kohel

arxiv:1601.03665 v1 · 2016-01-14 · 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{32ZIJ3WW72VSERM2JDGRLLF7K3}

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	2026-05-18T01:22:52.896449Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

deb284eed6feab22459a48cd15acbf56f7b58935df5d9ffaebb9bb0c5bc455e5

Aliases

arxiv: 1601.03665 · arxiv_version: 1601.03665v1 · doi: 10.48550/arxiv.1601.03665 · pith_short_12: 32ZIJ3WW72VS · pith_short_16: 32ZIJ3WW72VSERM2 · pith_short_8: 32ZIJ3WW

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/32ZIJ3WW72VSERM2JDGRLLF7K3 \
  | 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: deb284eed6feab22459a48cd15acbf56f7b58935df5d9ffaebb9bb0c5bc455e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a03be829eabb64e09bbc6b0a2894d47435cc0d6d539803a1f57f0f611854d49",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-01-14T16:59:43Z",
    "title_canon_sha256": "589fcd8fc1b4fd8ffdd656fa2994a54634a563654b88ea95f008a713492bc805"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.03665",
    "kind": "arxiv",
    "version": 1
  }
}