Pith Number

pith:O3ZMAFTV

pith:2013:O3ZMAFTVIAW22QCTTAOQSDZVUZ

not attested not anchored not stored refs pending

Formal Groups and Invariant Differentials of Elliptic Curves

Mohammad Sadek

arxiv:1303.6706 v2 · 2013-03-26 · 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{O3ZMAFTVIAW22QCTTAOQSDZVUZ}

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	2026-05-18T01:36:57.206498Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76f2c01675402dad4053981d090f35a648066d9d75616359f7f449adae167775

Aliases

arxiv: 1303.6706 · arxiv_version: 1303.6706v2 · doi: 10.48550/arxiv.1303.6706 · pith_short_12: O3ZMAFTVIAW2 · pith_short_16: O3ZMAFTVIAW22QCT · pith_short_8: O3ZMAFTV

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/O3ZMAFTVIAW22QCTTAOQSDZVUZ \
  | 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: 76f2c01675402dad4053981d090f35a648066d9d75616359f7f449adae167775

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65ccef82cb97f85093ec8aebcb658ff0bb3dfa32c31707ba9a6607fb86566243",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-03-26T23:42:06Z",
    "title_canon_sha256": "87e6eda0d6a20942f97b03172d172ec6a6820bf43c3f179ec12b3fa1d25fde0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.6706",
    "kind": "arxiv",
    "version": 2
  }
}