Pith Number

pith:MIHT2E6G

pith:2016:MIHT2E6GT3UCHLBZPBMPA2LNPD

not attested not anchored not stored refs pending

Congruences between Heegner points and quadratic twists of elliptic curves

Chao Li, Daniel Kriz

arxiv:1606.03172 v3 · 2016-06-10 · 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{MIHT2E6GT3UCHLBZPBMPA2LNPD}

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	2026-05-18T00:29:33.598140Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

620f3d13c69ee823ac397858f0696d78e068b7ac6e17be1ce738873839fd2e50

Aliases

arxiv: 1606.03172 · arxiv_version: 1606.03172v3 · doi: 10.48550/arxiv.1606.03172 · pith_short_12: MIHT2E6GT3UC · pith_short_16: MIHT2E6GT3UCHLBZ · pith_short_8: MIHT2E6G

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/MIHT2E6GT3UCHLBZPBMPA2LNPD \
  | 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: 620f3d13c69ee823ac397858f0696d78e068b7ac6e17be1ce738873839fd2e50

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d2485dee5a4c67c37ffecac24347a1f0bb60ccd220566545f6f995a624f456f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-06-10T03:56:00Z",
    "title_canon_sha256": "a1edff75c3362cbf4d2fc357375571e0161d6db196f4195a8c8343a7758caa8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.03172",
    "kind": "arxiv",
    "version": 3
  }
}