Pith Number

pith:EFCZCSP7

pith:2013:EFCZCSP7RX466BGFNAMJGM6VNK

not attested not anchored not stored refs pending

On quadratic points of classical modular curves

Francesc Bars

arxiv:1308.3267 v2 · 2013-08-14 · math.NT · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EFCZCSP7RX466BGFNAMJGM6VNK}

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	2026-05-18T03:15:44.808101Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

21459149ff8df9ef04c568189333d56aaf3380ad4c4e43186f224b2e3b5cde48

Aliases

arxiv: 1308.3267 · arxiv_version: 1308.3267v2 · doi: 10.48550/arxiv.1308.3267 · pith_short_12: EFCZCSP7RX46 · pith_short_16: EFCZCSP7RX466BGF · pith_short_8: EFCZCSP7

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/EFCZCSP7RX466BGFNAMJGM6VNK \
  | 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: 21459149ff8df9ef04c568189333d56aaf3380ad4c4e43186f224b2e3b5cde48

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8e5b1be232abe0e42d2f7f8cb770ec4e8b51e836469ecf429d6efecae786cf7",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-08-14T22:33:28Z",
    "title_canon_sha256": "d6b89720798e4d1ef473724157aa10609f15948452606f5b9bfc18133c909c67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.3267",
    "kind": "arxiv",
    "version": 2
  }
}