Pith Number

pith:PCVRR27J

pith:2024:PCVRR27J4JJVAXBIXKVESFU45T

not attested not anchored not stored refs pending

Kolyvagin's conjecture for modular forms

Maria Rosaria Pati, Matteo Longo, Stefano Vigni

arxiv:2412.02303 v2 · 2024-12-03 · 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{PCVRR27J4JJVAXBIXKVESFU45T}

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	2026-07-05T09:51:39.061773Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78ab18ebe9e253505c28baaa49169cecddc854303db2c5b518382c1ddc53f5c6

Aliases

arxiv: 2412.02303 · arxiv_version: 2412.02303v2 · doi: 10.48550/arxiv.2412.02303 · pith_short_12: PCVRR27J4JJV · pith_short_16: PCVRR27J4JJVAXBI · pith_short_8: PCVRR27J

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/PCVRR27J4JJVAXBIXKVESFU45T \
  | 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: 78ab18ebe9e253505c28baaa49169cecddc854303db2c5b518382c1ddc53f5c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "910cab5978b0036fb212be3f847b75ac88dc61871fc51b13ca2b29e8d963d62c",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-12-03T09:16:41Z",
    "title_canon_sha256": "e5aed329589d4237100e3672ad389aa209e0fae3e3ddfbbe95f83f03b0214806"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.02303",
    "kind": "arxiv",
    "version": 2
  }
}