Pith Number

pith:UXESJH3F

pith:2016:UXESJH3FZCQOHTUVPT37HIR4HB

not attested not anchored not stored refs pending

Rational torsion on the generalized Jacobian of a modular curve with cuspidal modulus

Takao Yamazaki, Yifan Yang

arxiv:1606.06362 v1 · 2016-06-20 · 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{UXESJH3FZCQOHTUVPT37HIR4HB}

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	2026-05-18T01:12:11.156712Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a5c9249f65c8a0e3ce957cf7f3a23c385c7963cbe646effe8e63373ee544e131

Aliases

arxiv: 1606.06362 · arxiv_version: 1606.06362v1 · doi: 10.48550/arxiv.1606.06362 · pith_short_12: UXESJH3FZCQO · pith_short_16: UXESJH3FZCQOHTUV · pith_short_8: UXESJH3F

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/UXESJH3FZCQOHTUVPT37HIR4HB \
  | 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: a5c9249f65c8a0e3ce957cf7f3a23c385c7963cbe646effe8e63373ee544e131

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17aa2b5eb893d2162b558a8cb00c6bb594744a6631629f193f610b43ad48b34e",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-06-20T23:30:56Z",
    "title_canon_sha256": "9446fec1255b973aa2bfff0b3ff253a34a20f2640b8014c93603a41dd4fbfd0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.06362",
    "kind": "arxiv",
    "version": 1
  }
}