Pith Number

pith:XZ4JEE6Y

pith:2016:XZ4JEE6YIREY2D6DDNBMUGLETX

not attested not anchored not stored refs pending

Potentially $\text{GL}_2$-type Galois representations associated to noncongruence modular forms

Ling Long, Tong Liu, Wen-Ching Winnie Li

arxiv:1609.06414 v2 · 2016-09-21 · 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{XZ4JEE6YIREY2D6DDNBMUGLETX}

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	2026-05-18T00:38:21.221085Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be789213d844498d0fc31b42ca19649de3ad80c1d7334722819091e565738207

Aliases

arxiv: 1609.06414 · arxiv_version: 1609.06414v2 · doi: 10.48550/arxiv.1609.06414 · pith_short_12: XZ4JEE6YIREY · pith_short_16: XZ4JEE6YIREY2D6D · pith_short_8: XZ4JEE6Y

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/XZ4JEE6YIREY2D6DDNBMUGLETX \
  | 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: be789213d844498d0fc31b42ca19649de3ad80c1d7334722819091e565738207

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a23d2d81ca7f833d388c24c1af786903fc1328800b99eae61ed686d850b24832",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-09-21T03:33:17Z",
    "title_canon_sha256": "ca1db047ed9bc98f101829aa45dc57bb957e1442bb1028dc0f806f2271a0a9e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06414",
    "kind": "arxiv",
    "version": 2
  }
}