Pith Number

pith:INGXFYLM

pith:2011:INGXFYLMKGBIXG2JQPAKIPPZUZ

not attested not anchored not stored refs pending

Simultaneous non-vanishing of $GL(3)\times GL(2)$ and GL(2) $L$-functions

Rizwanur Khan

arxiv:1103.5937 v2 · 2011-03-30 · 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{INGXFYLMKGBIXG2JQPAKIPPZUZ}

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	2026-05-18T02:02:42.739474Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

434d72e16c51828b9b4983c0a43df9a65f77f900caeaf8f53b9dd38c061c50b4

Aliases

arxiv: 1103.5937 · arxiv_version: 1103.5937v2 · doi: 10.48550/arxiv.1103.5937 · pith_short_12: INGXFYLMKGBI · pith_short_16: INGXFYLMKGBIXG2J · pith_short_8: INGXFYLM

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/INGXFYLMKGBIXG2JQPAKIPPZUZ \
  | 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: 434d72e16c51828b9b4983c0a43df9a65f77f900caeaf8f53b9dd38c061c50b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf298fb1ce016e692f70e0717cf06791f200fd5afc091b8681a0ae506c77014c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-03-30T14:25:48Z",
    "title_canon_sha256": "3f969d44be8fbc84c1a7d62f88b920b03bfc13e8b60f0ded96363576be925827"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.5937",
    "kind": "arxiv",
    "version": 2
  }
}