Pith Number

pith:Z2HPEE22

pith:2011:Z2HPEE22FXIPZCUAUPLQKVE32A

not attested not anchored not stored refs pending

Non-vanishing of L-functions, the Ramanujan conjecture, and families of Hecke characters

Farrell Brumley, Valentin Blomer

arxiv:1104.1067 v1 · 2011-04-06 · 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{Z2HPEE22FXIPZCUAUPLQKVE32A}

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	2026-05-18T02:22:10.812695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce8ef2135a2dd0fc8a80a3d705549bd03e7d6500c8883bbb0491c51617ead95b

Aliases

arxiv: 1104.1067 · arxiv_version: 1104.1067v1 · doi: 10.48550/arxiv.1104.1067 · pith_short_12: Z2HPEE22FXIP · pith_short_16: Z2HPEE22FXIPZCUA · pith_short_8: Z2HPEE22

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/Z2HPEE22FXIPZCUAUPLQKVE32A \
  | 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: ce8ef2135a2dd0fc8a80a3d705549bd03e7d6500c8883bbb0491c51617ead95b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40cbc567e5320d9d1d41df3dd83771bf92eb3309dfb2f103b44197b39db77f53",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-04-06T11:48:15Z",
    "title_canon_sha256": "274895b799baa12cd8dc98b175ad3e735cc292f7912e73faad6b2a05733bd952"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.1067",
    "kind": "arxiv",
    "version": 1
  }
}