Pith Number

pith:3VRBBM2B

pith:2015:3VRBBM2BY2H7CQ2WSV5RTCBHDN

not attested not anchored not stored refs pending

Stability of Rankin-Selberg gamma factors for $\textrm{Sp}(2n)$, $\widetilde{ \textrm{Sp}}(2n)$ and $\textrm{U}(n,n)$

Qing Zhang

arxiv:1511.03713 v2 · 2015-11-11 · math.NT · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3VRBBM2BY2H7CQ2WSV5RTCBHDN}

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	2026-05-18T00:44:09.930092Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd6210b341c68ff14356957b1988271b5a258109d816ad883d6ddc07797f2cc3

Aliases

arxiv: 1511.03713 · arxiv_version: 1511.03713v2 · doi: 10.48550/arxiv.1511.03713 · pith_short_12: 3VRBBM2BY2H7 · pith_short_16: 3VRBBM2BY2H7CQ2W · pith_short_8: 3VRBBM2B

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/3VRBBM2BY2H7CQ2WSV5RTCBHDN \
  | 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: dd6210b341c68ff14356957b1988271b5a258109d816ad883d6ddc07797f2cc3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29beb4558f9d63f014c3ecf11770a4535f0e41dcb453fcb7d0b57a74d3877e9c",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-11-11T22:20:26Z",
    "title_canon_sha256": "50ece2f9b5986982a5be6dda5dbc851395845790788c26e9be0f47b1001f5c11"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.03713",
    "kind": "arxiv",
    "version": 2
  }
}