Pith Number

pith:GQOQ7KNQ

pith:2019:GQOQ7KNQJ7GSZ2JQ6NIQGYA4UO

not attested not anchored not stored refs pending

Stability of symmetric cube gamma factors for GL(2)

Daniel Shankman, Dongming She

arxiv:1911.03428 v1 · 2019-11-08 · 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{GQOQ7KNQJ7GSZ2JQ6NIQGYA4UO}

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	2026-07-05T00:18:02.354579Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

341d0fa9b04fcd2ce930f35103601ca39c43dbc9c3e695e04f97b17f27df6f9c

Aliases

arxiv: 1911.03428 · arxiv_version: 1911.03428v1 · doi: 10.48550/arxiv.1911.03428 · pith_short_12: GQOQ7KNQJ7GS · pith_short_16: GQOQ7KNQJ7GSZ2JQ · pith_short_8: GQOQ7KNQ

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/GQOQ7KNQJ7GSZ2JQ6NIQGYA4UO \
  | 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: 341d0fa9b04fcd2ce930f35103601ca39c43dbc9c3e695e04f97b17f27df6f9c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58d73c3f6d257777cb9e78b6b88a2f4389de816fee60847c896088526d85a671",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-11-08T18:24:45Z",
    "title_canon_sha256": "63714208a1b83e6b07e0d4c8165a5ede3e75e4868c9a33b508683fe0bcdbc0e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1911.03428",
    "kind": "arxiv",
    "version": 1
  }
}