Pith Number

pith:GGT2WRCB

pith:2011:GGT2WRCB67IRMEFLUTAGQBIPL6

not attested not anchored not stored refs pending

On modular Galois representations modulo prime powers

Gabor Wiese, Ian Kiming, Imin Chen

arxiv:1105.1918 v2 · 2011-05-10 · 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{GGT2WRCB67IRMEFLUTAGQBIPL6}

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	2026-05-18T03:55:00.464477Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31a7ab4441f7d11610aba4c068050f5fbd5a66c4fb212c0865183f1771d49d7a

Aliases

arxiv: 1105.1918 · arxiv_version: 1105.1918v2 · doi: 10.48550/arxiv.1105.1918 · pith_short_12: GGT2WRCB67IR · pith_short_16: GGT2WRCB67IRMEFL · pith_short_8: GGT2WRCB

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/GGT2WRCB67IRMEFLUTAGQBIPL6 \
  | 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: 31a7ab4441f7d11610aba4c068050f5fbd5a66c4fb212c0865183f1771d49d7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2a9679e2e125e325db417bfa5697a2d39ff5dae05345b44f4b4a604ef54399f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-05-10T11:34:28Z",
    "title_canon_sha256": "8262c9cd5749ead718905adf293d56e752fb02929d1521e38ae43e016a1d725c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.1918",
    "kind": "arxiv",
    "version": 2
  }
}