Pith Number

pith:GPKA24HY

pith:2011:GPKA24HYQISSJ73EHNKM7XSEXH

not attested not anchored not stored refs pending

The densest lattices in PGL3(Q2)

Daniel Allcock, Fumiharu Kato

arxiv:1105.1860 v2 · 2011-05-10 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GPKA24HYQISSJ73EHNKM7XSEXH}

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	2026-05-18T01:02:14.520074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33d40d70f8822524ff643b54cfde44b9fbcf00ca9b0613c45455cec51dc0e145

Aliases

arxiv: 1105.1860 · arxiv_version: 1105.1860v2 · doi: 10.48550/arxiv.1105.1860 · pith_short_12: GPKA24HYQISS · pith_short_16: GPKA24HYQISSJ73E · pith_short_8: GPKA24HY

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/GPKA24HYQISSJ73EHNKM7XSEXH \
  | 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: 33d40d70f8822524ff643b54cfde44b9fbcf00ca9b0613c45455cec51dc0e145

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d873de6e932cb5c163e9d31c93f3b36044b461805801a26945e701760b646bc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-05-10T06:30:36Z",
    "title_canon_sha256": "484f2c3b39282abf8e37764f644c4df9c5bab82f9370f50b286c84890ac4f17f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.1860",
    "kind": "arxiv",
    "version": 2
  }
}