Pith Number

pith:42KYAQYL

pith:2012:42KYAQYLAWTXPHUVMS6GAJCIVM

not attested not anchored not stored refs pending

Compact forms of homogeneous spaces and higher-rank semisimple group actions

David Constantine

arxiv:1209.3940 v2 · 2012-09-18 · math.DG · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{42KYAQYLAWTXPHUVMS6GAJCIVM}

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	2026-05-18T01:12:38.300801Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e69580430b05a7779e9564bc602448ab3d44835a154a026f37fe300afcd3fb1f

Aliases

arxiv: 1209.3940 · arxiv_version: 1209.3940v2 · doi: 10.48550/arxiv.1209.3940 · pith_short_12: 42KYAQYLAWTX · pith_short_16: 42KYAQYLAWTXPHUV · pith_short_8: 42KYAQYL

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/42KYAQYLAWTXPHUVMS6GAJCIVM \
  | 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: e69580430b05a7779e9564bc602448ab3d44835a154a026f37fe300afcd3fb1f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc04166af6969942b85473d008b522ba874c5a327b85526b18ab8cb99e008060",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-09-18T12:55:49Z",
    "title_canon_sha256": "c86d30d57ea5ca26c26df8e00206ece53df3df2f3317b4c91cd955c4a833c1ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3940",
    "kind": "arxiv",
    "version": 2
  }
}