Pith Number

pith:QCACZTVR

pith:2011:QCACZTVRKHN7ED7ZKASJKPANR4

not attested not anchored not stored refs pending

The fundamental group of reductive Borel-Serre and Satake compactifications

John Scherk, Leslie Saper, Lizhen Ji, V. Kumar Murty

arxiv:1106.4810 v2 · 2011-06-23 · math.GT · math.GR · 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{QCACZTVRKHN7ED7ZKASJKPANR4}

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	2026-05-18T00:55:58.925797Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80802cceb151dbf20ff95024953c0d8f1691940d805945ed899afbe4c6af7dc9

Aliases

arxiv: 1106.4810 · arxiv_version: 1106.4810v2 · doi: 10.48550/arxiv.1106.4810 · pith_short_12: QCACZTVRKHN7 · pith_short_16: QCACZTVRKHN7ED7Z · pith_short_8: QCACZTVR

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/QCACZTVRKHN7ED7ZKASJKPANR4 \
  | 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: 80802cceb151dbf20ff95024953c0d8f1691940d805945ed899afbe4c6af7dc9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee5ac5766d1923dd3a69db7ebb8eeaf6205ad239c37c0ceb50607cff10f0252a",
    "cross_cats_sorted": [
      "math.GR",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-06-23T19:55:26Z",
    "title_canon_sha256": "699dc2dc16950ef5d94197e0c8cdcd09837c08cb6a9a7439b035251006161f4c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.4810",
    "kind": "arxiv",
    "version": 2
  }
}