Pith Number

pith:LLAALXOI

pith:2009:LLAALXOI2SV75DSYXEV5U4KAOK

not attested not anchored not stored refs pending

The sphericity of the Phan geometries of type Bn and Cn and the Phan-type theorem of type F4

Ralf K\"ohl, Stefan Witzel

arxiv:0901.1156 v2 · 2009-01-09 · math.GR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LLAALXOI2SV75DSYXEV5U4KAOK}

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	2026-05-18T00:44:20.026742Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ac005ddc8d4abfe8e58b92bda71407285549b8c6418225536ee886e0686e3a4

Aliases

arxiv: 0901.1156 · arxiv_version: 0901.1156v2 · doi: 10.48550/arxiv.0901.1156 · pith_short_12: LLAALXOI2SV7 · pith_short_16: LLAALXOI2SV75DSY · pith_short_8: LLAALXOI

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/LLAALXOI2SV75DSYXEV5U4KAOK \
  | 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: 5ac005ddc8d4abfe8e58b92bda71407285549b8c6418225536ee886e0686e3a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6da317574a85d1708318d57e9a22da6c9d680b40406103f8e534f241b5514885",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-01-09T00:27:22Z",
    "title_canon_sha256": "6aa3e6da1b4d7332639985dc5fe715efb68fd01aa332d206b9930aad99cbc6e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0901.1156",
    "kind": "arxiv",
    "version": 2
  }
}