Pith Number

pith:TCAYLIH4

pith:2010:TCAYLIH4MXZLGR55G4SG5BEKLD

not attested not anchored not stored refs pending

Ideal triangles in Euclidean buildings and branching to Levi subgroups

John J. Millson, Michael Kapovich, Thomas J. Haines

arxiv:1011.6636 v1 · 2010-11-30 · math.RT · math.AG · math.GR · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TCAYLIH4MXZLGR55G4SG5BEKLD}

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	2026-05-18T04:34:26.425448Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

988185a0fc65f2b347bd37246e848a58f6d3b1c6d134bb4de3b1b62745e63699

Aliases

arxiv: 1011.6636 · arxiv_version: 1011.6636v1 · doi: 10.48550/arxiv.1011.6636 · pith_short_12: TCAYLIH4MXZL · pith_short_16: TCAYLIH4MXZLGR55 · pith_short_8: TCAYLIH4

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/TCAYLIH4MXZLGR55G4SG5BEKLD \
  | 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: 988185a0fc65f2b347bd37246e848a58f6d3b1c6d134bb4de3b1b62745e63699

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9311864be9a8873a64c38136dd0cc4fc968f90a7b5b98ab935ac7bfdb17b95ec",
    "cross_cats_sorted": [
      "math.AG",
      "math.GR",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2010-11-30T18:28:36Z",
    "title_canon_sha256": "83f16a347eaaba2fa90f931cad4a78a8f5cd50f421c048d3664458b1d09fdf74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.6636",
    "kind": "arxiv",
    "version": 1
  }
}