Pith Number

pith:KUSFHF37

pith:2015:KUSFHF37EJOWYLNLQT6HHOBESF

not attested not anchored not stored refs pending

Finite quotients of Bruhat-Tits buildings as geometric expanders

Shai Evra

arxiv:1503.08626 v2 · 2015-03-30 · 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{KUSFHF37EJOWYLNLQT6HHOBESF}

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	2026-05-18T01:15:58.726853Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

552453977f225d6c2dab84fc73b824916b1e92bfce3ba00caeed069e4912ac16

Aliases

arxiv: 1503.08626 · arxiv_version: 1503.08626v2 · doi: 10.48550/arxiv.1503.08626 · pith_short_12: KUSFHF37EJOW · pith_short_16: KUSFHF37EJOWYLNL · pith_short_8: KUSFHF37

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/KUSFHF37EJOWYLNLQT6HHOBESF \
  | 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: 552453977f225d6c2dab84fc73b824916b1e92bfce3ba00caeed069e4912ac16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c64d80db05433729dbae889ac962206b66650836ffbeac2f799d6149419499b6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-03-30T10:27:28Z",
    "title_canon_sha256": "0a6c8e523d51b5fa9dfd7ea4767312e356441a578c61a5ba238a4f24590066a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.08626",
    "kind": "arxiv",
    "version": 2
  }
}