Pith Number

pith:CXJA27BP

pith:2015:CXJA27BPSZIWC3Q7OKOJY2563I

not attested not anchored not stored refs pending

Commutators in groups of piecewise projective homeomorphisms

Jos\'e Burillo, Lawrence Reeves, Yash Lodha

arxiv:1509.04586 v3 · 2015-09-15 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CXJA27BPSZIWC3Q7OKOJY2563I}

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	2026-05-18T00:20:40.291430Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15d20d7c2f9651616e1f729c9c6bbeda2878876fb0b1c5c65d95535a889cba60

Aliases

arxiv: 1509.04586 · arxiv_version: 1509.04586v3 · doi: 10.48550/arxiv.1509.04586 · pith_short_12: CXJA27BPSZIW · pith_short_16: CXJA27BPSZIWC3Q7 · pith_short_8: CXJA27BP

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/CXJA27BPSZIWC3Q7OKOJY2563I \
  | 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: 15d20d7c2f9651616e1f729c9c6bbeda2878876fb0b1c5c65d95535a889cba60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1ff7e5f7c633304bfd20681488e5f381a8cb5e75c21bf5646d7370a60ed8c37f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-09-15T14:47:50Z",
    "title_canon_sha256": "1f9086217f446b44591200703e916dd8048d21c9a11897bc45e541face1f740c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.04586",
    "kind": "arxiv",
    "version": 3
  }
}