Pith Number

pith:Y4QA526D

pith:2011:Y4QA526DC3Y6ZFYCKEKCGSX4E5

not attested not anchored not stored refs pending

Two approaches towards property (T) for groups acting on simplicial complexes

Izhar Oppenheim

arxiv:1111.1385 v3 · 2011-11-06 · 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{Y4QA526DC3Y6ZFYCKEKCGSX4E5}

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	2026-05-18T03:48:13.667972Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7200eebc316f1ec97025114234afc276e2b509b05a1292d66164acd7694dd47

Aliases

arxiv: 1111.1385 · arxiv_version: 1111.1385v3 · doi: 10.48550/arxiv.1111.1385 · pith_short_12: Y4QA526DC3Y6 · pith_short_16: Y4QA526DC3Y6ZFYC · pith_short_8: Y4QA526D

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/Y4QA526DC3Y6ZFYCKEKCGSX4E5 \
  | 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: c7200eebc316f1ec97025114234afc276e2b509b05a1292d66164acd7694dd47

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50148a2da5d7e93328caab1ef9e406552382bea63be0a3365091c15c0f617204",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-11-06T08:40:11Z",
    "title_canon_sha256": "f40e1a67c1ae7adaba4712870c0e4b4b581b09cd1c947de505d2e14d72aafa7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.1385",
    "kind": "arxiv",
    "version": 3
  }
}