Pith Number

pith:VBHR5GBJ

pith:2011:VBHR5GBJF3HIWTKILZNCATPDQD

not attested not anchored not stored refs pending

Vanishing of cohomology and property (T) for groups acting on weighted simplicial complexes

Izhar Oppenheim

arxiv:1110.5724 v5 · 2011-10-26 · 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{VBHR5GBJF3HIWTKILZNCATPDQD}

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	2026-05-18T02:46:04.815005Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a84f1e98292ece8b4d485e5a204de380e79f81b10daadb5cb363699cd1e7d735

Aliases

arxiv: 1110.5724 · arxiv_version: 1110.5724v5 · doi: 10.48550/arxiv.1110.5724 · pith_short_12: VBHR5GBJF3HI · pith_short_16: VBHR5GBJF3HIWTKI · pith_short_8: VBHR5GBJ

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/VBHR5GBJF3HIWTKILZNCATPDQD \
  | 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: a84f1e98292ece8b4d485e5a204de380e79f81b10daadb5cb363699cd1e7d735

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0d2ada154d48a0d31f20f7972752964d0e898ec76899072090a0acb6b77a677",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-10-26T07:40:25Z",
    "title_canon_sha256": "2b5ef6920fbd0f3c1656df034ba72253ab5f0961df53e34592deccb6bd84e28c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.5724",
    "kind": "arxiv",
    "version": 5
  }
}