Pith Number

pith:UZTXSANV

pith:2009:UZTXSANVZ46WW3GJ4JFWQWOOD3

not attested not anchored not stored refs pending

On Relative Property (T) and Haagerup's Property

Adrian Ioana, Ionut Chifan

arxiv:0906.5363 v1 · 2009-06-29 · math.GR · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UZTXSANVZ46WW3GJ4JFWQWOOD3}

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	2026-05-18T00:22:40.766752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6677901b5cf3d6b6cc9e24b6859ce1ee1c2d749a28fba78eb35a5957c0d83b6

Aliases

arxiv: 0906.5363 · arxiv_version: 0906.5363v1 · doi: 10.48550/arxiv.0906.5363 · pith_short_12: UZTXSANVZ46W · pith_short_16: UZTXSANVZ46WW3GJ · pith_short_8: UZTXSANV

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/UZTXSANVZ46WW3GJ4JFWQWOOD3 \
  | 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: a6677901b5cf3d6b6cc9e24b6859ce1ee1c2d749a28fba78eb35a5957c0d83b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3708dd5ee7b8a6fb4af28f26462b7d3657d8401d859f8d6485fb368a16a5cee",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-06-29T20:26:56Z",
    "title_canon_sha256": "61682d334c902c9dc68f30b93e373656cd79f25df5299967890023e8b9850363"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.5363",
    "kind": "arxiv",
    "version": 1
  }
}