Pith Number

pith:ZDX7MFD7

pith:2007:ZDX7MFD7CYJIKOKFVCRKUTZFXY

not attested not anchored not stored refs pending

Haagerup's Approximation Property and Relative Amenability

Jon P. Bannon, Junsheng Fang

arxiv:0709.3676 v4 · 2007-09-24 · math.OA · 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{ZDX7MFD7CYJIKOKFVCRKUTZFXY}

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	2026-05-18T04:09:14.364130Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8eff6147f1612853945a8a2aa4f25be14118664b117feef0a87df7a3e3f986a

Aliases

arxiv: 0709.3676 · arxiv_version: 0709.3676v4 · doi: 10.48550/arxiv.0709.3676 · pith_short_12: ZDX7MFD7CYJI · pith_short_16: ZDX7MFD7CYJIKOKF · pith_short_8: ZDX7MFD7

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/ZDX7MFD7CYJIKOKFVCRKUTZFXY \
  | 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: c8eff6147f1612853945a8a2aa4f25be14118664b117feef0a87df7a3e3f986a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d404a0afdda1dd9088e3151d35711d0df0dc288c592938013ecd5320e2f59c6e",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2007-09-24T17:12:11Z",
    "title_canon_sha256": "a4a317843bb39adf3119360e9aa41fe437a505b3eccda34eada7897790ee24a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.3676",
    "kind": "arxiv",
    "version": 4
  }
}