Pith Number

pith:VFB2OF53

pith:2016:VFB2OF53WTCMNCGSABGNSMTSSD

not attested not anchored not stored refs pending

Unitarizability, Maurey--Nikishin factorization, and Polish groups of finite type

Andreas Thom, Asger T\"ornquist, Hiroshi Ando, Yasumichi Matsuzawa

arxiv:1605.06909 v3 · 2016-05-23 · math.OA · math.FA · 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{VFB2OF53WTCMNCGSABGNSMTSSD}

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	2026-05-18T00:35:18.636979Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a943a717bbb4c4c688d2004cd9327290ecd4f16f07524760b3c60cd0af93b7d6

Aliases

arxiv: 1605.06909 · arxiv_version: 1605.06909v3 · doi: 10.48550/arxiv.1605.06909 · pith_short_12: VFB2OF53WTCM · pith_short_16: VFB2OF53WTCMNCGS · pith_short_8: VFB2OF53

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/VFB2OF53WTCMNCGSABGNSMTSSD \
  | 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: a943a717bbb4c4c688d2004cd9327290ecd4f16f07524760b3c60cd0af93b7d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "267f3727d07f5a492ef56911d17da7469afcd78b3fb637f55b6db99dcd6dfb22",
    "cross_cats_sorted": [
      "math.FA",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2016-05-23T07:02:43Z",
    "title_canon_sha256": "56eac894a5964290a49f8f37c572502a6a490090eca3b0c96eefeefd8495809b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.06909",
    "kind": "arxiv",
    "version": 3
  }
}