Pith Number

pith:5I6URZCW

pith:2010:5I6URZCWTS36WJ4DZISYSHX2BY

not attested not anchored not stored refs pending

Poincar\'e inequalities, embeddings, and wild groups

Assaf Naor, Lior Silberman

arxiv:1005.4084 v3 · 2010-05-21 · math.GR · math.FA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5I6URZCWTS36WJ4DZISYSHX2BY}

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	2026-05-17T23:53:19.739911Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea3d48e4569cb7eb2783ca25891efa0e050d1115b8c72d2755184d8b6bed8691

Aliases

arxiv: 1005.4084 · arxiv_version: 1005.4084v3 · doi: 10.48550/arxiv.1005.4084 · pith_short_12: 5I6URZCWTS36 · pith_short_16: 5I6URZCWTS36WJ4D · pith_short_8: 5I6URZCW

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/5I6URZCWTS36WJ4DZISYSHX2BY \
  | 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: ea3d48e4569cb7eb2783ca25891efa0e050d1115b8c72d2755184d8b6bed8691

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed5691f8d924c9e9205ec24f69db4f573694c701653e57b237177bad056cd2d4",
    "cross_cats_sorted": [
      "math.FA",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-05-21T21:23:53Z",
    "title_canon_sha256": "f0101a2a0d88454b79061fe21039ae7bb68c6ebf2fb6301a884cb4187b4593d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.4084",
    "kind": "arxiv",
    "version": 3
  }
}