Pith Number

pith:67B5A5AY

pith:2011:67B5A5AYLELKFHVKSHHLM6ES5C

not attested not anchored not stored refs pending

Borel equivalence relations between \ell_1 and \ell_p

Longyun Ding, Zhi Yin

arxiv:1105.4492 v1 · 2011-05-23 · math.LO · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{67B5A5AYLELKFHVKSHHLM6ES5C}

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	2026-05-18T04:21:29.194581Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7c3d074185916a29eaa91ceb67892e89d30747bd0f848e8c5d5fab48c9cbbee

Aliases

arxiv: 1105.4492 · arxiv_version: 1105.4492v1 · doi: 10.48550/arxiv.1105.4492 · pith_short_12: 67B5A5AYLELK · pith_short_16: 67B5A5AYLELKFHVK · pith_short_8: 67B5A5AY

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/67B5A5AYLELKFHVKSHHLM6ES5C \
  | 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: f7c3d074185916a29eaa91ceb67892e89d30747bd0f848e8c5d5fab48c9cbbee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "549a25f1a963f5b8385f35828816ce7743a67b2083d2183b78f87ca57d0c56aa",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2011-05-23T13:18:55Z",
    "title_canon_sha256": "0c18dc75b26f1236af8a950a2fdcbd9b1fab487cd35e431dba3ee2e7be5de0ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.4492",
    "kind": "arxiv",
    "version": 1
  }
}