Pith Number

pith:BVTHT5P2

pith:2011:BVTHT5P2FYJPRBTNON4PGDFPVX

not attested not anchored not stored refs pending

Bourgain's discretization theorem

Assaf Naor, Gideon Schechtman, Ohad Giladi

arxiv:1110.5368 v2 · 2011-10-24 · 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{BVTHT5P2FYJPRBTNON4PGDFPVX}

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	2026-05-18T02:26:19.129481Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d6679f5fa2e12f8866d7378f30cafadf4b6b43d093cb122952a3af1c30100f8

Aliases

arxiv: 1110.5368 · arxiv_version: 1110.5368v2 · doi: 10.48550/arxiv.1110.5368 · pith_short_12: BVTHT5P2FYJP · pith_short_16: BVTHT5P2FYJPRBTN · pith_short_8: BVTHT5P2

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/BVTHT5P2FYJPRBTNON4PGDFPVX \
  | 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: 0d6679f5fa2e12f8866d7378f30cafadf4b6b43d093cb122952a3af1c30100f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "239e904e267fe061f5f44e4bf829fea906e1c57e57da839dbd06631dca3104f6",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-10-24T22:32:43Z",
    "title_canon_sha256": "5b507dd3ff8d33ab2440195af57d85b30fb35c6d81592cb6da39b29407f65747"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.5368",
    "kind": "arxiv",
    "version": 2
  }
}