Pith Number

pith:KDZOMFHF

pith:2018:KDZOMFHFWTAT3GYKHYE6UW5CES

not attested not anchored not stored refs pending

Martingale approach to Sobolev embedding theorems

Dmitriy Stolyarov, Michal Wojciechowski, Rami Ayoush

arxiv:1811.08137 v1 · 2018-11-20 · math.CA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KDZOMFHFWTAT3GYKHYE6UW5CES}

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	2026-05-18T00:00:16.757026Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50f2e614e5b4c13d9b0a3e09ea5ba2249f984e715a19c12ea082ec26bee2bff5

Aliases

arxiv: 1811.08137 · arxiv_version: 1811.08137v1 · doi: 10.48550/arxiv.1811.08137 · pith_short_12: KDZOMFHFWTAT · pith_short_16: KDZOMFHFWTAT3GYK · pith_short_8: KDZOMFHF

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/KDZOMFHFWTAT3GYKHYE6UW5CES \
  | 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: 50f2e614e5b4c13d9b0a3e09ea5ba2249f984e715a19c12ea082ec26bee2bff5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf85477df5daee9b966e9e407e351ef2fed5bf9c439ec6f1d4648df8cb3028e3",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-11-20T09:17:11Z",
    "title_canon_sha256": "34b6adb325eb4272175e24a5e0a52555411804176e7e8a1c43587d3fd8f51768"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.08137",
    "kind": "arxiv",
    "version": 1
  }
}