Pith Number

pith:4MQDD6LM

pith:2012:4MQDD6LMFS5W2Y7MJFONFLGSXX

not attested not anchored not stored refs pending

The Structure of Sobolev Extension Operators

Arie Israel, Charles L. Fefferman, Garving K. Luli

arxiv:1206.1979 v2 · 2012-06-09 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4MQDD6LMFS5W2Y7MJFONFLGSXX}

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	2026-05-18T03:41:01.072485Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e32031f96c2cbb6d63ec495cd2acd2bdf27999356bebba57235302c912a11e87

Aliases

arxiv: 1206.1979 · arxiv_version: 1206.1979v2 · doi: 10.48550/arxiv.1206.1979 · pith_short_12: 4MQDD6LMFS5W · pith_short_16: 4MQDD6LMFS5W2Y7M · pith_short_8: 4MQDD6LM

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/4MQDD6LMFS5W2Y7MJFONFLGSXX \
  | 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: e32031f96c2cbb6d63ec495cd2acd2bdf27999356bebba57235302c912a11e87

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50d2ad718fe94d1d730b2cfe9f796b7fb0e0482e82a088727b4efb4e0adcd2cc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-06-09T22:59:12Z",
    "title_canon_sha256": "6d95629b5c428f44fa4c346ffe64c3efa6e59e9a3dd881a6f8bf3d4424ef84ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.1979",
    "kind": "arxiv",
    "version": 2
  }
}