Pith Number

pith:WKA4WAQ7

pith:2015:WKA4WAQ7CVRK7EZXIRV2REZA5F

not attested not anchored not stored refs pending

Some counterexamples to Sobolev regularity for degenerate Monge-Amp\`{e}re equations

Connor Mooney

arxiv:1509.05661 v1 · 2015-09-18 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WKA4WAQ7CVRK7EZXIRV2REZA5F}

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	2026-05-18T01:10:10.017274Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b281cb021f1562af9337446ba89320e943a23a95194ad3c13b749004b3016647

Aliases

arxiv: 1509.05661 · arxiv_version: 1509.05661v1 · doi: 10.48550/arxiv.1509.05661 · pith_short_12: WKA4WAQ7CVRK · pith_short_16: WKA4WAQ7CVRK7EZX · pith_short_8: WKA4WAQ7

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/WKA4WAQ7CVRK7EZXIRV2REZA5F \
  | 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: b281cb021f1562af9337446ba89320e943a23a95194ad3c13b749004b3016647

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aab89b7ebaf6bba1809e4891d2bd22b60acf8294164e58b4de10bd18fb7551e1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-09-18T15:22:12Z",
    "title_canon_sha256": "27d603c0b3679584b433d07d349c9a2c8ee99fd157802a841bea6c547c1e70b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05661",
    "kind": "arxiv",
    "version": 1
  }
}