Pith Number

pith:WM264ZT7

pith:2010:WM264ZT75UODZ3ZMI5ADYLG322

not attested not anchored not stored refs pending

On the Morse-Sard Property and Level Sets of Sobolev and BV Functions

Jan Kristensen, Jean Bourgain, Mikhail V. Korobkov

arxiv:1007.4408 v1 · 2010-07-26 · math.AP · 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{WM264ZT75UODZ3ZMI5ADYLG322}

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	2026-05-18T01:24:31.117611Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b335ee667fed1c3cef2c47403c2cdbd694df15d56f8a1e336c3e6de0cb4a2027

Aliases

arxiv: 1007.4408 · arxiv_version: 1007.4408v1 · doi: 10.48550/arxiv.1007.4408 · pith_short_12: WM264ZT75UOD · pith_short_16: WM264ZT75UODZ3ZM · pith_short_8: WM264ZT7

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/WM264ZT75UODZ3ZMI5ADYLG322 \
  | 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: b335ee667fed1c3cef2c47403c2cdbd694df15d56f8a1e336c3e6de0cb4a2027

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e67dd62c5a7ff0e7a30d4f522fe2abd2c439643a890b43cc780c0dae499e0576",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-07-26T09:31:04Z",
    "title_canon_sha256": "1eaa412982578b2dfc2aed868e1bed7b42bb3cd160c2d923bd11ab625d42447f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.4408",
    "kind": "arxiv",
    "version": 1
  }
}