Pith Number

pith:NT6AIZCE

pith:2015:NT6AIZCE4OSMDOPBN3XAF4FLJR

not attested not anchored not stored refs pending

The Dubovitski\u{\i}-Sard Theorem in Sobolev Spaces

Piotr Haj{\l}asz, Scott Zimmerman

arxiv:1506.00025 v1 · 2015-05-29 · 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{NT6AIZCE4OSMDOPBN3XAF4FLJR}

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	2026-05-18T01:59:55.642857Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6cfc046444e3a4c1b9e16eee02f0ab4c45539b7b96219c8492203f1840d9b6fd

Aliases

arxiv: 1506.00025 · arxiv_version: 1506.00025v1 · doi: 10.48550/arxiv.1506.00025 · pith_short_12: NT6AIZCE4OSM · pith_short_16: NT6AIZCE4OSMDOPB · pith_short_8: NT6AIZCE

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/NT6AIZCE4OSMDOPBN3XAF4FLJR \
  | 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: 6cfc046444e3a4c1b9e16eee02f0ab4c45539b7b96219c8492203f1840d9b6fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a2fa2499456268f64e2a3760a725998753d6865555819f0aebfcdecec7346dfc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-05-29T20:47:53Z",
    "title_canon_sha256": "40394efa027ff640bbd5f471f9b8b154a7a4c87ecf1ada41723508de4ac98d85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.00025",
    "kind": "arxiv",
    "version": 1
  }
}