Pith Number

pith:YTSHTE7L

pith:2010:YTSHTE7L4GOJT6BLTYN2QKP6CI

not attested not anchored not stored refs pending

On the lifting and approximation theorem for nonsmooth vector fields

Luca Brandolini, Marco Bramanti, Marco Pedroni

arxiv:1002.1331 v2 · 2010-02-05 · 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{YTSHTE7L4GOJT6BLTYN2QKP6CI}

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	2026-05-18T04:25:50.644132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4e47993ebe19c99f82b9e1ba829fe121c259940e5021b8226b869896b3a4624

Aliases

arxiv: 1002.1331 · arxiv_version: 1002.1331v2 · doi: 10.48550/arxiv.1002.1331 · pith_short_12: YTSHTE7L4GOJ · pith_short_16: YTSHTE7L4GOJT6BL · pith_short_8: YTSHTE7L

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/YTSHTE7L4GOJT6BLTYN2QKP6CI \
  | 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: c4e47993ebe19c99f82b9e1ba829fe121c259940e5021b8226b869896b3a4624

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b36b7ecb4c80f05b99d6fc584a7d359167e6612cb04a4d47c36c135606a59ce",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-02-05T22:59:41Z",
    "title_canon_sha256": "74049e0d48779be72b6563c171cfe17cf9bc0b5a1827cd3da39554bf7a82ed8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.1331",
    "kind": "arxiv",
    "version": 2
  }
}