Pith Number

pith:M4DYPY55

pith:2017:M4DYPY553V6XKECHUWHPRTVE4Q

not attested not anchored not stored refs pending

The closure of planar diffeomorphisms in Sobolev spaces

Aldo Pratelli, Guido De Philippis

arxiv:1710.07228 v1 · 2017-10-19 · 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{M4DYPY553V6XKECHUWHPRTVE4Q}

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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	2026-05-18T00:32:26.500449Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

670787e3bddd7d751047a58ef8cea4e4264e2e997e7834174fdd1a04eabf4f01

Aliases

arxiv: 1710.07228 · arxiv_version: 1710.07228v1 · doi: 10.48550/arxiv.1710.07228 · pith_short_12: M4DYPY553V6X · pith_short_16: M4DYPY553V6XKECH · pith_short_8: M4DYPY55

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/M4DYPY553V6XKECHUWHPRTVE4Q \
  | 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: 670787e3bddd7d751047a58ef8cea4e4264e2e997e7834174fdd1a04eabf4f01

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a58de8008fdb6108ce1746b0dc2ad18dda0e14c95359e1f06ea4ee3ae4adc40",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-10-19T16:17:59Z",
    "title_canon_sha256": "8674747113e1949ee4c3ec0fb92ab27bc512472252b63f6251325b6cd73ed401"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.07228",
    "kind": "arxiv",
    "version": 1
  }
}