Pith Number

pith:HOJFNVKR

pith:2018:HOJFNVKRXFDC662IPDLPM7MDLR

not attested not anchored not stored refs pending

Jacobians of $W^{1,p}$ homeomorphisms, case $p=[n/2]$

Pawe{\l} Goldstein, Piotr Haj{\l}asz

arxiv:1812.11888 v2 · 2018-12-31 · math.CA · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HOJFNVKRXFDC662IPDLPM7MDLR}

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	2026-05-17T23:44:07.316153Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3b9256d551b9462f7b4878d6f67d835c516a6a5fbc60ee32d221ad17ab3f58bd

Aliases

arxiv: 1812.11888 · arxiv_version: 1812.11888v2 · doi: 10.48550/arxiv.1812.11888 · pith_short_12: HOJFNVKRXFDC · pith_short_16: HOJFNVKRXFDC662I · pith_short_8: HOJFNVKR

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/HOJFNVKRXFDC662IPDLPM7MDLR \
  | 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: 3b9256d551b9462f7b4878d6f67d835c516a6a5fbc60ee32d221ad17ab3f58bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ebaf41b8948f21a9a00e87332520b627b917b87d426c6b2c8b94385aecd222b2",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2018-12-31T16:39:04Z",
    "title_canon_sha256": "32e6eca22fd8313c15fc65562b0d80ede9d5405e5e925502fbb1087a2315cf1e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.11888",
    "kind": "arxiv",
    "version": 2
  }
}