Pith Number

pith:Z2N7LNNF

pith:2024:Z2N7LNNFSGHN4WWZHTVS6WQ3KP

not attested not anchored not stored refs pending

On the local character of the extension of traces for Sobolev mappings

Jean Van Schaftingen

arxiv:2412.12713 v1 · 2024-12-17 · math.AP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z2N7LNNFSGHN4WWZHTVS6WQ3KP}

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	2026-07-05T09:50:19.603472Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce9bf5b5a5918ede5ad93ceb2f5a1b53cc85968f8998114f942a1933694578c2

Aliases

arxiv: 2412.12713 · arxiv_version: 2412.12713v1 · doi: 10.48550/arxiv.2412.12713 · pith_short_12: Z2N7LNNFSGHN · pith_short_16: Z2N7LNNFSGHN4WWZ · pith_short_8: Z2N7LNNF

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/Z2N7LNNFSGHN4WWZHTVS6WQ3KP \
  | 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: ce9bf5b5a5918ede5ad93ceb2f5a1b53cc85968f8998114f942a1933694578c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21a0b33fcc9d3c68729364dc2af580d8af88f97e6bc4024db953869ab9b36e96",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-12-17T09:28:31Z",
    "title_canon_sha256": "2cac2aeb6c652cbda640f80de134a86a7c1c2dcba019153b905610a3cb805d36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.12713",
    "kind": "arxiv",
    "version": 1
  }
}