Pith Number

pith:U35BO6A6

pith:2015:U35BO6A6DBASK4UPVOEGTW2SJ5

not attested not anchored not stored refs pending

Density of bounded maps in Sobolev spaces into complete manifolds

Augusto C. Ponce, Jean Van Schaftingen, Pierre Bousquet

arxiv:1501.07136 v4 · 2015-01-28 · 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{U35BO6A6DBASK4UPVOEGTW2SJ5}

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	2026-05-18T00:10:24.805268Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6fa17781e184125728fab8869db524f64380cc154a1fc5e514acba626d7e376

Aliases

arxiv: 1501.07136 · arxiv_version: 1501.07136v4 · doi: 10.48550/arxiv.1501.07136 · pith_short_12: U35BO6A6DBAS · pith_short_16: U35BO6A6DBASK4UP · pith_short_8: U35BO6A6

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/U35BO6A6DBASK4UPVOEGTW2SJ5 \
  | 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: a6fa17781e184125728fab8869db524f64380cc154a1fc5e514acba626d7e376

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb22c27c04d32edc9c553bb6fe7868d60eafc51394d41298a20de05a99b0971a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-01-28T15:13:20Z",
    "title_canon_sha256": "659feca5579acd01d86c5e9386867d007baa20a8ef6947a03a4e96e9109e0d77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.07136",
    "kind": "arxiv",
    "version": 4
  }
}