Pith Number

pith:N3TCAYQS

pith:2015:N3TCAYQSGK3AUMSETTSHO4QEEJ

not attested not anchored not stored refs pending

Controlled singular extension of critical trace Sobolev maps from spheres to compact manifolds

Jean Van Schaftingen, Mircea Petrache

arxiv:1508.07813 v1 · 2015-08-31 · math.FA · 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{N3TCAYQSGK3AUMSETTSHO4QEEJ}

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	2026-05-18T00:41:08.390146Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ee620621232b60a32449ce4777204224764a27786d2ec5a50263ced6e4fbbb7

Aliases

arxiv: 1508.07813 · arxiv_version: 1508.07813v1 · doi: 10.48550/arxiv.1508.07813 · pith_short_12: N3TCAYQSGK3A · pith_short_16: N3TCAYQSGK3AUMSE · pith_short_8: N3TCAYQS

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/N3TCAYQSGK3AUMSETTSHO4QEEJ \
  | 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: 6ee620621232b60a32449ce4777204224764a27786d2ec5a50263ced6e4fbbb7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "425d623b17cd5c4658346fae8ef070213e829b0aa69edb8fd3b0c825e3d4c048",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-08-31T13:16:37Z",
    "title_canon_sha256": "a5331144a0275b0dc071b58affb7f15b175148e809efed53e2e0dd345bdf33de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.07813",
    "kind": "arxiv",
    "version": 1
  }
}