Pith Number

pith:JQFXLFWW

pith:2012:JQFXLFWWO5PJRLKT2732MOGLNY

not attested not anchored not stored refs pending

Density of smooth maps for fractional Sobolev spaces $W^{s, p}$ into $\ell$ simply connected manifolds when $s \ge 1$

Augusto C. Ponce, Jean Van Schaftingen, Pierre Bousquet

arxiv:1210.2525 v2 · 2012-10-09 · math.FA · 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{JQFXLFWWO5PJRLKT2732MOGLNY}

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	2026-05-18T00:07:44.211118Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4c0b7596d6775e98ad53d7f7a638cb6e28fc86332d1c89d047503f791e717b9d

Aliases

arxiv: 1210.2525 · arxiv_version: 1210.2525v2 · doi: 10.48550/arxiv.1210.2525 · pith_short_12: JQFXLFWWO5PJ · pith_short_16: JQFXLFWWO5PJRLKT · pith_short_8: JQFXLFWW

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/JQFXLFWWO5PJRLKT2732MOGLNY \
  | 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: 4c0b7596d6775e98ad53d7f7a638cb6e28fc86332d1c89d047503f791e717b9d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad76a3556f942886d507aabdca2107be6c09c44fffd8465e23071e9d1b68940a",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-10-09T08:18:00Z",
    "title_canon_sha256": "c49a98f0219eb1683bf75ebcf26f90e303f8ec2c9d2e46d6650f706c6188adda"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.2525",
    "kind": "arxiv",
    "version": 2
  }
}