Pith Number

pith:K5CO4LUM

pith:2016:K5CO4LUMOPNIUAPTMRPNZ3WR3A

not attested not anchored not stored refs pending

Sharp pointwise estimates for functions in the Sobolev spaces Hs(Rn)

Janaina P. Zingano, Juliana S. Ziebel, Lineia Schutz, Paulo R. Zingano

arxiv:1602.01902 v1 · 2016-02-05 · 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{K5CO4LUMOPNIUAPTMRPNZ3WR3A}

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	2026-05-18T01:21:15.101497Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5744ee2e8c73da8a01f3645edceed1d810dd2c217eb2f100ee63fd21526005fd

Aliases

arxiv: 1602.01902 · arxiv_version: 1602.01902v1 · doi: 10.48550/arxiv.1602.01902 · pith_short_12: K5CO4LUMOPNI · pith_short_16: K5CO4LUMOPNIUAPT · pith_short_8: K5CO4LUM

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/K5CO4LUMOPNIUAPTMRPNZ3WR3A \
  | 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: 5744ee2e8c73da8a01f3645edceed1d810dd2c217eb2f100ee63fd21526005fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "22abebf2904ab101705247a64337cddc488f171761d61d20632a785a6cdfbac6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-02-05T00:59:32Z",
    "title_canon_sha256": "ab66b96040ba9b34b0624a91cf7564984da3c1f911e568b56b789ee000da86e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.01902",
    "kind": "arxiv",
    "version": 1
  }
}