Pith Number

pith:Y4UFTNXJ

pith:2015:Y4UFTNXJAL3RTYJS6UNXBABD5A

not attested not anchored not stored refs pending

A note on the sublinear Sobolev inequality

Daniel Spector

arxiv:1508.01237 v3 · 2015-08-05 · 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{Y4UFTNXJAL3RTYJS6UNXBABD5A}

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	2026-05-18T01:15:06.793235Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c72859b6e902f719e132f51b708023e80f73f36c0eef698264fc98f4dac59cc9

Aliases

arxiv: 1508.01237 · arxiv_version: 1508.01237v3 · doi: 10.48550/arxiv.1508.01237 · pith_short_12: Y4UFTNXJAL3R · pith_short_16: Y4UFTNXJAL3RTYJS · pith_short_8: Y4UFTNXJ

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/Y4UFTNXJAL3RTYJS6UNXBABD5A \
  | 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: c72859b6e902f719e132f51b708023e80f73f36c0eef698264fc98f4dac59cc9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2816a1d22a895726db90731e1c12b6ea8455e46ac845d27964906f22644a22ee",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-08-05T21:59:47Z",
    "title_canon_sha256": "51347bae22be636dd0c30c9684daf85778fddbbb4b0c7eaead609ae4381e633a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.01237",
    "kind": "arxiv",
    "version": 3
  }
}