Pith Number

pith:BUL5V7SX

pith:2015:BUL5V7SXES362Y27KPFSYD3EBS

not attested not anchored not stored refs pending

Optimal decay of extremals for the fractional Sobolev inequality

Lorenzo Brasco, Marco Squassina, Sunra Mosconi

arxiv:1508.00132 v2 · 2015-08-01 · 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{BUL5V7SXES362Y27KPFSYD3EBS}

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	2026-05-18T01:21:08.503522Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d17dafe5724b7ed635f53cb2c0f640cba250cef4aca7bde872d4bbe4044763f

Aliases

arxiv: 1508.00132 · arxiv_version: 1508.00132v2 · doi: 10.48550/arxiv.1508.00132 · pith_short_12: BUL5V7SXES36 · pith_short_16: BUL5V7SXES362Y27 · pith_short_8: BUL5V7SX

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/BUL5V7SXES362Y27KPFSYD3EBS \
  | 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: 0d17dafe5724b7ed635f53cb2c0f640cba250cef4aca7bde872d4bbe4044763f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "22d4353bb2311d0c60ab9b924c2cccb9d83051a6446cd167d68bea34aec0b2ca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-08-01T15:04:24Z",
    "title_canon_sha256": "dc551758b4c3aa78f1fdcab6e98232e791b960c54e27170db400d5c95e27ac62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.00132",
    "kind": "arxiv",
    "version": 2
  }
}