Pith Number

pith:LBEPN3BV

pith:2015:LBEPN3BVS53LVFRP7N4MFPHGVB

not attested not anchored not stored refs pending

Weyl and Bernstein Numbers of Embeddings of Sobolev Spaces with Dominating Mixed Smoothness

Van Kien Nguyen

arxiv:1506.00115 v2 · 2015-05-30 · 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{LBEPN3BVS53LVFRP7N4MFPHGVB}

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	2026-05-18T01:33:51.560993Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5848f6ec359776ba962ffb78c2bce6a845372eeb9e04687d5041b4c2bf8513c7

Aliases

arxiv: 1506.00115 · arxiv_version: 1506.00115v2 · doi: 10.48550/arxiv.1506.00115 · pith_short_12: LBEPN3BVS53L · pith_short_16: LBEPN3BVS53LVFRP · pith_short_8: LBEPN3BV

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/LBEPN3BVS53LVFRP7N4MFPHGVB \
  | 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: 5848f6ec359776ba962ffb78c2bce6a845372eeb9e04687d5041b4c2bf8513c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2281595b0d302f910d77ae601c347b33092ff72a588ce5c7a54bec4ef169ca70",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-05-30T13:25:26Z",
    "title_canon_sha256": "6d12b54591ef991d1b547a715d0807781a01f11e3dcb269d37234d6c9389d8d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.00115",
    "kind": "arxiv",
    "version": 2
  }
}