Pith Number

pith:UTLKUMHB

pith:2015:UTLKUMHBXTYYGBGWRPFXXTESV2

not attested not anchored not stored refs pending

Multilinear Multiplier Theorems and Applications

Danqing He, Hanh Van Nguyen, Lixin Yan, Loukas Grafakos

arxiv:1511.08117 v4 · 2015-11-25 · 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{UTLKUMHBXTYYGBGWRPFXXTESV2}

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	2026-05-18T00:54:52.957299Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4d6aa30e1bcf18304d68bcb7bcc92ae8c3d148223d2f53b5ae1473f12f8afe8

Aliases

arxiv: 1511.08117 · arxiv_version: 1511.08117v4 · doi: 10.48550/arxiv.1511.08117 · pith_short_12: UTLKUMHBXTYY · pith_short_16: UTLKUMHBXTYYGBGW · pith_short_8: UTLKUMHB

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/UTLKUMHBXTYYGBGWRPFXXTESV2 \
  | 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: a4d6aa30e1bcf18304d68bcb7bcc92ae8c3d148223d2f53b5ae1473f12f8afe8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0922dfa876a6edad593832c812539b4f35da852c9d088dc4582a1888ff0557e0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-11-25T16:55:49Z",
    "title_canon_sha256": "45ca0870d18e398259dde0e57a58ac3b3c46cacf19a5416344747d1cfffa387f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.08117",
    "kind": "arxiv",
    "version": 4
  }
}