Pith Number

pith:JPOA5TST

pith:2015:JPOA5TST6QAOP6MNMMWXU6DNEX

not attested not anchored not stored refs pending

Landau's theorems for certain biharmonic mappings

Ming-Sheng Liu, Yu-Can Zhu, Zhi-Wen Liu

arxiv:1511.04642 v1 · 2015-11-15 · math.CV

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JPOA5TST6QAOP6MNMMWXU6DNEX}

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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	2026-05-18T01:26:52.145647Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4bdc0ece53f400e7f98d632d7a786d25ccd4cf11ace6dd7dcb3d922b72a6a05f

Aliases

arxiv: 1511.04642 · arxiv_version: 1511.04642v1 · doi: 10.48550/arxiv.1511.04642 · pith_short_12: JPOA5TST6QAO · pith_short_16: JPOA5TST6QAOP6MN · pith_short_8: JPOA5TST

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/JPOA5TST6QAOP6MNMMWXU6DNEX \
  | 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: 4bdc0ece53f400e7f98d632d7a786d25ccd4cf11ace6dd7dcb3d922b72a6a05f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0dcd67b4af96ebf67e00400ff38d7a9054eb0297052e2083658c29e788ab25a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2015-11-15T02:13:03Z",
    "title_canon_sha256": "b93997df20b9e149e1108e04ed23d4b81bc5f82aba2ee59d2505e097de92a123"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.04642",
    "kind": "arxiv",
    "version": 1
  }
}