Pith Number

pith:KR4CH4OY

pith:2017:KR4CH4OYH46CQAY6EVEJFCJQHP

not attested not anchored not stored refs pending

A Liouville-type theorem for biharmonic maps between complete Riemannian manifolds with small energies

Volker Branding

arxiv:1712.03870 v2 · 2017-12-11 · math.DG · 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{KR4CH4OYH46CQAY6EVEJFCJQHP}

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	2026-05-18T00:09:04.134577Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

547823f1d83f3c28031e25489289303bdf1b67b57c268b7616944d688eefde92

Aliases

arxiv: 1712.03870 · arxiv_version: 1712.03870v2 · doi: 10.48550/arxiv.1712.03870 · pith_short_12: KR4CH4OYH46C · pith_short_16: KR4CH4OYH46CQAY6 · pith_short_8: KR4CH4OY

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/KR4CH4OYH46CQAY6EVEJFCJQHP \
  | 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: 547823f1d83f3c28031e25489289303bdf1b67b57c268b7616944d688eefde92

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a228adb203b433b0f25c87caed02044cab52109770ba483b0f3567ef43276667",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2017-12-11T16:25:30Z",
    "title_canon_sha256": "c67d4ba9761bc98d106b31ea78611c10bf52347fa622785fff57bafa12f50d90"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.03870",
    "kind": "arxiv",
    "version": 2
  }
}