Pith Number

pith:KWTTEM3N

pith:2026:KWTTEM3NNOTA4XQWTAMJFMIALC

not attested not anchored not stored refs pending

Liouville theorem for immersed minimal surfaces in any codimension

Tobias Holck Colding, William P. Minicozzi II

arxiv:2605.15038 v1 · 2026-05-14 · 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{KWTTEM3NNOTA4XQWTAMJFMIALC}

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	2026-05-17T23:38:54.512011Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

55a732336d6ba60e5e16981892b10058a2bd452c3edd16e802838c3af2c09deb

Aliases

arxiv: 2605.15038 · arxiv_version: 2605.15038v1 · doi: 10.48550/arxiv.2605.15038 · pith_short_12: KWTTEM3NNOTA · pith_short_16: KWTTEM3NNOTA4XQW · pith_short_8: KWTTEM3N

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/KWTTEM3NNOTA4XQWTAMJFMIALC \
  | 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: 55a732336d6ba60e5e16981892b10058a2bd452c3edd16e802838c3af2c09deb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06f9ef19ba9197bf8cad8fcfe204223c0cff90da51cd4be384de45c0a1640524",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-14T16:30:59Z",
    "title_canon_sha256": "68bdec77f86cf69cf16d37ad9a26465e660b47461b40dd41ba3e2be81c3e3ba8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15038",
    "kind": "arxiv",
    "version": 1
  }
}