Pith Number

pith:QPZYQRKL

pith:2012:QPZYQRKLYV5WORK4PLK4WIJL6I

not attested not anchored not stored refs pending

Almgren and topological minimality for the set $Y\times Y$

Xiangyu Liang

arxiv:1203.0564 v2 · 2012-03-02 · math.CA · math.DG · 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{QPZYQRKLYV5WORK4PLK4WIJL6I}

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	2026-05-18T04:00:15.182782Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83f388454bc57b67455c7ad5cb212bf201482cd9de91bd08ddc5db951c0d7e32

Aliases

arxiv: 1203.0564 · arxiv_version: 1203.0564v2 · doi: 10.48550/arxiv.1203.0564 · pith_short_12: QPZYQRKLYV5W · pith_short_16: QPZYQRKLYV5WORK4 · pith_short_8: QPZYQRKL

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/QPZYQRKLYV5WORK4PLK4WIJL6I \
  | 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: 83f388454bc57b67455c7ad5cb212bf201482cd9de91bd08ddc5db951c0d7e32

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19a43f21642dfa67dd3de321f52a832a4e0058842fda2fe040b0a1fed6ac4da8",
    "cross_cats_sorted": [
      "math.DG",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-03-02T20:57:04Z",
    "title_canon_sha256": "6daa827fd38d9a99d691cf28f93c601d4bd51ee54b67b1e37da1810e0b7b735e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.0564",
    "kind": "arxiv",
    "version": 2
  }
}