Pith Number

pith:YUPCJO4C

pith:2008:YUPCJO4CKCU2WUBRVLFJWOASPZ

not attested not anchored not stored refs pending

A Variational Principle for Block Operator Matrices and its Application to the Angular Part of the Dirac Operator in Curved Spacetime

Monika Winklmeier

arxiv:0806.1866 v1 · 2008-06-11 · math-ph · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YUPCJO4CKCU2WUBRVLFJWOASPZ}

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	2026-05-18T02:39:46.096866Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c51e24bb8250a9ab5031aaca9b38127e7f3f75e769bac9c75e043f79d49452b5

Aliases

arxiv: 0806.1866 · arxiv_version: 0806.1866v1 · doi: 10.48550/arxiv.0806.1866 · pith_short_12: YUPCJO4CKCU2 · pith_short_16: YUPCJO4CKCU2WUBR · pith_short_8: YUPCJO4C

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/YUPCJO4CKCU2WUBRVLFJWOASPZ \
  | 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: c51e24bb8250a9ab5031aaca9b38127e7f3f75e769bac9c75e043f79d49452b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e315744a946b931b907eb6543219b935b9a63dbd5cf1229a64ea7cf1c7d3972",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2008-06-11T13:08:43Z",
    "title_canon_sha256": "010f4eb4213811820cf0b0aed15d8742519453d069e990878b00cb94bbcdb714"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0806.1866",
    "kind": "arxiv",
    "version": 1
  }
}