Pith Number

pith:7NDAQ7BW

pith:2009:7NDAQ7BWTOORON3TUKQJ2YP7G6

not attested not anchored not stored refs pending

The Riemann-Roch Theorem and Zero Energy Solutions of the Dirac Equation on the Riemann Sphere

Geoffrey Lee

arxiv:0909.0085 v3 · 2009-09-01 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7NDAQ7BWTOORON3TUKQJ2YP7G6}

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	2026-05-18T04:35:05.289443Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb46087c369b9d173773a2a09d61ff37b14a46e11c234756c8e602dd6895591c

Aliases

arxiv: 0909.0085 · arxiv_version: 0909.0085v3 · doi: 10.48550/arxiv.0909.0085 · pith_short_12: 7NDAQ7BWTOOR · pith_short_16: 7NDAQ7BWTOORON3T · pith_short_8: 7NDAQ7BW

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/7NDAQ7BWTOORON3TUKQJ2YP7G6 \
  | 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: fb46087c369b9d173773a2a09d61ff37b14a46e11c234756c8e602dd6895591c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02ee8174284e6743c9da9decac07e3e27709ae42ddb9056c171402f4bd4077df",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2009-09-01T17:13:57Z",
    "title_canon_sha256": "6af7ea8dd37fa33ac6c5a3be7b881c49b84d17232733cf631e995a8eab1fc4fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.0085",
    "kind": "arxiv",
    "version": 3
  }
}