Pith Number

pith:OKX5F5RD

pith:2004:OKX5F5RDG352DZYWUUROVSITA2

not attested not anchored not stored refs pending

Footballs, Conical Singularities and the Liouville Equation

Michele Redi

arxiv:hep-th/0412189 v3 · 2004-12-17 · hep-th · hep-ph · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OKX5F5RDG352DZYWUUROVSITA2}

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	2026-07-04T16:49:07.989882Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72afd2f62336fba1e716a522eac91306a9f7fdc9c1952e85cac85621f930f3f9

Aliases

arxiv: hep-th/0412189 · arxiv_version: hep-th/0412189v3 · doi: 10.48550/arxiv.hep-th/0412189 · pith_short_12: OKX5F5RDG352 · pith_short_16: OKX5F5RDG352DZYW · pith_short_8: OKX5F5RD

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/OKX5F5RDG352DZYWUUROVSITA2 \
  | 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: 72afd2f62336fba1e716a522eac91306a9f7fdc9c1952e85cac85621f930f3f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3db62593ff0a8818fc43a1366a76b23906c80993033cbbc8dab546057893fcf",
    "cross_cats_sorted": [
      "hep-ph",
      "math.CV"
    ],
    "license": "",
    "primary_cat": "hep-th",
    "submitted_at": "2004-12-17T19:16:32Z",
    "title_canon_sha256": "9fbf02d14209938a5e5cb276ed161cee42b1cfe51c549e1c7def7c7c2271b357"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-th/0412189",
    "kind": "arxiv",
    "version": 3
  }
}