Pith Number

pith:KA5LAHZL

pith:2011:KA5LAHZLBALTAUM2CBAQPJXY7P

not attested not anchored not stored refs pending

A Dynamical Systems Approach to Schwarzschild Null Geodesics

Edward Belbruno, Frans Pretorius

arxiv:1103.0585 v1 · 2011-03-03 · gr-qc · astro-ph.HE · 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{KA5LAHZLBALTAUM2CBAQPJXY7P}

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	2026-05-18T02:03:00.658671Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

503ab01f2b081730519a104107a6f8fbd7707d82379c3c701edeb43e3c2bcf63

Aliases

arxiv: 1103.0585 · arxiv_version: 1103.0585v1 · doi: 10.48550/arxiv.1103.0585 · pith_short_12: KA5LAHZLBALT · pith_short_16: KA5LAHZLBALTAUM2 · pith_short_8: KA5LAHZL

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/KA5LAHZLBALTAUM2CBAQPJXY7P \
  | 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: 503ab01f2b081730519a104107a6f8fbd7707d82379c3c701edeb43e3c2bcf63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c0085e18af0b2667124f4e9ecc5e17f3d91ec323b034072796a65f1e10c3e8a",
    "cross_cats_sorted": [
      "astro-ph.HE",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2011-03-03T00:25:55Z",
    "title_canon_sha256": "1040786fd7d86cb58393ff5fc07a0e3303a9d05dc2ee33938a49701b928c94eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.0585",
    "kind": "arxiv",
    "version": 1
  }
}