Pith Number

pith:J3FWONS7

pith:2011:J3FWONS7NRET3VRKMSQJZGOZTU

not attested not anchored not stored refs pending

Schwarzschild geodesics in terms of elliptic functions and the related red shift

Gunter Scharf

arxiv:1101.1207 v2 · 2011-01-06 · astro-ph.GA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J3FWONS7NRET3VRKMSQJZGOZTU}

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	2026-05-18T02:04:12.328252Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ecb67365f6c493dd62a64a09c99d99d0ad982052a50e8b48b4632e6e146ff76

Aliases

arxiv: 1101.1207 · arxiv_version: 1101.1207v2 · doi: 10.48550/arxiv.1101.1207 · pith_short_12: J3FWONS7NRET · pith_short_16: J3FWONS7NRET3VRK · pith_short_8: J3FWONS7

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/J3FWONS7NRET3VRKMSQJZGOZTU \
  | 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: 4ecb67365f6c493dd62a64a09c99d99d0ad982052a50e8b48b4632e6e146ff76

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c98f9b39f4105ad0aaac843bc9c215f3ee1382fe5fe802350544c9b898646e03",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.GA",
    "submitted_at": "2011-01-06T13:21:24Z",
    "title_canon_sha256": "c19b3e5f6df209a9e82445e8e467c9186f02e08c8b878a2ac89848cd8a3e38c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.1207",
    "kind": "arxiv",
    "version": 2
  }
}