Pith Number

pith:6CXTJ64B

pith:2009:6CXTJ64BKYYDN7QQG5LJWABYJQ

not attested not anchored not stored refs pending

Exact gravitational lensing and rotation curve

Gerhard Braunlich, Gunter Scharf

arxiv:0912.5058 v1 · 2009-12-27 · 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{6CXTJ64BKYYDN7QQG5LJWABYJQ}

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	2026-05-18T04:30:59.808555Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f0af34fb81563036fe1037569b00384c345d3289707da97de00e3886172f1b9d

Aliases

arxiv: 0912.5058 · arxiv_version: 0912.5058v1 · doi: 10.48550/arxiv.0912.5058 · pith_short_12: 6CXTJ64BKYYD · pith_short_16: 6CXTJ64BKYYDN7QQ · pith_short_8: 6CXTJ64B

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/6CXTJ64BKYYDN7QQG5LJWABYJQ \
  | 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: f0af34fb81563036fe1037569b00384c345d3289707da97de00e3886172f1b9d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ba114930c8750b5988bfa612928a02ecda7e3a5d37d9ebdc4e1d6db527d7e03",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.GA",
    "submitted_at": "2009-12-27T08:34:05Z",
    "title_canon_sha256": "6a933258172246726e875b1d918b4d9af1666bd3261bd069a8dd5cdcdb3ba758"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.5058",
    "kind": "arxiv",
    "version": 1
  }
}