Pith Number

pith:4FETCAQ3

pith:2004:4FETCAQ3GMOF3WOB77F2ZEKR7B

not attested not anchored not stored refs pending

Gravitational lens under perturbations: Symmetry of perturbing potentials with invariant caustics

Cambridge), Jin H. An (IoA

arxiv:astro-ph/0410388 v2 · 2004-10-15 · astro-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4FETCAQ3GMOF3WOB77F2ZEKR7B}

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	2026-07-04T14:13:49.935414Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e14931021b331c5dd9c1ffcbac9151f8510752caa8a0e7bb417e2f6d4325cb63

Aliases

arxiv: astro-ph/0410388 · arxiv_version: astro-ph/0410388v2 · doi: 10.48550/arxiv.astro-ph/0410388 · pith_short_12: 4FETCAQ3GMOF · pith_short_16: 4FETCAQ3GMOF3WOB · pith_short_8: 4FETCAQ3

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/4FETCAQ3GMOF3WOB77F2ZEKR7B \
  | 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: e14931021b331c5dd9c1ffcbac9151f8510752caa8a0e7bb417e2f6d4325cb63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5aa7abb6bb69f01ef45b5493bc63d28753f90201ce7e5e144451a7fb560903f9",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2004-10-15T17:13:25Z",
    "title_canon_sha256": "f43f97f457494c9041893a75e26b48367c848ac191b4dde7328a38cab5286f41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0410388",
    "kind": "arxiv",
    "version": 2
  }
}