Pith Number

pith:AN3NNONV

pith:2019:AN3NNONVWMNDUHQXO2NSEBXON3

not attested not anchored not stored refs pending

Gravitational lensing beyond geometric optics: II. Metric independence

Abraham I. Harte

arxiv:1906.10708 v2 · 2019-06-25 · gr-qc · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AN3NNONVWMNDUHQXO2NSEBXON3}

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	2026-07-05T00:24:39.093363Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0376d6b9b5b31a3a1e17769b2206ee6ed3ce2c889854228fe966ec1cf0ccfaf9

Aliases

arxiv: 1906.10708 · arxiv_version: 1906.10708v2 · doi: 10.48550/arxiv.1906.10708 · pith_short_12: AN3NNONVWMND · pith_short_16: AN3NNONVWMNDUHQX · pith_short_8: AN3NNONV

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/AN3NNONVWMNDUHQXO2NSEBXON3 \
  | 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: 0376d6b9b5b31a3a1e17769b2206ee6ed3ce2c889854228fe966ec1cf0ccfaf9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0663dc5047f8c297889aaf1d5e807a8aecac868b442d55bc5d055af8e0d11a1a",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2019-06-25T18:00:56Z",
    "title_canon_sha256": "4d5496adc8e8dafdc39852841d2c21f4542eda6bc8febd77564cf54c980d0b81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.10708",
    "kind": "arxiv",
    "version": 2
  }
}