Pith Number

pith:NJ4FFPXH

pith:2013:NJ4FFPXHMA6R4LO4LCZQTTWFD2

not attested not anchored not stored refs pending

Embedded Lensing Time Delays, the Fermat Potential, and the Integrated Sachs-Wolfe Effect

Bin Chen, Ronald Kantowski, Xinyu Dai

arxiv:1310.6351 v4 · 2013-10-23 · astro-ph.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NJ4FFPXHMA6R4LO4LCZQTTWFD2}

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	2026-05-18T01:26:58.539419Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a7852bee7603d1e2ddc58b309cec51ea11d276b49b8a64d330e4abef960ee21

Aliases

arxiv: 1310.6351 · arxiv_version: 1310.6351v4 · doi: 10.48550/arxiv.1310.6351 · pith_short_12: NJ4FFPXHMA6R · pith_short_16: NJ4FFPXHMA6R4LO4 · pith_short_8: NJ4FFPXH

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/NJ4FFPXHMA6R4LO4LCZQTTWFD2 \
  | 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: 6a7852bee7603d1e2ddc58b309cec51ea11d276b49b8a64d330e4abef960ee21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a83ef615ccbdd41f22286d88313366765cd6230719f7cdbea62d24d433b8e292",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2013-10-23T20:00:00Z",
    "title_canon_sha256": "3e7dd374a7c4297973bfa31e880b523ddd8cbae2a21238f2e7bb9aa0b06126ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.6351",
    "kind": "arxiv",
    "version": 4
  }
}