Pith Number

pith:HFPTEXJ7

pith:2015:HFPTEXJ7YRHVKLXTW26QIHTN7A

not attested not anchored not stored refs pending

The geometry of gravitational lensing magnification

Amir Babak Aazami, Marcus C. Werner

arxiv:1507.02765 v2 · 2015-07-10 · gr-qc · astro-ph.GA · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HFPTEXJ7YRHVKLXTW26QIHTN7A}

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	2026-05-18T01:22:14.398073Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

395f325d3fc44f552ef3b6bd041e6df83e849b5166c195a17331228d04e8157a

Aliases

arxiv: 1507.02765 · arxiv_version: 1507.02765v2 · doi: 10.48550/arxiv.1507.02765 · pith_short_12: HFPTEXJ7YRHV · pith_short_16: HFPTEXJ7YRHVKLXT · pith_short_8: HFPTEXJ7

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/HFPTEXJ7YRHVKLXTW26QIHTN7A \
  | 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: 395f325d3fc44f552ef3b6bd041e6df83e849b5166c195a17331228d04e8157a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79642347fc5e32c66fab8fa5f0d6d328d3a92a98f30bc3125740e595885a9834",
    "cross_cats_sorted": [
      "astro-ph.GA",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2015-07-10T02:22:29Z",
    "title_canon_sha256": "c1aba8c6e25c8d1e0af39f94f821731e869ebd74af20f0d95c88b376509586af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.02765",
    "kind": "arxiv",
    "version": 2
  }
}