Pith Number

pith:PNTM3TSA

pith:2026:PNTM3TSAUAFIAUISD5UF2AI4CK

not attested not anchored not stored refs pending

Beyond-eikonal diffraction integral in gravitational lensing

Cyril Pitrou, Emma Bruy\`ere, Giulia Cusin

arxiv:2607.24723 v1 · 2026-07-27 · 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{PNTM3TSAUAFIAUISD5UF2AI4CK}

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	2026-07-28T02:24:24.224122Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b66cdce40a00a8051121f685d011c12a0352057be8638e432abdef53b33e6fb

Aliases

arxiv: 2607.24723 · arxiv_version: 2607.24723v1 · doi: 10.48550/arxiv.2607.24723 · pith_short_12: PNTM3TSAUAFI · pith_short_16: PNTM3TSAUAFIAUIS · pith_short_8: PNTM3TSA

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/PNTM3TSAUAFIAUISD5UF2AI4CK \
  | 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: 7b66cdce40a00a8051121f685d011c12a0352057be8638e432abdef53b33e6fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6141224b689d379932df3505aba9b630c9054fe9fa5b4a18ee5e3cc4833b4f0e",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-07-27T17:55:26Z",
    "title_canon_sha256": "9bba26a02574fddd36d070e0a5628ff5a281f521525f66fd51f95e36c6a924f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.24723",
    "kind": "arxiv",
    "version": 1
  }
}