Pith Number

pith:GLE5DKRR

pith:2011:GLE5DKRRXCUUJUEGLVUXBL32HR

not attested not anchored not stored refs pending

Gravitational microlensing in modified gravity theories: Inverse-square theorem

Hideki Asada

arxiv:1101.0864 v1 · 2011-01-05 · astro-ph.CO · 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{GLE5DKRRXCUUJUEGLVUXBL32HR}

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	2026-05-18T04:27:35.526030Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32c9d1aa31b8a944d0865d6970af7a3c7c1026174e9960686b4443071c97e2e3

Aliases

arxiv: 1101.0864 · arxiv_version: 1101.0864v1 · doi: 10.48550/arxiv.1101.0864 · pith_short_12: GLE5DKRRXCUU · pith_short_16: GLE5DKRRXCUUJUEG · pith_short_8: GLE5DKRR

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/GLE5DKRRXCUUJUEGLVUXBL32HR \
  | 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: 32c9d1aa31b8a944d0865d6970af7a3c7c1026174e9960686b4443071c97e2e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64fb0975cad22bf0acef8fda057fa4c93894cefe7059b05c781d17665236ba3d",
    "cross_cats_sorted": [
      "gr-qc",
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2011-01-05T01:16:35Z",
    "title_canon_sha256": "35b0a73ddcf86cb14679218b2c9270dd647e9ba5343cc3206dbb4f0f799e4a14"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.0864",
    "kind": "arxiv",
    "version": 1
  }
}