Pith Number

pith:ND7R7C2C

pith:2016:ND7R7C2CJG5XNFLLRM3CITTHLR

not attested not anchored not stored refs pending

Gravitational microlensing in Verlinde's emergent gravity

Lei-Hua Liu, Tomislav Prokopec

arxiv:1612.00861 v2 · 2016-12-01 · 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{ND7R7C2CJG5XNFLLRM3CITTHLR}

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	2026-05-18T00:47:07.579153Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68ff1f8b4249bb76956b8b36244e675c48c1488f9e6d86964f9a768e0d36ea56

Aliases

arxiv: 1612.00861 · arxiv_version: 1612.00861v2 · doi: 10.48550/arxiv.1612.00861 · pith_short_12: ND7R7C2CJG5X · pith_short_16: ND7R7C2CJG5XNFLL · pith_short_8: ND7R7C2C

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/ND7R7C2CJG5XNFLLRM3CITTHLR \
  | 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: 68ff1f8b4249bb76956b8b36244e675c48c1488f9e6d86964f9a768e0d36ea56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07894fd8c8832b5759bcaca9dbdd85e661cf642397cead316439823c00e302b7",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2016-12-01T16:48:38Z",
    "title_canon_sha256": "8841f66a0ac19c54ca23ddc770201d42fc4a9539241a95085aa598c3571d6b91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.00861",
    "kind": "arxiv",
    "version": 2
  }
}