Pith Number

pith:E2WAFMUC

pith:2012:E2WAFMUCUT7CEPOG4IO3CIOVRA

not attested not anchored not stored refs pending

Gravitational lensing with $ f(\chi)=\chi^{3/2} $ gravity in accordance with astrophysical observations

J.C. Hidalgo, L.A. Torres, S. Mendoza, T. Bernal, X. Hernandez

arxiv:1208.6241 v2 · 2012-08-30 · astro-ph.CO · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E2WAFMUCUT7CEPOG4IO3CIOVRA}

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	2026-05-18T03:18:18.628690Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26ac02b282a4fe223dc6e21db121d5880c04761b805232a6317fff0a442d9471

Aliases

arxiv: 1208.6241 · arxiv_version: 1208.6241v2 · doi: 10.48550/arxiv.1208.6241 · pith_short_12: E2WAFMUCUT7C · pith_short_16: E2WAFMUCUT7CEPOG · pith_short_8: E2WAFMUC

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/E2WAFMUCUT7CEPOG4IO3CIOVRA \
  | 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: 26ac02b282a4fe223dc6e21db121d5880c04761b805232a6317fff0a442d9471

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7077c0fc2a243c50d44af4bffbe7066df4475f4c917e21a12356bdcc2f7bf41",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2012-08-30T17:12:02Z",
    "title_canon_sha256": "b8f620db33461232d89f6d5cedefd810516771e6f9e4b04c537e8ed5f5d30827"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.6241",
    "kind": "arxiv",
    "version": 2
  }
}