Pith Number

pith:L3JJ3DLB

pith:2016:L3JJ3DLB4DKGIVRA6WME5KSGXN

not attested not anchored not stored refs pending

Constraining cosmic curvature by using age of galaxies and gravitational lenses

Akshay Rana, Amitabha Mukherjee, Deepak Jain, Shobhit Mahajan

arxiv:1611.07196 v2 · 2016-11-22 · astro-ph.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L3JJ3DLB4DKGIVRA6WME5KSGXN}

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	2026-05-18T00:48:36.965495Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ed29d8d61e0d4645620f5984eaa46bb522f9e459599f93c68914a50c25ed8cd

Aliases

arxiv: 1611.07196 · arxiv_version: 1611.07196v2 · doi: 10.48550/arxiv.1611.07196 · pith_short_12: L3JJ3DLB4DKG · pith_short_16: L3JJ3DLB4DKGIVRA · pith_short_8: L3JJ3DLB

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/L3JJ3DLB4DKGIVRA6WME5KSGXN \
  | 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: 5ed29d8d61e0d4645620f5984eaa46bb522f9e459599f93c68914a50c25ed8cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce55b063c027ea46263519b4eea95f6266bd9b1e559df82f8be6a62cebffbaf5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2016-11-22T08:41:47Z",
    "title_canon_sha256": "edf94062c5755929b1667e916445ddc54b5c792ef29bd4a1f7ae436c52edfe7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.07196",
    "kind": "arxiv",
    "version": 2
  }
}