Pith Number

pith:TWWR3ITD

pith:2012:TWWR3ITDJZFOVCHHZSWOZKXB2X

not attested not anchored not stored refs pending

Ricci focusing, shearing, and the expansion rate in an almost homogeneous Universe

Krzysztof Bolejko, Pedro G. Ferreira

arxiv:1204.0909 v2 · 2012-04-04 · 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{TWWR3ITDJZFOVCHHZSWOZKXB2X}

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	2026-05-18T03:56:33.728709Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9dad1da2634e4aea88e7ccacecaae1d5edda99d9a3663958f878b0b28c8fff7b

Aliases

arxiv: 1204.0909 · arxiv_version: 1204.0909v2 · doi: 10.48550/arxiv.1204.0909 · pith_short_12: TWWR3ITDJZFO · pith_short_16: TWWR3ITDJZFOVCHH · pith_short_8: TWWR3ITD

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/TWWR3ITDJZFOVCHHZSWOZKXB2X \
  | 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: 9dad1da2634e4aea88e7ccacecaae1d5edda99d9a3663958f878b0b28c8fff7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "338f1b4db2e7b78c081efb9b8fcd8b2d0a93a4101834af0cf67ef64d61af4031",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2012-04-04T10:07:14Z",
    "title_canon_sha256": "896eba2053227c8a6b9e2e772429bed470a729c52ff298bd834989b7ebfb6033"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.0909",
    "kind": "arxiv",
    "version": 2
  }
}