Pith Number

pith:NULT3U6J

pith:2010:NULT3U6J746KC4FKVJLOHFNB3T

not attested not anchored not stored refs pending

A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on T3

Alan D. Rendall, Philippe G. LeFloch

arxiv:1004.0427 v4 · 2010-04-03 · gr-qc · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NULT3U6J746KC4FKVJLOHFNB3T}

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	2026-05-18T02:08:14.649167Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d173dd3c9ff3ca170aaaa56e395a1dcd5b36fc8efa10eb66420f90849080320

Aliases

arxiv: 1004.0427 · arxiv_version: 1004.0427v4 · doi: 10.48550/arxiv.1004.0427 · pith_short_12: NULT3U6J746K · pith_short_16: NULT3U6J746KC4FK · pith_short_8: NULT3U6J

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/NULT3U6J746KC4FKVJLOHFNB3T \
  | 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: 6d173dd3c9ff3ca170aaaa56e395a1dcd5b36fc8efa10eb66420f90849080320

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f2018157d6a63cde180c3ef2d9ba24fe9163230004aa63dfd29914d5aa348887",
    "cross_cats_sorted": [
      "math.AP",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2010-04-03T08:23:56Z",
    "title_canon_sha256": "8e31b4e81981dfd841e9cc96ff2608d15e55d14bc7943f8b5f8f4722d76db629"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.0427",
    "kind": "arxiv",
    "version": 4
  }
}