Pith Number

pith:5JUGKVLB

pith:2010:5JUGKVLBGHNK3SSTYVLBUQSXMR

not attested not anchored not stored refs pending

On Breakdown Criteria for Nonvacuum Einstein Equations

Arick Shao

arxiv:1008.1605 v2 · 2010-08-09 · math.AP · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5JUGKVLBGHNK3SSTYVLBUQSXMR}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T01:04:46.210417Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea6865556131daadca53c5561a425764773f0f53dcb5d8c4b14d491a78048017

Aliases

arxiv: 1008.1605 · arxiv_version: 1008.1605v2 · doi: 10.48550/arxiv.1008.1605 · pith_short_12: 5JUGKVLBGHNK · pith_short_16: 5JUGKVLBGHNK3SST · pith_short_8: 5JUGKVLB

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/5JUGKVLBGHNK3SSTYVLBUQSXMR \
  | 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: ea6865556131daadca53c5561a425764773f0f53dcb5d8c4b14d491a78048017

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43d38d21a61c67bde472eabbd8dc0947c49798ece5142845b2bc41045262e3ac",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-08-09T23:43:46Z",
    "title_canon_sha256": "f725871425171c94da7ecaead08a1e7764f3def7bab45f2c4707f3ad14ee4491"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.1605",
    "kind": "arxiv",
    "version": 2
  }
}