Pith Number

pith:K653ZMZP

pith:1999:K653ZMZPLM5BM5FP35ASKRLKQO

not attested not anchored not stored refs pending

Averaging Einstein's Equations: The Linearized Case

Amina Helmi, Diego F. Torres, William R. Stoeger

arxiv:gr-qc/9904020 v1 · 1999-04-07 · 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{K653ZMZPLM5BM5FP35ASKRLKQO}

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.

Cited by

1 paper in Pith

Scalar-tensor theories at different scales: averaging the scalar sector

Receipt and verification

First computed	2026-07-04T15:20:44.326200Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

57bbbcb32f5b3a1674afdf4125456a839d7c2cb48e8eb145f3e3884cc05745ca

Aliases

arxiv: gr-qc/9904020 · arxiv_version: gr-qc/9904020v1 · doi: 10.48550/arxiv.gr-qc/9904020 · pith_short_12: K653ZMZPLM5B · pith_short_16: K653ZMZPLM5BM5FP · pith_short_8: K653ZMZP

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/K653ZMZPLM5BM5FP35ASKRLKQO \
  | 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: 57bbbcb32f5b3a1674afdf4125456a839d7c2cb48e8eb145f3e3884cc05745ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "072888453e5471f7849b6d5911d91a5f4202e7f868422d15750716a9b5c69b2e",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "1999-04-07T17:17:20Z",
    "title_canon_sha256": "2393fedfab522c7cb351a148379a745a7c95262025d8016033b89b14df63f23c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/9904020",
    "kind": "arxiv",
    "version": 1
  }
}