Pith Number

pith:LBPBRPF4

pith:2001:LBPBRPF4UVCMA4LSLWSGHS2FCY

not attested not anchored not stored refs pending

Rough solution for the Einstein Vacuum equations

I. Rodnianski, S. Klainerman

arxiv:math/0109173 v1 · 2001-09-23 · math.AP · gr-qc · math.CA · 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{LBPBRPF4UVCMA4LSLWSGHS2FCY}

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	2026-05-18T01:05:37.562745Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

585e18bcbca544c071725da463cb45160ec4dfa6cecbceff4bdda3c71e2cc822

Aliases

arxiv: math/0109173 · arxiv_version: math/0109173v1 · doi: 10.48550/arxiv.math/0109173 · pith_short_12: LBPBRPF4UVCM · pith_short_16: LBPBRPF4UVCMA4LS · pith_short_8: LBPBRPF4

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/LBPBRPF4UVCMA4LSLWSGHS2FCY \
  | 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: 585e18bcbca544c071725da463cb45160ec4dfa6cecbceff4bdda3c71e2cc822

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "867575d9edab02cb2f82e276ea32046a67d62897fa8e7b33ac01ef8aba22b2e1",
    "cross_cats_sorted": [
      "gr-qc",
      "math.CA",
      "math.DG"
    ],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2001-09-23T18:52:51Z",
    "title_canon_sha256": "088c8bb79ec632bbc3530423d0dd1dce4bd701d5cc43e05d22bcd4164cf6b6a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0109173",
    "kind": "arxiv",
    "version": 1
  }
}