Pith Number

pith:KOUBEKOK

pith:2001:KOUBEKOKVQJQU7U4MVECDZKGBL

not attested not anchored not stored refs pending

The causal structure of microlocalized Einstein metrics

I. Rodnianski, S. Klainerman

arxiv:math/0109174 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{KOUBEKOKVQJQU7U4MVECDZKGBL}

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	2026-05-18T01:05:37.556924Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53a81229caac130a7e9c654821e5460aec90a249f9fb6354399388e08e083ecd

Aliases

arxiv: math/0109174 · arxiv_version: math/0109174v1 · doi: 10.48550/arxiv.math/0109174 · pith_short_12: KOUBEKOKVQJQ · pith_short_16: KOUBEKOKVQJQU7U4 · pith_short_8: KOUBEKOK

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/KOUBEKOKVQJQU7U4MVECDZKGBL \
  | 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: 53a81229caac130a7e9c654821e5460aec90a249f9fb6354399388e08e083ecd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d8b023ec20c750144e20eee55f677926fc0030befca50af2e340b4b5e79446e",
    "cross_cats_sorted": [
      "gr-qc",
      "math.CA",
      "math.DG"
    ],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2001-09-23T19:04:31Z",
    "title_canon_sha256": "b8a66225aba76021416b36c2c72d884b466d73bf5730d6d7ff55531ee88a0e02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0109174",
    "kind": "arxiv",
    "version": 1
  }
}