Pith Number

pith:63N4J6LW

pith:2012:63N4J6LW7ZL3Y5RWDLCQLLT3JC

not attested not anchored not stored refs pending

Simple, explicitly time-dependent and regular solutions of the linearized vacuum Einstein equations on a null cone

Thomas M\"adler

arxiv:1212.3316 v3 · 2012-12-13 · 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{63N4J6LW7ZL3Y5RWDLCQLLT3JC}

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	2026-05-18T01:52:38.557638Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f6dbc4f976fe57bc76361ac505ae7b488a11d79d7ebdcaf1c341bf4a1e97a3cf

Aliases

arxiv: 1212.3316 · arxiv_version: 1212.3316v3 · doi: 10.48550/arxiv.1212.3316 · pith_short_12: 63N4J6LW7ZL3 · pith_short_16: 63N4J6LW7ZL3Y5RW · pith_short_8: 63N4J6LW

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/63N4J6LW7ZL3Y5RWDLCQLLT3JC \
  | 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: f6dbc4f976fe57bc76361ac505ae7b488a11d79d7ebdcaf1c341bf4a1e97a3cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55c12516ff49888e4eec6060453b828d46be2500cb3af75de64a6d3f245aed23",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2012-12-13T20:49:48Z",
    "title_canon_sha256": "98e96de8d363b674ebcc5ed4824a1817c3b6311e138c3b6a365be46c4e474029"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.3316",
    "kind": "arxiv",
    "version": 3
  }
}