Pith Number

pith:DADU4JDK

pith:2007:DADU4JDKMH2RQTS7PRKWPFWCAV

not attested not anchored not stored refs pending

The wave equation on Schwarzschild-de Sitter spacetimes

Igor Rodnianski, Mihalis Dafermos

arxiv:0709.2766 v1 · 2007-09-18 · gr-qc · math.AP · 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{DADU4JDKMH2RQTS7PRKWPFWCAV}

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	2026-07-04T15:04:20.548773Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

18074e246a61f5184e5f7c556796c205498dd33716e27c9e08268fba26771c5a

Aliases

arxiv: 0709.2766 · arxiv_version: 0709.2766v1 · doi: 10.48550/arxiv.0709.2766 · pith_short_12: DADU4JDKMH2R · pith_short_16: DADU4JDKMH2RQTS7 · pith_short_8: DADU4JDK

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/DADU4JDKMH2RQTS7PRKWPFWCAV \
  | 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: 18074e246a61f5184e5f7c556796c205498dd33716e27c9e08268fba26771c5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d0bf2d94549996348f29c4dcca85954b5b41df03e442509d4324afbd7340861",
    "cross_cats_sorted": [
      "math.AP",
      "math.DG"
    ],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "2007-09-18T08:01:45Z",
    "title_canon_sha256": "066ca70289bbf8d2aa620aa6332601690e6f05d363d36b59959f1e030cfe64d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.2766",
    "kind": "arxiv",
    "version": 1
  }
}