Pith Number

pith:APM3SRQV

pith:2012:APM3SRQVX6YFBJKSTD7EWPSSKQ

not attested not anchored not stored refs pending

Global infinite energy solutions for the cubic wave equation

Laurent Thomann (LMJL), Nicolas Burq (LM-Orsay), Nikolay Tzvetkov (AGM)

arxiv:1210.2086 v1 · 2012-10-07 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{APM3SRQVX6YFBJKSTD7EWPSSKQ}

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	2026-05-18T03:43:51.148380Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03d9b94615bfb050a55298fe4b3e52543ad36c259da06ba1dce302ff995a0b67

Aliases

arxiv: 1210.2086 · arxiv_version: 1210.2086v1 · doi: 10.48550/arxiv.1210.2086 · pith_short_12: APM3SRQVX6YF · pith_short_16: APM3SRQVX6YFBJKS · pith_short_8: APM3SRQV

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/APM3SRQVX6YFBJKSTD7EWPSSKQ \
  | 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: 03d9b94615bfb050a55298fe4b3e52543ad36c259da06ba1dce302ff995a0b67

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "58132959ed05a7822b9242c088c837f409836ca8fef945bd3e7df115e72022e8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-10-07T18:28:59Z",
    "title_canon_sha256": "c9f8edeab2589d92ea6478d7607a6201b6d1bd7a1b5db5067d35ecd1d541eb8e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.2086",
    "kind": "arxiv",
    "version": 1
  }
}