Pith Number

pith:EYBS37LA

pith:2011:EYBS37LAJN4GSQ3NNIWIPGTOOC

not attested not anchored not stored refs pending

Global dynamics of the nonradial energy-critical wave equation above the ground state energy

Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag

arxiv:1112.5663 v2 · 2011-12-23 · 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{EYBS37LAJN4GSQ3NNIWIPGTOOC}

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	2026-05-18T03:32:05.731506Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26032dfd604b7869436d6a2c879a6e7086266ba0781862e0711ae02489335bd3

Aliases

arxiv: 1112.5663 · arxiv_version: 1112.5663v2 · doi: 10.48550/arxiv.1112.5663 · pith_short_12: EYBS37LAJN4G · pith_short_16: EYBS37LAJN4GSQ3N · pith_short_8: EYBS37LA

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/EYBS37LAJN4GSQ3NNIWIPGTOOC \
  | 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: 26032dfd604b7869436d6a2c879a6e7086266ba0781862e0711ae02489335bd3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce9ffd751e2225657d93e3c74372a36d6ea757cbd64f019bccc6ddbe0f54c050",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-12-23T21:23:55Z",
    "title_canon_sha256": "0f0d1b092be517c795d1806f926082bb152cc2a711ebb74d23c6390f0445b556"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.5663",
    "kind": "arxiv",
    "version": 2
  }
}