Pith Number

pith:3WBDLZKT

pith:2013:3WBDLZKTF4M3U3GIYXOQIT7OXC

not attested not anchored not stored refs pending

Center-stable manifold of the ground state in the energy space for the critical wave equation

Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag

arxiv:1303.2400 v1 · 2013-03-11 · 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{3WBDLZKTF4M3U3GIYXOQIT7OXC}

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	2026-05-18T03:31:19.128599Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd8235e5532f19ba6cc8c5dd044feeb8a945e645264442ef6f8e0ebedd7b6cd7

Aliases

arxiv: 1303.2400 · arxiv_version: 1303.2400v1 · doi: 10.48550/arxiv.1303.2400 · pith_short_12: 3WBDLZKTF4M3 · pith_short_16: 3WBDLZKTF4M3U3GI · pith_short_8: 3WBDLZKT

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/3WBDLZKTF4M3U3GIYXOQIT7OXC \
  | 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: dd8235e5532f19ba6cc8c5dd044feeb8a945e645264442ef6f8e0ebedd7b6cd7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "201a366157b4b467c22a1dc52f22fc77ca6d1085bd77ffb61ccd4b16d5cb4db5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-03-11T00:21:51Z",
    "title_canon_sha256": "8e8aa5c5360c4501e80310610623fbe117ad5814425bfc283c01e0aaeef4e772"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.2400",
    "kind": "arxiv",
    "version": 1
  }
}