Pith Number

pith:MUU6TWUT

pith:2017:MUU6TWUTFYCRREWZDCBWCBCG7G

not attested not anchored not stored refs pending

Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on R^{3+1}

Joachim Krieger, Stefano Burzio

arxiv:1709.06408 v2 · 2017-09-19 · 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{MUU6TWUTFYCRREWZDCBWCBCG7G}

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	2026-05-17T23:59:43.940526Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6529e9da932e051892d91883610446f98b35b95388b253c0cf7439e9c5ef392f

Aliases

arxiv: 1709.06408 · arxiv_version: 1709.06408v2 · doi: 10.48550/arxiv.1709.06408 · pith_short_12: MUU6TWUTFYCR · pith_short_16: MUU6TWUTFYCRREWZ · pith_short_8: MUU6TWUT

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/MUU6TWUTFYCRREWZDCBWCBCG7G \
  | 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: 6529e9da932e051892d91883610446f98b35b95388b253c0cf7439e9c5ef392f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6203d2699013453cd320b692ae594f4f1438bd06b2866be03f01456192bf07f4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-09-19T13:35:54Z",
    "title_canon_sha256": "e13b21ee6f7cdbfa723aac58a682edc0341271dc108a8e1255fe6bbd7c574d5d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.06408",
    "kind": "arxiv",
    "version": 2
  }
}