Pith Number

pith:SKGQ4LLC

pith:2011:SKGQ4LLCVDPRELVKZQVR5E3WPK

not attested not anchored not stored refs pending

Blow up dynamics for smooth equivariant solutions to the energy critical Schr\"odinger map

Frank Merle, Igor Rodnianski, Pierre Rapha\"el

arxiv:1106.0912 v1 · 2011-06-05 · 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{SKGQ4LLCVDPRELVKZQVR5E3WPK}

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	2026-05-18T04:20:37.045786Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

928d0e2d62a8df122eaacc2b1e93767aa00a6b5bdf9eca12cf9478b757172be1

Aliases

arxiv: 1106.0912 · arxiv_version: 1106.0912v1 · doi: 10.48550/arxiv.1106.0912 · pith_short_12: SKGQ4LLCVDPR · pith_short_16: SKGQ4LLCVDPRELVK · pith_short_8: SKGQ4LLC

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/SKGQ4LLCVDPRELVKZQVR5E3WPK \
  | 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: 928d0e2d62a8df122eaacc2b1e93767aa00a6b5bdf9eca12cf9478b757172be1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "132436003c314cd04d7613ba8870d4029a3c0d358cbe70623e7afb970fa62003",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-06-05T16:44:52Z",
    "title_canon_sha256": "c97e5f91be77092ff6084617c0dfc5328f77e5103dc207ee0cfcb8bbdae95934"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.0912",
    "kind": "arxiv",
    "version": 1
  }
}