Pith Number

pith:AUZDNZOI

pith:2009:AUZDNZOIZQWGHQIFEPPRWDKQ34

not attested not anchored not stored refs pending

Almost Morawetz estimates and global well-posedness for the defocusing $L^2$-critical nonlinear Schr{\"o}dinger equation in higher dimensions

Benjamin Dodson

arxiv:0909.4332 v1 · 2009-09-23 · 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{AUZDNZOIZQWGHQIFEPPRWDKQ34}

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	2026-07-04T15:50:26.101614Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

053236e5c8cc2c63c10523df1b0d50df1c4ae37e6e0ccd74cfd5f73b87460f6c

Aliases

arxiv: 0909.4332 · arxiv_version: 0909.4332v1 · doi: 10.48550/arxiv.0909.4332 · pith_short_12: AUZDNZOIZQWG · pith_short_16: AUZDNZOIZQWGHQIF · pith_short_8: AUZDNZOI

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/AUZDNZOIZQWGHQIFEPPRWDKQ34 \
  | 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: 053236e5c8cc2c63c10523df1b0d50df1c4ae37e6e0ccd74cfd5f73b87460f6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10dde4dc54dab1a7f46091ed5c94d278e97f5108ca7c2705a0c4a9bb3ba26bfa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2009-09-23T22:25:47Z",
    "title_canon_sha256": "39df2ad31b8fa08e1beaa1ab7f6455266f241b7d188ab1995cdeab0437c48c38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.4332",
    "kind": "arxiv",
    "version": 1
  }
}