Pith Number

pith:VY6IZZB5

pith:2007:VY6IZZB5MKJYIPUBR33AZH3FRV

not attested not anchored not stored refs pending

Global well-posedness and polynomial bounds for the defocusing $L^{2}$-critical nonlinear Schr\"odinger equation in $\R$

Daniela De Silva, Gigliola Staffilani, Nata\v{s}a Pavlovi\'c, Nikolaos Tzirakis

arxiv:math/0702707 v2 · 2007-02-23 · 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{VY6IZZB5MKJYIPUBR33AZH3FRV}

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	2026-05-18T01:09:15.350155Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae3c8ce43d6293843e818ef60c9f658d7396567b5c1eabc9402dae570278c7f8

Aliases

arxiv: math/0702707 · arxiv_version: math/0702707v2 · doi: 10.48550/arxiv.math/0702707 · pith_short_12: VY6IZZB5MKJY · pith_short_16: VY6IZZB5MKJYIPUB · pith_short_8: VY6IZZB5

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/VY6IZZB5MKJYIPUBR33AZH3FRV \
  | 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: ae3c8ce43d6293843e818ef60c9f658d7396567b5c1eabc9402dae570278c7f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bcbd69b5211070887b323c9fc9264c5d2b83eb8f6ec43dec5dfea07b4847b6ad",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2007-02-23T16:29:35Z",
    "title_canon_sha256": "fd6cfe82014ab8b92f349bef613ff75ab6765b66e4b1769aec8627e4aef4fabb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0702707",
    "kind": "arxiv",
    "version": 2
  }
}