Pith Number

pith:XCIUT5PO

pith:2015:XCIUT5PO4WG3JNB6LHRLIZC4Z7

not attested not anchored not stored refs pending

Growth of Sobolev norms for the analytic NLS on $\mathbb T^2$

Emanuele Haus, Marcel Guardia, Michela Procesi

arxiv:1503.02468 v2 · 2015-03-09 · math.AP · math.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XCIUT5PO4WG3JNB6LHRLIZC4Z7}

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	2026-05-18T00:42:22.129898Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b89149f5eee58db4b43e59e2b4645ccfe44e321554e5e24fe28c005e8410dc9e

Aliases

arxiv: 1503.02468 · arxiv_version: 1503.02468v2 · doi: 10.48550/arxiv.1503.02468 · pith_short_12: XCIUT5PO4WG3 · pith_short_16: XCIUT5PO4WG3JNB6 · pith_short_8: XCIUT5PO

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/XCIUT5PO4WG3JNB6LHRLIZC4Z7 \
  | 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: b89149f5eee58db4b43e59e2b4645ccfe44e321554e5e24fe28c005e8410dc9e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "239bcb6c5efc69c4af93210edd16e4df1e188f34ab0b01a0f3fca1b15f6c8cc7",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-03-09T13:25:38Z",
    "title_canon_sha256": "f08c065eaf80755aabf8006839258137ff1d604ad0cfc4f87c931a2f13c1d27b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.02468",
    "kind": "arxiv",
    "version": 2
  }
}