Pith Number

pith:GDWGVKDY

pith:2010:GDWGVKDY6RW4KJEEQ52V5HQGQD

not attested not anchored not stored refs pending

Quasi-periodic solutions with Sobolev regularity of NLS on T^d with a multiplicative potential

Massimiliano Berti, Philippe Bolle

arxiv:1012.1427 v1 · 2010-12-07 · 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{GDWGVKDY6RW4KJEEQ52V5HQGQD}

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	2026-05-18T04:34:01.082248Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30ec6aa878f46dc5248487755e9e0680f9f7c49a3375c7d43f1152fe7d8e26cc

Aliases

arxiv: 1012.1427 · arxiv_version: 1012.1427v1 · doi: 10.48550/arxiv.1012.1427 · pith_short_12: GDWGVKDY6RW4 · pith_short_16: GDWGVKDY6RW4KJEE · pith_short_8: GDWGVKDY

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/GDWGVKDY6RW4KJEEQ52V5HQGQD \
  | 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: 30ec6aa878f46dc5248487755e9e0680f9f7c49a3375c7d43f1152fe7d8e26cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e6c4344eedbaa5296edd8f3b345d238096993d22bb24ea279e3da9804cde210",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-12-07T08:25:58Z",
    "title_canon_sha256": "578894813a961d73675c342065ced025931dbb2037adfd8210c59bc2df3a9e57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.1427",
    "kind": "arxiv",
    "version": 1
  }
}