Pith Number

pith:V4FF4MJY

pith:2010:V4FF4MJYTRSXPVUJFOBLYKPD7H

not attested not anchored not stored refs pending

Dispersive estimates and NLS on product manifolds

Vittoria Pierfelice (MAPMO)

arxiv:1012.0442 v1 · 2010-12-02 · 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{V4FF4MJYTRSXPVUJFOBLYKPD7H}

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	2026-05-18T04:34:17.819183Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af0a5e31389c6577d6892b82bc29e3f9d48ace4ce95403cb408300226c67b904

Aliases

arxiv: 1012.0442 · arxiv_version: 1012.0442v1 · doi: 10.48550/arxiv.1012.0442 · pith_short_12: V4FF4MJYTRSX · pith_short_16: V4FF4MJYTRSXPVUJ · pith_short_8: V4FF4MJY

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/V4FF4MJYTRSXPVUJFOBLYKPD7H \
  | 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: af0a5e31389c6577d6892b82bc29e3f9d48ace4ce95403cb408300226c67b904

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0219fd116fc2057839e0c49e6ebed6bee24c6e5b7e996948e4623b2d6c497da",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-12-02T14:57:13Z",
    "title_canon_sha256": "59cda89943e7bb38f96fb47bd39df4f5ca212ef6351d255c11c3ad70b35d7f3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0442",
    "kind": "arxiv",
    "version": 1
  }
}