Pith Number

pith:PTJTFNRI

pith:2015:PTJTFNRIICYPWKNAHKWG7XM2DM

not attested not anchored not stored refs pending

On the generalized Zakharov-Kuznetsov equation at critical regularity

Axel Gruenrock

arxiv:1509.09146 v1 · 2015-09-30 · 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{PTJTFNRIICYPWKNAHKWG7XM2DM}

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.

Cited by

1 paper in Pith

Scattering of the 3D Zakharov-Kuznetsov equation

Receipt and verification

First computed	2026-05-18T01:31:26.980689Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cd332b62840b0fb29a03aac6fdd9a1b332e33c428b4df21b5ef52b9a7800365

Aliases

arxiv: 1509.09146 · arxiv_version: 1509.09146v1 · doi: 10.48550/arxiv.1509.09146 · pith_short_12: PTJTFNRIICYP · pith_short_16: PTJTFNRIICYPWKNA · pith_short_8: PTJTFNRI

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/PTJTFNRIICYPWKNAHKWG7XM2DM \
  | 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: 7cd332b62840b0fb29a03aac6fdd9a1b332e33c428b4df21b5ef52b9a7800365

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f08d3b9c0ab526d17ab3e400d3a1c7131c1302163b0fbf87cc4073f56b12013",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-09-30T12:23:31Z",
    "title_canon_sha256": "e2d6c6f7f7d4fda561b0b12692bf0e41e912a5a2737ea47c0d1c95a31024ec79"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.09146",
    "kind": "arxiv",
    "version": 1
  }
}