Pith Number

pith:FVJFX5IU

pith:2019:FVJFX5IUVK63YLKCDAFELGY76F

not attested not anchored not stored refs pending

Multiple solutions for Grushin operator without odd nonlinearity

Mohamed Karim Hamdani

arxiv:1909.03417 v1 · 2019-09-08 · 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{FVJFX5IUVK63YLKCDAFELGY76F}

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	2026-07-05T00:03:05.408588Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d525bf514aabdbc2d42180a459b1ff17de9b0e9d7df52b46a1c8d3f87d5c9a7

Aliases

arxiv: 1909.03417 · arxiv_version: 1909.03417v1 · doi: 10.48550/arxiv.1909.03417 · pith_short_12: FVJFX5IUVK63 · pith_short_16: FVJFX5IUVK63YLKC · pith_short_8: FVJFX5IU

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/FVJFX5IUVK63YLKCDAFELGY76F \
  | 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: 2d525bf514aabdbc2d42180a459b1ff17de9b0e9d7df52b46a1c8d3f87d5c9a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8608782c55b3162fe09f12877d45aeb5b018f27a3040d2e0e16389dbdf7a6538",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-09-08T09:50:18Z",
    "title_canon_sha256": "27b8161e9a4bd0bfe9bf366a4c4f3bd8c04378f2ca1e6ca39c72088f79f35dfd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.03417",
    "kind": "arxiv",
    "version": 1
  }
}