Pith Number

pith:7L2FXHJ5

pith:2019:7L2FXHJ5X5SZJ27ZVZ5E5NKDD5

not attested not anchored not stored refs pending

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity

Alessandro Palmieri, Vladimir Georgiev

arxiv:1908.02989 v1 · 2019-08-08 · 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{7L2FXHJ5X5SZJ27ZVZ5E5NKDD5}

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	2026-07-05T00:29:20.353949Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

faf45b9d3dbf6594ebf9ae7a4eb5431f5600d838ca432f8df943bfa42bc4ae04

Aliases

arxiv: 1908.02989 · arxiv_version: 1908.02989v1 · doi: 10.48550/arxiv.1908.02989 · pith_short_12: 7L2FXHJ5X5SZ · pith_short_16: 7L2FXHJ5X5SZJ27Z · pith_short_8: 7L2FXHJ5

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/7L2FXHJ5X5SZJ27ZVZ5E5NKDD5 \
  | 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: faf45b9d3dbf6594ebf9ae7a4eb5431f5600d838ca432f8df943bfa42bc4ae04

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "294780afbae8f13581870dbf26d595cb57af650f274963714f6fe06145a5725d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-08-08T09:47:43Z",
    "title_canon_sha256": "2952f4cd86214c02468107c12a719ddcf1f3d67b5e6eb5d91985421c9d3cdb33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.02989",
    "kind": "arxiv",
    "version": 1
  }
}