Pith Number

pith:KHBHVTOC

pith:2012:KHBHVTOC2HLTVH6M5CJFXEX3KR

not attested not anchored not stored refs pending

Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient perturbation

Piotr Graczyk, Tomasz Jakubowski, Tomasz Luks

arxiv:1203.3064 v2 · 2012-03-14 · 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{KHBHVTOC2HLTVH6M5CJFXEX3KR}

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	2026-05-18T03:57:52.724744Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51c27acdc2d1d73a9fcce8925b92fb5471204aa30a550bb668272ed0ddd383e5

Aliases

arxiv: 1203.3064 · arxiv_version: 1203.3064v2 · doi: 10.48550/arxiv.1203.3064 · pith_short_12: KHBHVTOC2HLT · pith_short_16: KHBHVTOC2HLTVH6M · pith_short_8: KHBHVTOC

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/KHBHVTOC2HLTVH6M5CJFXEX3KR \
  | 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: 51c27acdc2d1d73a9fcce8925b92fb5471204aa30a550bb668272ed0ddd383e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bba0d9039c6bc1f5a416152aafea51eedc2ca68f2750dfcf51ae2a93a81ca71f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-03-14T12:22:20Z",
    "title_canon_sha256": "7933f61cd2a0fcb34334f3b4f8ef504cecea094acf2b164a7c8da7c6f102dc8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.3064",
    "kind": "arxiv",
    "version": 2
  }
}