Pith Number

pith:ELP3E2LR

pith:2017:ELP3E2LRIDVUDDT6Y2W46PXQZV

not attested not anchored not stored refs pending

Dirichlet forms and critical exponents on fractals

Ka-Sing Lau, Qingsong Gu

arxiv:1703.07061 v2 · 2017-03-21 · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ELP3E2LRIDVUDDT6Y2W46PXQZV}

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	2026-05-18T00:18:04.151986Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

22dfb2697140eb418e7ec6adcf3ef0cd78b847f5bd5d3594e434ff0a8af3ae0d

Aliases

arxiv: 1703.07061 · arxiv_version: 1703.07061v2 · doi: 10.48550/arxiv.1703.07061 · pith_short_12: ELP3E2LRIDVU · pith_short_16: ELP3E2LRIDVUDDT6 · pith_short_8: ELP3E2LR

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/ELP3E2LRIDVUDDT6Y2W46PXQZV \
  | 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: 22dfb2697140eb418e7ec6adcf3ef0cd78b847f5bd5d3594e434ff0a8af3ae0d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf9fcc5a897fce043902949a316c637f1c033fee04176d18f05db452a89bf5dc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2017-03-21T05:47:18Z",
    "title_canon_sha256": "7f162ad9782d3674cb5fabafe04e0efb4d66437b7ff5d96843eefbfef577ba24"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.07061",
    "kind": "arxiv",
    "version": 2
  }
}