Pith Number

pith:LTHDZ4ER

pith:2013:LTHDZ4ERG6X7DW7A23546RB5LZ

not attested not anchored not stored refs pending

The q-fractional analogue for Gronwall-type inequality

Jehad Alzabut, Thabet Abdeljawad

arxiv:1305.2082 v1 · 2013-05-09 · math.DS · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LTHDZ4ERG6X7DW7A23546RB5LZ}

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	2026-05-18T01:04:30.611054Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5cce3cf09137aff1dbe0d6fbcf443d5e5efeea34bc539bf2250a61142bb9a566

Aliases

arxiv: 1305.2082 · arxiv_version: 1305.2082v1 · doi: 10.48550/arxiv.1305.2082 · pith_short_12: LTHDZ4ERG6X7 · pith_short_16: LTHDZ4ERG6X7DW7A · pith_short_8: LTHDZ4ER

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/LTHDZ4ERG6X7DW7A23546RB5LZ \
  | 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: 5cce3cf09137aff1dbe0d6fbcf443d5e5efeea34bc539bf2250a61142bb9a566

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe0d9ccb53b9f80a2a356f0ad2577a0aa6ad9fd94a10fae55ec9fbad2859f294",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-05-09T13:14:24Z",
    "title_canon_sha256": "8f6e72b8b1aae504d44cc45eff68baac00dfefc24811861a159fc01d6a8c2e19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.2082",
    "kind": "arxiv",
    "version": 1
  }
}