Pith Number

pith:VUCFFD3F

pith:2012:VUCFFD3F4GICNECNTUWDKXSF5S

not attested not anchored not stored refs pending

Harnack Extension for Abstract Perron-Stiletjes Integral and Its Application in LSRSS Property

Umi Mahnuna Hanung

arxiv:1212.5296 v4 · 2012-12-20 · 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{VUCFFD3F4GICNECNTUWDKXSF5S}

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	2026-05-18T03:33:49.558187Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad04528f65e19026904d9d2c355e45ecae74963a91fb200f0f1fd6250ef2dfb5

Aliases

arxiv: 1212.5296 · arxiv_version: 1212.5296v4 · doi: 10.48550/arxiv.1212.5296 · pith_short_12: VUCFFD3F4GIC · pith_short_16: VUCFFD3F4GICNECN · pith_short_8: VUCFFD3F

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/VUCFFD3F4GICNECNTUWDKXSF5S \
  | 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: ad04528f65e19026904d9d2c355e45ecae74963a91fb200f0f1fd6250ef2dfb5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46d951e8ced611de3e3059525a32e0f973f17e5b01b1908183dc79ab1f6430e9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-12-20T23:06:25Z",
    "title_canon_sha256": "8a8dfa605256d4cd4098627dc3de9d80f0f984b5dc2de7c353f8a1e93663c3ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.5296",
    "kind": "arxiv",
    "version": 4
  }
}